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Optimizing Bus Transfer Coordination Casestudy of Asia Jaya Bus Stop

Klang Valley Region - Malaysia

Ahmed Abdel Shakour Abdel Aziz Abdel Dayem April, 2005

Optimizing Bus Transfer Coordination Casestudy of Asia Jaya Bus Stop Klang Valley Region - Malaysia

By

Ahmed Abdel Shakour Abdel Aziz Abdel Dayem

Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation, Specialisation: (Urban Infrastructure Management) Thesis Assessment Board Dr. R.V. Sliuzas (Chair) Ir. M.H.P. Zuidgeest (External Examiner) T.G.Munshi, MSc (First Supervisor) Ing. F.H.M Van Den Bosch (Second Supervisor)

INTERNATIONAL INSTITUTE FOR GEO-INFORMATION SCIENCE AND EARTH OBSERVATION ENSCHEDE, THE NETHERLANDS

Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute.

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Abstract

In big metropolitan cities and large urban areas the demand for public transit is often widely spread and significantly varies over space and time. In such a situation providing a door to door trip between all pairs of origins and destinations is neither applicable nor cost-effective. An attractive and efficient alternative is to serve the passengers by an efficient intermodal system. In such a system, passengers may need one or more transfers to complete the journey to their final destination. Consequently, coordinating transit schedules to reduce transfer time can contribute significantly in improving the transit service quality and increasing the passengers’ ridership levels. Such coordination should be dealt with carefully to grantee the satisfaction of the inherently conflicting objectives of the passengers and the transit system operator. In the present research the benefits of coordinating the schedules of main stage buses with secondary feeder buses at a transfer stop is assessed and evaluated through a 3-stage optimization model. A total cost objective function that represents both the passengers and the operator objectives is formulated and optimized for each stage of the optimization model to determine the optimal coordination status among the coordinated bus route at the selected transfer stop. In the first stage the operating headways of both the stage and the feeder buses are optimized under uncoordinated service, the corresponding total cost is also obtained and compared with the total costs under the current existing situation. In the second stage all possible combinations of stage-feeder bus coordination at the stop are tested and corresponding total costs cost of each combination is also obtained. The results of the second stage are compared with the existing situation results as well as the first stage results and the coordinated combination resulting in the minimum total costs is identified. In the third and last stage the optimal slack time added to the schedule of the coordinated buses to increase the probability of a successful connection and overcome the stochastic arrivals of buses to the stop under the varying traffic conditions. Furthermore, the present research also explores and investigates the potential role that Advanced Public Transport Systems (APTS) fleet management technologies can play if deployed in enhancing and improving the handling of the transfer coordination problem in the real-time context as well as in the long run. Firstly, the APTS fleet management technologies that can play a role in improving the efficiency of coordinated transfers are identified. Then the integration of the out put data of these technologies is discussed and elaborated. Finally potential improvements to the handling of the transfer coordination problem in both the real-time context and the long run are cleared and emphasized. The concluded study is that coordinated transfers between the stage and feeder buses under a common headway is beneficial when the increase the in-vehicle and waiting time costs can be compensated by the savings in the transfer time costs . Also the desirability of coordinated transfers is highly dependent on the transfer passengers' volume, the standard deviation of vehicle arrivals to the stop. It was also found that the integration of APTS fleet management technologies specifically Global Positioning Systems (GPS), Automatic Passengers Counters (APC), Geographical Information Systems (GIS) and Communication Systems can play a very significant role in facilitating coordinated transfers in the real-time context making the bus system more dynamic and demand responsive.

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Acknowledgements

First and foremost, I would like to express my thankfulness to Allah God Almighty for giving me the strength and willingness to work in this research till it finally saw the light.

I would like to express my sincere appreciation to both my supervisors. Firstly, to my first supervisor MSc.Talat Munshi, for his unlimited and continuous support and his critical comments aiming to enhance and improve the present research. Secondly, to my second supervisor Ing. Frans van den Bosch, for his help and assistance during the whole study period at the UPLA program and for his guidance as my second supervisor. In the hard times of this research which as I recall were many, both of them stood by me and supported me, for that I am very thankful and grateful.

I am greatly indebted to Ir. Mark Brussel, UIM specialization coordinator. In the last three years, we have interacted in so many ways, firstly, as a colleague and partner in UTI, secondly as a lecturer in ITC and thirdly as a research proposal advisor. Throughout that time, I have gained a plenty of valuable experience from him. I hope that will not be the end of it.

Special thanks go to Ir. Mark Zuidgeest for his help and support in the conceptualizing and solving some parts of this research, whenever I asked for his help he was there for me. Thanks are also due to Dr. Clement Atzberger for helping me to formulate my model in MatLab, it was really a necessity for my research to be completed.

I would like also to pay tribute to Dr. Luc Boerboom for his help during the formulation of the proposal and for making it possible for me to do my fieldwork in Malaysia. I am also thankful to all those who assisted me in collecting the required data in Malaysia specially to the staff and the students of the transportation department at the Malaysian University of Science and Technology M.U.S.T, to the staff of the Malaysian Ministry of Federal Territory, to Mr. Kamalruddin Shamsuddin, Mr. Loga veeramuthu, and En. Mohd Razif.

Needless to say, that I am grateful to all of my colleagues at the Urban Planning and Land Administration Program UPLA 2003 specially Sohel, Indra, Prat, Ilham, Pratima, Zack, Refat, Ai Ping and Abdel Aziz. With them, I shared many wonderful moments, thoughts and experiences and from each and every one of them I have learned something new. Special thanks and deep gratefulness to my friend, roommate and colleague both at work and at ITC Amr, together we have been through both good and bad times in the last one and half years. Thanks also to my fellow Egyptians, Aiman and Naser from the year before and Mohamed from the year after. Thanks to my newest friend Bakim from India for lending me his laptop in the last day before submission when mine unfortunately crashed Finally yet importantly, I would like to�recognize the unrelenting long-distance support of my family back home in Cairo. Their prayers for me were the main source of inspiration, motivation and encouragement to continue this work. To my Parents, this work is dedicated for you. Ahmed Abdel Dayem April 2005

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Table of contents

1. Introduction, Problem Statement and Research Methodology.........................................................1

1.1. Introduction.............................................................................................................................1 1.2. General Overview of Study Area and Justification ...............................................................2 1.3. Problem statement...................................................................................................................4 1.4. Main Objective .......................................................................................................................5 1.5. Sub objectives.........................................................................................................................5

1.5.1. Research Questions ............................................................................................................5 1.6. Research Design .....................................................................................................................5 1.7. Overview of Research Methodology ......................................................................................6

1.7.1. Data Collection and Current Situation Analysis (Stage 1).................................................7 1.7.2. Optimization of Transfer Coordination (Stage 2) ..............................................................7 1.7.3. Potential Role of APTS Technologies in facilitating coordinated transfers (Stage 3).......8

1.8. Outline of the Thesis...............................................................................................................9 2. Public Transport Network Design A Transfer Coordination Approach ....................................11

2.1. Public Transport Network Design Problem..........................................................................11 2.1.1. Main Characteristic ..........................................................................................................11 2.1.2. Stakeholders Identification...............................................................................................11 2.1.3. Public Transport Optimization Problem Description.......................................................13 2.1.4. Intermodalism – Main Concept ........................................................................................15

2.2. The Transfer Coordination Problem....................................................................................15 2.2.1. Decision variables ............................................................................................................16 2.2.2. Previous Models on Transfer Coordination .....................................................................16 2.2.3. Important Issues in Transfer Coordination.......................................................................19

2.3. Advanced Public Transport Technologies – Potential Role in solving the Transfer Coordination Problem in the Real-time Context................................................................................20 2.4. Conclusions...........................................................................................................................24

3. Case Study Location, Data Collection, and Current Situation Analysis........................................26 3.1. Asia Jaya – Stop Selection....................................................................................................26

3.1.1. Expert Knowledge ............................................................................................................26 3.1.2. Quick Overview................................................................................................................26 3.1.3. Brief Description of the Stop Location ............................................................................27

3.2. Data Collection .....................................................................................................................27 3.2.1. Primary Data Collection ...................................................................................................27 3.2.2. Secondary Data Collection...............................................................................................28

3.3. Present Situation Analysis ....................................................................................................29 3.3.1. Network Analysis .............................................................................................................29 3.3.2. Transfer Demand Percentage ...........................................................................................31

3.4. Selected Routes Passenegrs' Demand Calculations..............................................................32 3.4.1. Stage Buses Passengers Demand......................................................................................32 3.4.2. Feeder Buses Passengers Demand....................................................................................33

3.5. Headway Devation................................................................................................................34

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3.6. Transfer Time Analysis ........................................................................................................36 3.6.1. Passengers Transfer Times and Transfer Time Appreciation ..........................................36 3.6.2. Transfer Time Fluctuation................................................................................................37 3.6.3. Value of Time...................................................................................................................38 3.6.4. Transfer Time Losses .......................................................................................................39 3.6.5. Transfer Time Financial Losses .......................................................................................40

3.7. Conclusions...........................................................................................................................40 4. ASIA JAYA - OPTIMIZATION OF TRANSFER COORDINATION.........................................42

4.1. Problem Identification ..........................................................................................................42 4.2. Model Assumptions ..............................................................................................................42 4.3. Rationale of The Optimization Model..................................................................................44

4.3.1. Transfer Direction ............................................................................................................45 4.4. Demand Functions Formulation ...........................................................................................46

4.4.1. Stage Bus Passengers Demand.........................................................................................46 4.4.2. Feeder Bus Passengers Demand.......................................................................................46

4.5. Building Blocks of The Optimization Model .......................................................................46 4.6. Conclusions...........................................................................................................................75

5. APTS Provision – Potential Role in the Transfer Coordination Problem .....................................77 5.1. Technology Data Output.......................................................................................................77

5.1.1. GPS Data Output ..............................................................................................................77 5.1.2. APC Data Output..............................................................................................................78 5.1.3. GIS Data ...........................................................................................................................79

5.2. GPS and APC Output Data Integration within a GIS Platfom .............................................80 5.3. Potential Improvements in Coordinating Bus Transfers and limitations..............................82

Real-time improvement ..................................................................................................................82 5.4. Conclusions...........................................................................................................................83

6. Conclusions and Recommendations...............................................................................................85 6.1. Introduction...........................................................................................................................85 6.2. Results against research outline............................................................................................85 6.3. General Conclusions.............................................................................................................89 6.4. Study area Recommendations...............................................................................................89 6.5. Further Research Recommendations ....................................................................................90

References ..............................................................................................................................................93 Appendix (A): Value of time Calculation for the study Area................................................................95 Appendix (B): Passengers Questionnaire ..............................................................................................96 Appendix (C): MatLab Script ................................................................................................................97

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List of figures

Figure �1-1 Malaysia in The regional Settings ..........................................................................................3 Figure �1-2 TheCase Study Location - Klang Valley Region - Malaysia ................................................4 Figure �1-3 Structure of Research Methodology.......................................................................................6 Figure �2-1 Illustration of Passenger and Operators Optimal Design of the Public transport Network (Source: Van Nes 2000) .........................................................................................................................12 Figure �2-2 Structure of the Analytical Approach...................................................................................13 Figure �2-3 APTS Fleet Management Technologies...............................................................................21 Figure �3-1 Asia Jaya Stop Location .......................................................................................................27 Figure �3-2 The Service Area of The Slected Bus Routes ......................................................................30 Figure �3-3 Feeder Bus Route 904A & 904B .........................................................................................30 Figure �3-4 Overall Stage Bus Passengers Demand at Asia Jaya stop – Survey Results........................31 Figure �3-5 Percentage of Transfer to Non Transfer ...............................................................................31 Figure �3-6 Headway Deviation – Stage Bus 47 - PM Peak – Outbound Direction ...............................34 Figure �3-7 Headway Deviation – Stage Bus 47 - PM Peak – Outbound and Inbound Direction ..........34 Figure �3-8 Headway deviation – Feeder Bus 904B - AM Peak.............................................................35 Figure �3-9 Headway deviation – Feeder Buse 904A - AM Peak...........................................................35 Figure �3-10 Average transfer time at Asia Jaya Stop.............................................................................36 Figure �3-11 Bus Passengers Preference .................................................................................................37 Figure �3-12 Transfer Time - 47 and 904A - AM Peak - Outbound and Inbound Direction .................38 Figure �3-13 Transfer Time - 47 and 904B - AM Peak - Outbound and Inbound Direction ................38 Figure �3-14 Transfer Time Loss - Asia Jaya stop - AM Peak - Outbound Direction and Inbound Direction.................................................................................................................................................39 Figure �3-15 Transfer Time Loss -Asia Jaya stop -PM Peak –Outbound and Inbound Direction ..........39 Figure �3-16 Transfer Time Financial Losses - Asia Jaya Stop -AM Peak & PM Peak .........................40 Figure �4-1 Stages of the Optimization Model........................................................................................44 Figure �4-2 Passengers Transfer Movement at Asia Jaya Stop- Outbound and Inbound Directions......45 Figure �4-3 Steps of the Optimization Model – Stage (1) .......................................................................47 Figure �4-4 Total Cost Structure - Stage (1)............................................................................................47 Figure �4-5 The Headway - Passengers Cost Relationship .....................................................................52 Figure �4-6 The Headway-Operators Cost Relationship .........................................................................53 Figure �4-7 The Headway -Total Cost Relationship ...............................................................................53 Figure �4-8 Steps of the Optimization Model – Stage (2) .......................................................................57 Figure �4-9 Total Cost Structure - Stage (2)............................................................................................58 Figure �4-10 Joint Probabilty of successful Connection – Stage 2 -Outbound Direction.......................60 Figure �4-11 Joint Probabilty of successful Connection – Stage 2 - Inbound Direction.........................60 Figure �4-12 Joint Probabilty of Missed Connection – Stage 2 - Inbound Direction.............................62 Figure �4-13 Joint Probabilty of successful Connection- Stage 2 - Inbound Direction ..........................63 Figure �4-14 Steps of the Optimization Model – Stage (3) .....................................................................67 Figure �4-15 Total Cost Structure - Stage (3)..........................................................................................67 Figure �4-16 Joint Probabilty of successful Connection - Stage 3 - Outbound Direction......................70 Figure �4-17 Joint Probabilty of successful Connection –Stage 3 - Inbound Direction.........................70 Figure �4-18 Joint Probabilty of Missed Connection – Stage 3- Outbound Direction............................72

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Figure �4-19 Joint Probabilty of Missed Connection – Stage 3 - Inbound Direction –..........................72 Figure �5-1 Traditional way of modeling public transport in a transport mode......................................79 Figure �5-2 GPS data collected for stage bus 13 - AM Peak...................................................................80 Figure �5-3 Schematic representation of relating the GPS data to the bus network data using (LRS) ...81

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List of tables

Table �2-1 Analytical and Numerical Solutions - Advantages and Disadvantages ................................14 Table �2-2 APTS Fleet Management Technologeis – ............................................................................20 Table �2-3 GPS Technology - Advantages and Disadvantages..............................................................22 Table �3-1 Data Survey Methds - Passengers Questionnare ...................................................................28 Table �3-2 Selected buses operating headway ........................................................................................29 Table �3-3 Overall Selected Stage Bus Passengers Demand - Asia Jaya Stop........................................32 Table �3-4 Transfer Demand - Selected Stage Buses to Feeder Buses ...................................................32 Table �3-5 Overall Passengers Demand for Feeder Buses – Asia Jaya Stop ..........................................33 Table �3-6 Stage to Feeder Bus Transfer Demand ..................................................................................33 Table �3-7 Transfer Demand - Selected Stage Buses to Feeder Buses ..................................................33 Table �3-8 Headway Standard Deviation / Mean Headway - Selected Stage Buses - Asia Jaya Stop....35 Table �4-1Optimal headway of stage buses - stage (1) ...........................................................................54 Table �4-2 Optimal headway of feeder buses - stage (1).........................................................................55 Table �4-3 Financial gains from resulting from stage (1)........................................................................55 Table �4-4 Total Costs Under Coordinated Service (RM) - Stage (2) ...................................................65 Table �5-1GPS survey – Bus 13 – AM Peak ...........................................................................................78 Table �5-2 Manual Passengers Counting - Bus 13 - AM Peak...............................................................79

OPTIMIZING BUS TRANSFER COORIDNATION

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1. Introduction, Problem Statement and Research Methodology

1.1. Introduction

With the rapid growth of urbanization all over the world the demand for public transit is dramatically increasing. Providing a door to door public transit service in large cities and widely spread urban areas is neither applicable nor affordable for a number of reasons. Firstly the number of origins and destinations to be covered is huge and widely spread. Secondly in big cities the transport network for road based transportation is over congested and cannot accommodate the large volumes of public transit services resulting from providing a door to door trip from all origins to all destinations. Thirdly providing a door to door trip between all origins and destinations is not a cost effective approach because of the demand variations over space and time. Finally there are more environmental issues to be considered such as the air pollution resulting from large traffic volumes in big cities and large urban areas. An efficient alternative is to have a well designed intermodal transit network with acceptable transfer time for passengers. An intermodal network can be defined as an integrated transportation system consisting of two or more modes. In contrast to multimodal networks, modes on intermodal networks are connected through facilities which allow travellers and or freight to transfer from one mode to another during a trip from an origin to a destination. Intermodal networks aim to provide efficient, seamless transport of people and goods from one place to another (Boiler 2001). Unfortunately, transfers involve certain inconveniences connected with discomfort of boarding a new vehicle (necessity of passenger orientation and walking between vehicles on feeder and receiving lines), negative perception of waiting for arrival new vehicle and existence of some delay during a trip (Adamski and Bryniarska 1997).A well designed intermodal transit network should be able to facilitate the passengers' transfers between transit modes in order to reach their final destination. When facilitating passengers transfers there are more than one element to be considered such as transfer time, total trip time, number of transfers, comfort of transfers, and the fare of transfers. All theses elements should be considered and designed to balance and fulfil the interests of the stakeholders involved namely the passengers, the service providers and the authorities. Transfer time tends to be the common measure of intermodal systems performance (Miller and Tsao 1999). The transfer time is the time duration that passengers coming from one transit mode have to spend at a transfer stations waiting for the other mode to arrive to take them to their destination. Transfer time is one of the most important public transit service quality indicators. The higher the transfer time the lower the riderdhip and the service quality. One possible alternative to minimize the transfer time is to increase the service frequency or in other words decrease the service headway by increasing the number of vehicles operating on the transit line. Low operating headway, which can


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substantially reduce transfer time, is not always cost effective due to variations of demand among transit routes over space and time (Chowdhury 2000). Aside from decreasing the service headway, a well designed and implemented passengers transfer coordination on the main transfer stops is a more attractive and effective solution to minimize the transfer time. In a bus transit system a timed transfer exists when multiple bus routes are scheduled to arrive on or about the same time at a transfer stop, with the goal of enabling short waiting times when transferring between routes (Dessouky 1999). Although a well designed and implemented transfer coordination might work perfectly in rural areas and uncongested urban areas that might not be the case for the large urban areas with high congestion rates. Public transit in those areas is subject to on street traffic environment and transit agencies may find it more difficult to maintain its vehicles as scheduled. To overcome such an obstacle a holding time at the transfer stop called the slack time is added to the schedule of the connecting vehicles to increase the probability of a successful connection in case one or more of the connecting vehicles are late. The determination of the optimal common headway and slack times for the connecting vehicles is a part of the design of the intermodal transit network. Both the common headway and the slack times should be determined in such away that satisfies the objectives of the threes stakeholders involved. In transit networks design three stakeholders are involved, each of them having their own point of view on the objective that has to be used for the design; the passengers, the service providers and the authorities respectively (Van Nes2000). In the case of transfer coordination passengers are mainly concerned with minimizing their travel time including their waiting, transfer and in-vehicle time while the service providers are concerned achieving an acceptable profit and revenue. All of this should be done taking into account the regulation and the constraints imposed by the responsible authorities. Still and even with an efficient design of the optimal common headway and slack times that satisfies the stakeholders' objectives the system reliability cannot be fully granted. In the absence of communication and tracking technology, timed transfer systems must rely on set schedules, combined with driver observations, for bus coordination. Buses can be held beyond their normal departure time if drivers observe that connecting buses are late. However, they can have no idea of how late the buses will be, or whether they will arrive at all (Dessouky 1999). With the deployment of Advanced Public Transportation Systems APTS such as Automatic Vehicle Location AVL, Automatic Passenger Counting APC and Geographical information systems GIS this problem can be better dealt with. With the help of these technologies the transit agencies will be able to monitor its whole fleet in the Real-time context and instruct the drivers to take certain actions to maintain the level of service and to keep the situation running as planned. In the case of transfer coordination, these technologies can be used to develop real-time control strategies at the main transfer stops for holding or dispatching the involved buses making the process of transfer coordination more efficient and demand responsive.

1.2. General Overview of Study Area and Justification

Malaysia, Country of Southeast Asia. From the Mid-1970 to the Mid-1990, Malaysia had one of the world's fastest growing economies. As expected, the rapid of growth of the economy encouraged rapid urbanization and motorization all over the whole country.


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Figure �1-1 Malaysia in The regional Settings (Source: www.theodora.com)

The highest urbanization and motorization is observed in the commercial capital city Kuala Lumpur and the Klang Valley region. Common to most towns in Malaysia, the existing public transport system in the Klang Valley region is dominated by buses (PTK report 2003). The bus services in Klang Valley consist of stage buses and express buses. The stage buses in the Klang Valley can be further divided into two categories namely the stage buses and the feeder buses. There more than 12 stage bus companies operating at the study area. The three main operators are IntraKota, MetroBus and City Liner. Apart from the stage bus, operators there are two feeder bus operators providing services to the passengers in the Klang Valley namely the PUTRA feeder buses and the STAR feeder buses. The feeder bus service is meant to provide the LRT passengers and stage bus passengers in the major public transport corridors with a trip to their final destination on the surrounding suburban areas after alighting the LRT or the stage bus or from the suburban areas to the nearest LRT station or stage bus stop. As stated in Schwarcz (2003) the bus ridership which is one of the main public transportation modes in the Klang Valley region in Malaysia is very low in general, representing approximately 20% of the total person trips in the region, as compared with other big cities in the neighbouring countries where it ranges from at least 40% to over 70%. One of the main causes of the low bus ridership levels in the region as mentioned in the study is that transferring between buses run by different operators represents a great difficulty since there is no coordinated service between them or even between buses ran by the same operator not to mention transferring between different modes. Another study was carried out in the year 2004 by the special task force for public transportation restructuring in the Klang Valley region. The study found out that 26% of the trips made by public bus in the region involve transferring to another bus to continue the journey to the final destination. The study indicates that this 26% is a very significant proportion and those transfers needs to be facilitated with efficient connectivity. The same study further implies that the maximum transfer time should not exceed time duration of 3.5 minutes and uses this value as the basis of their proposed public transportation network design.


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Figure �1-2 TheCase Study Location - Klang Valley Region - Malaysia

1.3. Problem statement

In the klang Valley region transferring between buses operated by different companies with uncoordinated routes and schedules have made intermodality in the system unfavourable to the users (Zakaria 2003). The transfer coordination problem is inherently conflicting. Passengers are mainly interested in having their trip with the lowest possible transfer time, which implies a higher service frequency and consequently a higher operating cost. On the other hand the service provider is interested in having the lowest operating costs and the highest revenue which implies a lower service frequency. A trade-off solution is needed that provides the passengers with acceptable transfer times while interchanging between different buses and the same time provides the service operator with acceptable revenue that allows them to maintain their service quality and continuity of their business.


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1.4. Main Objective

The objective of this research is to evaluate and assess the benefits of coordinated transfers between the different bus providers at the study area and to emphasis the role that APTS technologies can play to support the desired coordinated transfers.

1.5. Sub objectives

1- To assess the current transfer situation between the selected bus routes in the study area 2- To optimize the transfer coordination between the selected bus routes in the study area 3- To explore, investigate and emphasis the role that APTS technologies can play to facilitate,

control and improve the efficiency and of the desired coordinated bus transfers.

1.5.1. Research Questions

• To assess the current transfer situation between the selected bus routes in the study area 1- How important is the transfer time as one of the quality service indicators for the

passengers at the selected stop? 2- How long is the transfer time between connecting buses at the study area under the

current situation? And what are the equivalent financial losses to the lost time in transferring at the selected location?

• To optimize the transfer coordination between the selected bus routes in the study area 3- What are the major objectives (costs and benefits) of the passengers and the

operators? 4- How can those objectives be formulated mathematically? 5- What is the approach for evaluating the optimal value of the optimization model

decision variables? 6- What are the optimal values of the decision variables after solving the optimization

problem and their corresponding financial gains? • To explore, investigate and emphasis the role that APTS technologies can play to

facilitate, control and improve the efficiency and of the desired coordinated bus transfers

7- What are the relevant APTS technologies that can play a role in solving the transfer coordination problem in the real-time context?

8- How to integrate these technologies to solve the transfer coordination problem? 9- How can the transit agency make use of the integrated data available from to facilitate

the coordinated transfers in both the real-time context and the long term?

1.6. Research Design

The present research has three main components, identifying the transfer Time losses and the subsequent financial losses for the study location, conducting a transfer coordination study at the study location to evaluate the benefits of coordination and finally exploring and emphasising the potential role of APTS technologies in improving and supporting the handling of the transfer coordination problem in the real-time context. The study is a pilot study since it cannot be carried out for the whole bus network of the study area due to time, manpower and equipment constraints and complexity of the problem. Hence a representative part of the bus network is selected and the study will be carried out for that part.


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1.7. Overview of Research Methodology

Figure (1-3) gives an overview of the methodology followed in the present research. The stages of the proposed methodology are discussed and highlighted one by one in the following sections. The steps followed in each stage are discussed as well as the tools used to conduct them and the expected output of each stage.

Figure �1-3 Structure of Research Methodology


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1.7.1. Data Collection and Current Situation Analysis (Stage 1)

In the first stage the following procedure was followed in the data collection process and the assessment of the current situation at the study area. For Further detail on the data collection process and the assessment of current situation see chapter (3).

1) Data Collection Plan: Based upon the literature reviewed a fieldwork data collection plan was designed and followed to collect the minimal data required for the proposed research.

2) Expert Knowledge: An expert in public transportation modelling in the Klang Valley region was consulted for assistance in selecting a potential transfer stop to carry out the proposed research

3) Data Collection: A data collection process took place at the selected transfer stop. The data collection aimed to achieve the following three aims. Firstly to select the bus routes that are most suitable for a transfer coordination study based on criteria developed from the literature study. Secondly to collect the data required for the selected routes to assess the current transfer situation between them and the time and financial losses under the present uncoordinated situation. Thirdly to provide the data input for the proposed subsequent transfer coordination study.

4) Current Situation Analysis: Using the data collected in the previous step the transfer time losses are determined, quantified and analyzed for the selected bus routes under the present situation.

There are three main outputs resulting from the first stage;

• The selection of the stop and routes that are most suitable for coordination based on expert knowledge and criteria identified through literature.

• The collection of the data required to pursue the remaining stages of the research • The assessment of the current situation with respect to transfer time losses using both

time and financial analysis.

1.7.2. Optimization of Transfer Coordination (Stage 2)

In the second stage the following procedure was followed in the formulation of the optimization model For Further detail on the optimization process see chapter (4).

1) Problem Identification and Model Assumptions: Guided by the literature reviewed and complying with the data limitations, the problem is identified and the basic assumptions required to be able to model the problem are made.

2) Mathematical Formulation of Stakeholders Objectives: Guided by the literature reviewed the stakeholders objectives are formulated mathematically in terms of the problem decision variables and other involved parameters.

3) Stages of Coordination and Objective Function Formulation: In this step the approach and the stages to be followed for transfer coordination in the present study is discussed and explained. The corresponding objective function is formulated for each of the proposed coordination stages

4) Optimization of Transfer Coordination: In this step the solution technique to be followed for each of the proposed coordination stages is identified and followed. The results of the optimization process are obtained in terms of the problem decision variables.


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5) Assessment of the Transfer Coordination Benefits: Using the results obtained from solving the optimization model the benefits of coordination are identified and highlighted compared with the current situation.

6) Sensitivity Analysis: In this step a sensitivity analysis is conducted to measure the sensitivity of the optimization model decision variables to the other parameters involved in the problem formulation. The sensitivity analysis is a good tool to understand the problem behaviour and to overcome the limitations and the unreliability of the data collection

There are four main outputs resulting from the second stage;

• The identification of the best combination for transfer coordination among all possible combinations of the selected stage and feeder buses.

• The determination of the optimal values for the problem decision variables and their sensitivity to the other parameters involved in the problem formulation

• The determination of the financial costs of the proposed coordination for each of the stakeholders involved and for all of them as a whole.

• The determination of financial gains resulting from the proposed coordination when compared to the current situation.

1.7.3. Potential Role of APTS Technologies in facilitating coordinated transfers (Stage 3)

In the third stage the following procedure was followed to explore and emphasis the role of APTS technologies in facilitating coordinated transfers. For Further detail on the APTS see chapter (5).

1) Review of Relevant APTS Technologies: Based upon the literature reviewed a number of APTS technologies related to the improving and dealing with the transfer coordination problem in the real-time context are to be identified. In this step a brief description of each of these technologies and its benefits is provided

2) Integration of the Selected APTS Technologies: Guided by the review of the related APTS technologies conducted on the previous step integration issues between these technologies are also discussed and presented

3) Potential Improvements and Expected Benefits: In this step the potential improvement and the expected benefits of using these technologies are discussed with respect to their role in handling the transfer coordination problem.

There are three main outputs resulting from the second stage;

• The identification of the APTS technologies relevant to the enhancement of solving the transfer coordination problem in the real-time context

• The development of the proposed integrated methodology that improves the manipulation and the visualization of the transfer coordination problem in the real-time context

• The identification of the main benefits expected from the implementation of the proposed methodology


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1.8. Outline of the Thesis

Chapter 2: "Literature Review" The second Chapters provide detailed insight into the transfer coordination problem as one of the intermodal network design problems. Major stakeholders involved in the problem are identified with their interests. Solution techniques are also discussed as well as pervious models used to solve the problems. An overview of the relevant APTS technologies is also provided that can assist in solving the transfer coordination problem in the real-time context.

Chapter 3: "Data Collection, Case Study Location and Current Situation Analysis" The fourth chapter provides a detailed description of the data collection process, the selection of the case study location and the assessment of the current situation with respect to the transfer time losses.

Chapter 4: "Optimization of Transfer Coordination" The fifth chapter contains the development of the transfer coordination optimization model, the optimization model results, the evaluation of the benefits coordination study and the sensitivity analysis.

Chapter 5: "APTS Provision – Potential Role in the Transfer Coordination Problem" The sixth chapter provides a review of the related APTS technologies and their integration issues with the aim of emphasising the potential role and the expected benefits of the deployment of APTS technologies with respect to the handling of the transfer coordination problem in the real-time context.

Chapter 6: "Conclusions and Recommendations" The seventh and the last chapter highlight the main conclusions of the research and provide recommendation for the study location as well as for future research.


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2. Public Transport Network Design A Transfer Coordination Approach

The present chapter provides an insight into the different aspects of the transfer coordination problem as one of the problems of the intermodal public transport network design. It starts with a definition of the public transport network design problem and the identification of stakeholders involved in it, their main interests, concerns, and its effect on the network design objectives. Then an overview of the transfer problem and all its related aspects is given with a specific emphasis on transfer coordination being the main element of concern in present research. The transfer coordination problem basic elements and variables are also discussed with available solution techniques. A review of previous models developed on the transfer coordination problem is then conducted with their advantages and the shortcomings. Finally, an overview of related Advanced Public transport technologies APTS is conducted with its potential role in improving the management of the transfer coordination problem in the real-time context.

2.1. Public Transport Network Design Problem

2.1.1. Main Characteristic

The main characteristic of public transport network design is the balance between opposing objectives. A design that is optimal with respect to one objective is not optimal for the other objective, and vice versa (Van Nes 2000). While passengers are interested in a fully connected network between all origins and destinations with minimum travel times, fees and maximum comfort the operator or the service provider is interested on having the smallest network possible with the highest revenue and the lowest operational costs. Accordingly, Attention should be paid while selecting the network design objectives so that they satisfy, represent and consider the conflictive views and the opposing interests of the stakeholders involved.

2.1.2. Stakeholders Identification

In public transport network design there are three parties involved, each of them having their own point of view on the objective that has to be used: traveller, operator, and authorities respectively (Van Nes 2000). The passenger’s judge or value the public transport services by three main components: travel time, costs, and comfort. The major and the most crucial component to the passenger is the perceived door-to door travel time. The door-to door travel time consists of various time elements namely access time, waiting time, transfer time, in-vehicle time and egress time. Each of these travel time elements is perceived, weighted and appreciated differently for each passenger. A suitable network design objective for the passenger might to be to minimize one of theses time elements or to minimize the weighted total travel time. Using this objective for the network design will result in fully connected networks with very high public transport frequencies. This is obviously not a suitable design for the operators since the operational costs will be huge when compared to the revenue or the profit coming from operating the public transport system.


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The operator’s view of the system is very different; his main concern is the continuity and the of the profitability business. A suitable network design objective for the operator might be to maximize the profit, which is the revenue minus the operational cost or to minimize the operational costs. Obviously using this objective for design will result in poorly connected network with very long travel times and very low frequency public transport services. Ultimately, if such an objective is used in network design the ridership levels will decrease and as a result, the system profitability will decrease as well (Van Nes 2000).

Figure �2-1 Illustration of Passenger and Operators Optimal Design of the Public transport Network (Source: Van Nes 2000)

The authorities, the third and the last stakeholder involved have their own different agenda. A suitable objective for the network design from the authority’s point of view might be minimizing the total costs of the system including both the passenger’s and the operator’s costs. The authorities might also be interested on minimizing the subsidy given to the operator. Apart from defining design objectives, the authorities might play another role in public transport network design, namely setting constraints such as a maximum access distance or a minimum frequency. In that case the operator can use his own objective in the public transport network design as long as those constrains are fulfilled and satisfied (Van Nes 2000). In Conclusion, it can be clearly seen that the stakeholders’ objectives are mainly opposing and conflictive. With respect to figure (2-1) an optimum design of public transport network should be close to the operator optimum but with introducing transfer stops or hubs in intermediate locations where large passengers' volumes are generated. At those hubs various routes coming from different origins and going to different destinations should be connecting. Providing transfer passengers at those hubs with seamless mobility by coordinating the services of the connecting buses to minimize the time spent in transfers is a good alternative to the unrealistic door to door trip. A suitable analytical approach to reach this optimum design is mathematical optimization. The objective of optimization is to select the best possible decision for a given set of circumstances without having to enumerate all of the possibilities (Giordano and Weir 2001).

A - Passenger Optimum B- Operator Optimum


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2.1.3. Public Transport Optimization Problem Description

The goal of an optimization problem can be defined as follows: find the combination of parameters (independent variables) which optimize a given quantity, possibly subject to some restrictions on the allowed parameters range. The quantity to be optimized (maximized or minimized) is termed the objective function; the parameters, which may be changed in the quest for the optimum are called control or decision variables; the restrictions on allowed parameters values are known as constraints ((Giordano and Weir 2001). With respect to section (2.1.2) the goal of the optimization problem will be to find the optimal value of the design variables such as stop spacing, stop location and service headway that best satisfies the operators, the passengers and the authorities' objectives. Van Nes (2000) formulated an optimization based analytical approach that can be used for public transport network design (Figure 2-1). In his approach, he used the following terminology:

Figure �2-2 Structure of the Analytical Approach (Source: Van Nes 2000)

• Objective: The Criterion or set of criteria to be optimized, for instance minimizing travel time;

• Objective function: Mathematical formulation of the objective using the decision variables; • Design Variables or Decision Variables: endogenous variables for which optimal

relationships or optimal values have to be determined , in his case design variables are stop spacing and line spacing

• Design parameters: exogenously given parameters used in the mathematical formulation that are not determined by public transport system itself, for instance, the weights of different time elements ;

• System Parameters: exogenously given parameters used in the mathematical formulation that are determined by public transport system itself, for instance the costs of operating a bus

• Output: results of analytical model, for instance, the value of the objective function; • Outcome: the total set of criteria used to judge a network design, such as travel time,


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In his study, the mathematical descriptions of these relationships were formulated and used as building blocks to define objective functions, which are mathematical representations of the formulated objectives. Those objective functions were then optimized with respect to the decision variables stop spacing and line spacing yielding the optimal relationships for these decision variables under certain fixed parameters and a set of constraints.

General Structure

Based on van Nes (2000) the general structure of the problem description for such an analytical model is as follows:

1) The Decision Variables 2) Objective Function: The main objective function used in literature is minimizing the total costs,

either the sum of travel costs and operating costs, or the sum of travel costs, operating costs and capital costs that is investment costs and fleet costs.

3) Problem Constraints (Optional): The use of constraints in analytical models is limited. Capacity and budget constraints are the most commonly used constraints.

Solution Techniques

Van Nes (2000) furthers explains that there are two solution techniques for the optimization problems, the analytical approach and the numerical approach (enumeration). Table (2-1) shows the advantages and the disadvantages of both approaches Table �2-1 Analytical and Numerical Solutions - Advantages and Disadvantages (Based on Van Nes 2000)

Method Advantages Disadvantages Analytical Approach For each decision variable the

optimal relationships with parameters and other decision variables are defined explicitly

The objective function must be formulated in such a way that is suitable for mathematical analysis

Numerical Approach (enumeration)

Can deal with mathematically less tractable objective functions

Provides less insight into the main relationships of the decision variables

Characteristics of the Results

Based on Van Nes (2000), the main characteristics found in nearly all studies is that optimal relationships for the decision variables can be described using a square root or cubic route functions. This finding implies that the optimal values have a limited sensitivity with respect to the parameters and the variables used. Doubling the value of decision variables `or of a system parameter, results in an increase of the decision variable of 41% (square root relationship) or 26% (cubic root relationship) at most. Also the objective functions were found to be shallow around the optimum which allows for varying or rounding the values in planning practice, for instance to account for typical characteristics of an urban area, without serious consequences on the design objectives. However, for it was found that due to the square and cubic root relationships, lower values of the decision variables would have more impact on the value of the objective function than higher values.


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2.1.4. Intermodalism – Main Concept

In the last two or three decade’s an outstanding large increase in traffic congestion, air pollution, pressure on the infrastructure and passengers volumes has occurred. Having a well-designed public transport network that works individually without any coordination with the other modes of public transport was found not to be sufficient. As a result, the concept of intermodalism emerged. Intermodalism refers to a transportation system in which individual modes work together or within their own niches to provide the user with the best choices of service, and in which the consequences on all modes of polices for a single mode are considered (U.S.D.O.T 2000). There are many advantages of having an intermodal public transport system in place such as reducing fuel consumption, air pollution, pressure on the infrastructure and traffic congestion; increasing the accessibility to the infrastructure through better coordination of the scheduling process within the same public transport mode as well as between different modes. An efficient intermodal public transport system should be able to achieve all these benefits and at the same time maintain the attractiveness of the public transport network to all the stakeholders involved. The present research is limited to the transfer coordination problem as one of the intermodal public transport network design problems. The same optimization based analytical approach can be followed in the present research. The following sections provide a detailed description of the transfer coordination problem, main decision variables involved, objective functions, and constraints. A review of previous models in transfer coordination is also conducted with its advantages and shortcomings.

2.2. The Transfer Coordination Problem

Transfers play significant role in daily transit operations in terms of ridership, cost-effectiveness and customer satisfaction. Riders usually have a negative perception of transfers because of their inconvenience, which can be thought of as a transfer penalty Understanding what affects transfer penalty can have significant implications for the transit authority. It can help in identifying which type of improvement to the system can most-effectively improve transfers, thus attracting new customers (Guo and Wilson 2004). There are many factors affecting the transfer penalty such as the transfer time, the total trip time, the number of transfer, the comfort of transfers (i.e. Landscape, weather...) and the financial costs of transfers. The level of service of an intermodal transit system is dependent significantly on transfer times (Chowdhury 2000). Indeed the transfer time between public transport modes or within the same mode is the most weighted and appreciated element for passengers when assessing the quality of transfers. Transfer time is the waiting time penalty encountered by passengers at a transfer stop or terminal while changing between public transport lines. The higher the transfer time the higher the passengers inconvenience and the lower the ridership rates. As mentioned in the previous chapter the transfer time can be reduced by increasing the service frequency or in other words decreasing the service headway. The service headway is the difference in time between two subsequent vehicles operating at the same line. Decreasing the service headway might be a suitable design objective from the passenger’s point of view but not always cost effective from the operators’ point of view. Low operating headway, which can substantially reduce transfer time, is not always cost effective due to variations of demand among transit routes over space and time (Chowdhury 2000). Aside from


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decreasing the service headway considerable user waiting time may be saved at transfer terminals if the arrivals of vehicles from different routes can be synchronized or otherwise coordinated (Lee and Schonfeld 1991). The synchronization of vehicle arrivals can be achieved through the implementation of common operating headways for the connecting routes. Schedule synchronization is a suitable approach for rural areas and uncongested pubic transport networks. The traffic conditions in that case are stable and schedule delays are minimum. In large cities and congested urban areas, the schedule synchronization alone might not be a suitable approach to minimize passengers transfer time because of unreliable traffic conditions that might cause vehicles to deviate from schedule. Vehicle breakdowns and accident are also frequent under those traffic conditions. In that case, transfer coordination is a better approach. Holding times (slack times) added into the schedule of coordinated routes may be required to increase the probability of successful connections (Chowdhury 2000). The slack time is an additional time added to the schedule of a vehicle to wait for other connecting vehicles at a transfer stop in case of delay. The feasibility and desirability of such coordination depends on the variability of traffic conditions and stopping times, service frequencies, fractions of users involved on the transfers and relative costs of vehicle delays and user times (Lee and Schonfeld 1991). Accordingly, not all connecting routes are suitable for schedule synchronization or transfer coordination and all those measures should be tested first to ensure the feasibility of coordination. The feasibility of coordination is assessed and evaluated based on the objectives of the three stakeholders involved. Still and even if connecting routes are suitable for coordination the optimal values of the problem variables should be obtained in such away that fulfils the three stakeholders objectives.

2.2.1. Decision variables

From the previous discussion, (see 2.1.1) it should be clear that the transfer coordination problem is a function of two decision variables namely the common headway of the connecting vehicles and the slack times added to their schedule to increase the probability of a successful connection. An increase in the common headway, for instance will result in longer waiting times for non-transfer passengers waiting at the stop and higher passengers volumes and consequently longer stoppage time and longer overall travel time. If the common headway is decreased, the waiting times will be reduced but the operational costs for the operators will increase due to the increase in the operational fleet size. For the slack times, an increase in the slack time will increase the probability of a successful connection and will minimize the transfer time but at the same time will increase the stoppage time and the overall travel time of the in-vehicle passengers and will also increase the operator’s costs. The effect of increasing or decreasing any of the decision variables on the travel time components (waiting time, transfer time, stoppage time…) and on the operators, costs should be measured and analyzed. To do so, the travel time components and the operator costs should be defined and formulated as a function the decision variables and other fixed system parameters. Then optimal values of the decision variables can be obtained based on the used design objective.

2.2.2. Previous Models on Transfer Coordination

Salzborn (1980) discussed some rules for scheduling a bus system consisting of an intertown bus route linking a string of interchanges each of which is the centre of a set of feeder routes. The problem of scheduling the feeder bus departures and arrivals for better connections with the intertown bus was solved using combinational group theory. The model is based on preset values for minimum


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and maximum passengers transfer times, stopping times at interchanges and minimum terminal times. The main shortcomings of this model are that it did not consider the passengers demand and the transfer time costs and it assumed deterministic arrivals of buses at the interchanges, which might be an unrealistic assumption especially in congested urban areas with unreliable traffic conditions. In addition, no mathematical model to optimize the system characteristics was formulated. Lee and Schonfeld (1991) formulated a model to determine optimal vehicle holding times (slack times) for a transfer terminal. The basic system model consists of a bus route connecting with a rail transit route at transit terminal. In their model, the scheduled headway is assumed equal for the connecting routes and bus arrivals at the terminal were assumed stochastic. Discrete, Normal and Gumbel distributions were used to represent the pattern of bus arrivals at the terminal. A total cost function was formulated that includes all cost components that are sensitive to the slack time, that is, (1) scheduled delay costs for the passengers at the stop and the operator (due to holding the buses, their drivers and non transferring passengers for a scheduled slack time), (2) the missed connection cost of bus passengers transferring to the rail and (3) the missed connection delay of rail passengers transferring to bus. The time cost is converted into financial losses using the value of passengers' time. Passengers demand is assumed fixed and independent of the quality of service provided. The optimal slack time was obtained analytically for the discrete distribution and numerically for the normal distribution. They found that the standard deviation of vehicle arrival times is an important factor affecting the duration of slack time needed and desirability of such coordination. Bookbinder (1992) follows a slightly different approach by optimizing an objective function measuring the overall inconveniences to passengers who must transfer between lines in a transit network. In his model, trips are not actually required to meet at transfer points. Instead, their departures from the terminal are scheduled in order to minimize transfer passengers inconveniences. The model is based upon a grid transit network with decentralized transfers. A mean disutility function was formulated to evaluate the passengers' inconveniences under random bus arrivals at the stops. The transfers were optimized for a single connection in the network as well as for many connections simultaneously in the network. Knoppers and Muller (1995) investigated the possibilities and limitations of coordinated transfers in public transit systems, the optimal transfer times were obtained while considering stochastic arrival of feeder vehicles and deterministic arrivals of vehicles operating on a major transport route. The study aimed at minimizing passengers transfer time. It was found that coordination was worthwhile only when the arrival time standard deviation on the feeder line at the transfer point is less than 40% of the headway on the major service network. Only one direction transfer was considered in this study. Adamaski and Bryniarska (1997) formulated and solved two schedule synchronization problems. The first one is concerned with a transfer synchronization when passengers changing transit lines at transfer points, whereas the second with harmonization of headways. A tabu search and genetic method were used to solve the problem Chowdhury (2000) developed a two-stage procedure for the optimization of transfer coordination in intermodal transit networks. His model consists of a rail transit line and different numbers of feeder routes connecting at different transfer stations. The decision variables optimized are transfer time and


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slack times reserved in schedules at the railway stations. In the first stage of his model, optimal headways are obtained analytically for uncoordinated services of both rail and feeder buses. In the second stage, optimal common headways and slack times are optimized jointly for bus route coordination at isolated transfer stations, best group of feeder buses to be coordinated in each transfer station is obtained in this stage based on the minimization of the total costs of both the passengers' and the operator's costs. In the third stage, the best group of buses to be coordinated at each transfer stop obtained from the second stage is coordinated with rail line. Finally, in the fourth stage of his model a network wide coordination is considered to achieve rail-bus coordination for multiple transfer stations. The study considers fixed passenger demand for both the rail and the feeder buses. The model assumed a fixed passengers demand, fixed location of transit facilities (e.g. routes and stations), supply parameters (e.g. vehicle size, operating speeds and costs) and demand parameters (e.g. value of passengers time). A deterministic arrival of rail is assumed while a stochastic normal distribution of buses arrivals is assumed. The study considered one common headway per transfer station if coordination is desirable. The passengers' cost is defined as the summation of the waiting time costs, transfer time costs and the in-vehicle time costs. The access and the egress time costs are omitted since the network is fixed and given in his study. The waiting time cost is defined as the product of the average waiting time, passengers demand, and the value of passengers waiting time. The passengers waiting time is assumed equal to half the headway since random passengers' arrivals to the stop is considered in the study.

n m

i 1 j 1ww b i j i j

1C H I u 2 = =

= � � (�2-1)

Cwb Bus Passengers waiting time costs ($) Hij Headway of stage bus (j) at stop (i). (hr) Iij� Demand of bus route (j ) at station (i). (pass/hr) uw Value of passengers waiting time ($/hr) The transfer time cost is defined as the product of the average transfer time, transfer passengers demand and the value of passengers waiting time. The transfer time is calculated based on welding (1957) formula in case of uncoordinated services. The study assumed a uniform distribution of transfer passengers at the transfer stop within the headway. In case of coordinated services, transfer time is calculated based on a joint probability function of vehicle arrivals times under a normal distribution. Several possible scenarios for vehicles arrival are formulated and corresponding transfer time is obtained for each case.

[ ) ]C Nn m m

i 2 j 1 k 1wt b b i k j i k j i k j i k j i k j

1C y T + ( 1 - y T U u 2 = = =

= � � � (�2-2)

Ctbb Bus Passengers transfer time costs ($) yikj Binary variable (i.e. 0 or 1) indicating the status of coordination between the buses.

CikjT Transfer time from bus to (j) to bus route (k) at station (i) under coordinated service. (hr) N

ikjT Transfer time from bus to (j) to bus route (k) at station (i) under uncoordinated service.

(hr) Uikj The transfer demand from bus route (k) to bus route (j) at station (i) (pass/hr) uw Value of passengers waiting time ($/hr) The In-vehicle time cost is defined as the product of the average in-vehicle time, the corresponding demand and the value of passengers' in-vehicle time. The in-vehicle time is disaggregated into moving


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time and dwelling time. The moving time is defined as the route length over the average speed while the dwelling time is defined as the demand divided by the passengers boarding/alighting rate.

n m 2

i 1 j 1 1

i j i j i jvv b i j

i j b

L H IC ( + ) I u

2 S 2 q= = δ == = δ == = δ == = δ =

δδδδδδδδ==== � � �� (�2-3)

The operator's costs are defined as the product of fleet size and the vehicle operating costs. The fleet size is obtained from the round trip time (moving and Stoppage time) divided by the operating headway.

Rn m

i i j 1

i j i jb0 b

i j

T KC ( ) u

H= == == == =

++++==== � �� (�2-4)

Kij Slack time added to the schedule of bus route (j) at station (i) R

ijT Bus round trip time. (hr)

Hij Headway of stage bus (j) at stop (i). (hr) Ub Bus operational costs ($/hr) A total cost objective function is formulated that minimizes the above-formulated passengers and operators costs. The objective function differs for each stage of coordination. Still it is purely a function of the operating headway of buses and rail and the added slack times. Optimal values of operating headways are obtained analytically in case of uncoordinated service. In case of coordinated services, common headway and slack times are obtained numerically for the different stages.

2.2.3. Important Issues in Transfer Coordination

Passengers' Arrival Distribution and Corresponding Waiting Times The most commonly assumed average passengers waiting time is one-half the vehicle headway. It can be sustained only if the headways are completely regular and passengers' arrivals are random. However, this approximation is not always valid specially when transit headway is long and the passenger arrivals are not random (Chowdhury 2000). Welding (1957) formulated a model for estimating the passengers waiting time E (W).

( ) ( )/=E w E H 2 + V(H) / 2E(H) �2-5)

Where; E (H) and V (H) represent the mean and the variance of vehicle headways respectively. The model can be used only when passengers' arrivals are uniformly distributed within the headway (H).

Value of Passengers time The values of Passengers time (e.g. wait time, transfer time and in-vehicle time) covered reflects passengers willingness to pay to save that time. The value of time is a dependent on many aspects such as; Gross Domestic Product (GDP) per capita in real terms, Trip Distance, Journey Purpose, and

Bus Passengers in-vehicle time costs. ($) Length of bus route (j). (Km) Average speed of bus rout (j) . (Km/hr) Headway of stage bus (j) at stop (i). (hr) Demand of bus route (j) in direction (�) at station I. (pass/hr) Boarding/Alighting rate (hr/pass) Value of passengers In-vehicle time ($/hr)

Cvb Lij Sij Hij Iij� qb uv


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Mode of Transport (Wardman 2001). Many studies were conducted to evaluate the passengers' value of time in different countries. Due to the lack of such a study for the study area, the values used in this research is based upon one of the first studies to estimate values of waiting and walking and transfer time by Merlin and Barbier 1965 (In Wardman 2001). They established that the waiting time valued as three times as the in-vehicle time and the transfer time is valued as two times as the in-vehicle time Boarding and alighting time The boarding/alighting time is time needed for one passenger to go inside or outside the bus at a bus stop. In this study the average boarding and alighting time are taken as 4.2 and 2.1 seconds respectively (FTA 2002)

2.3. Advanced Public Transport Technologies – Potential Role in solving the Transfer Coordination Problem in the Real-time Context

APTS technologies are collections of technologies that increase the efficiency and safety of public transportation systems and offer users greater access top information on system operations. The goal is to provide public transportation decision-makers more information to make effective decisions on systems and operations and to increase travellers’ convenience and ridership. APTS technologies can be organized into five broad categories that describe the technologies relevance to transit applications. Since the transfer coordination problem is mainly a scheduling problem it falls under the fleet management category. Fleet management systems aid in boosting the efficiency of transit systems, reducing operating costs, and improving transit services through more precise adherence to schedules. This is done by using technology to monitor the fleet effectiveness in meeting customer demand, identifying incidents, managing response, and restoring service more effectively. More efficient planning, scheduling, and operations can also increase ridership, as customers are able to better depend on transit (USDOT 2000). Fleet management systems provide transit agencies with real-time management of bus systems through a number of technologies namely Automatic Vehicle Location systems AVL, Transit Operations Software, Communication Systems, Geographic Information Systems GIS, Automatic Passengers Counters APC and Traffic Signal priority Systems. Table �2-2 APTS Fleet Management Technologeis – Based on the ( USDOT 2000)

Technology Description

Automatic Vehicle location (AVL)

AVL systems are computer-based vehicle tracking systems that function by measuring the real-time position of each vehicle and relaying the information back to a central location. They are used most frequently to identify the location coordinates of vehicles in order to satisfy demand. They also serve to provide location coordinate to respond to emergencies.

Transit Operations Software

Data collected from vehicle-based fleet management systems is relayed to centralized computer systems and is made useful by the transit operations software. This software helps the operator to monitor the fleet’s effectiveness in meeting demand, identify incidents, manage response, and restore service more effectively

Communication Systems

Communication systems pass voice, data and information between transit vehicles and transit agency dispatching centres. Transit communication systems are comprised mostly of wireless technologies


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Geographic Information Systems

(GIS)

GIS are a special type of computerized database management system in which geographic databases are related to one another. GIS are used for developing and displaying information to assist operators, dispatchers, and street supervisors to make on-the-spot decisions.

Automatic Passengers Counters (APC)

APC collects data on passengers boarding and alighting by time and location. The information is then delivered to the transit operations centre for monitoring the demand in the real-time context

Traffic Signal Priority

Traffic signal priority is a technology by which a traffic signal may be held green (or made green earlier than scheduled) so that a vehicle may pass through the intersection more quickly. Applying this technology to buses allows for an increased number of people to pass through an intersection during a light cycle.

As previously discussed, the transfer coordination problem is mainly a function of the common headway and the slack times added to the schedule to increase the probability of a successful connection. The slack times added to schedule of the connecting vehicles are inherently static. They are based on data collected on average passengers demand and probability distributions of buses arrivals at the stop. In other words, if one of the connecting buses arrive a transfer stop it has to be held for the slack time duration blindly without having any information on whether the other connecting buses can make it to the transfer stop within the time left in the slack time or not. In addition, no data is also available on the real-time transfer demand between the connecting vehicles. The connection might still be successful but useless if no passengers are transferring between the connecting lines. With the implementation of APTS fleet management technologies, these deficiencies can be better dealt with. Having APTS fleet management technologies in place, the transfer coordination problem can be handled in the real-time context. The four most important fleet management technologies that can deal with the static approach deficiencies making the system dynamic and demand responsive are AVL, APC, communication systems and GIS technologies.

Figure �2-3 APTS Fleet Management Technologies (Based on USDOT 2000)


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• Automatic vehicle location (AVL) AVL systems are computer-based vehicle tracking systems that function by measuring the real-time position of each vehicle and relaying the information back to a central location. They are used most frequently to identify the location coordinates of vehicles in order to better satisfy demand. They also serve to provide location coordinates to respond to emergency situations. The location technologies found on AVL systems are usually one of the following, but can also be used in combination: Global Positioning System (GPS); Signpost and Odometer interpolation, active and passive; Ground-Based Radio, such as Loran C; and Dead Reckoning. Global positing systems GPS is becoming more and more the dominating technology for vehicle positioning in transit agencies. As mentioned in the (USDOT 2000) there has been a great shift in the location technology used away from signpost and odometer and towards GPS. Consequently, and since the GPS technology is the one used in the present research it will be the only AVL technology discussed in the following section GPS, which stands for Global Positioning System, is a radio navigation system that allows land, sea, and airborne users to determine their exact location, velocity, and time 24 hours a day, in all weather conditions, anywhere in the world (Drane and Rizos 1998). For transit agency, stand-alone GPS is not sufficient for real-time monitoring of bus system because of the low accuracy which is around 100 m (Drane and Rizos 1998). Higher accuracy standalone GPS’s are not also cost effective for the agency. Instead, stand-alone GPS’s can be complemented with deferential GPS navigation DGPS. The main principle is to have one of the GPS receivers located at a base station or a known location, normally at the transit operations control room. The position of the base station is continuously computed using the available satellites and compared with the actual know position. Correction parameters are generated and transmitted to the stand-alone GPS for immediate real time corrections. The relative accuracies expected in such schemes are of the order of 1m to 10 m. Table �2-3 GPS Technology - Advantages and Disadvantages

Technology Operation Advantages Disadvantages Global Positioning System (GPS)

A network of satellites in orbit transmits signals to the ground. Special receivers on each vehicle read the signals available to them and triangulate to determine location.

- Can be operated anywhere GPS signal can be received - Does not require purchase, installation, or maintenance of wayside equipment - Very accurate especially if complement by DGPS - Can be integrated with other AVL technologies to overcome signals block resulting from high rise buildings , tree covers, tunnels, or overpasses

Signals can be blocked by high rise buildings , tree covers, tunnels, or overpasses


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In relation to the transfer coordination problem GPS technology provide the transit agency with the exact location of the buses in the real-time context making it possible for the transit agencies to control the movement of the connecting buses so that they connect at the transfer stop within the slack time window obtained through the optimization. Even without any control of the connecting buses, the AVL technology can be used to determine whether the late vehicle will be able to arrive at the transfer stop within the slack time of the other connecting vehicle or not. • Automatic passengers Counter (APC) Automatic Passengers Counters (APCs) are devices for counting passengers automatically as they board and as they alight buses at each stop along a route. The benefits of APCs come both in a reduced cost to collect ridership information and in an increase in the amount and quality of the information gathered. APCs reduce or eliminate the need for manual checkers and are less likely to miscount passengers at busy stops (USDOT 2000).

APCs typically use one of two counting technologies, either treadle mats or infrared beams (APTS update 200). Treadle mats, placed on the steps of the bus, register passengers as they step on a mat and infrared beams (mounted either horizontally or vertically), directed across the path of boarding and alighting passengers, register riders when they break the beam.

In relation to the transfer coordination problem APC technology can play a role in estimating and transmitting the exact in-vehicle and transfer passengers demand. The data collected can be used as an input to the slack time optimization model instead of the average demand data used making the optimization model dynamic and demand responsive. It can also be used to inform the to inform the bus drivers not to wait for the late connecting vehicles in case there are no transfer demand or the transfer demand is very low.

• Communication Systems Often the deployment of an AVL system on a bus network results in the need for increased capacity to the communications systems. The system is used to transmit voice and data between vehicles and operations centres, and to transmit commands between operators and technologies. These communication systems are used for routine activities such as talking to dispatch, aligning transfers from one bus to another, or for emergency situations such as bus breakdowns. Mobile transit communications systems involve the broadcast of information over Radio Frequency (RF) waves from a transmitter to receiver. The technology and methods used to perform this function, which includes both voice and data transmissions, vary widely from traditional two-way radios to personal communication system (PCS) devices. In relation to the transfer coordination problem communication technologies are used to transmit commands and directions from the transit agency control room to the bus drivers based on the data collected from the AVL and APC technologies regarding the connecting buses locations with respect to the schedule and the existing passengers demand.


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• Geographic Information Systems (GIS) Implementation of a Geographic Information System (GIS) provides an extremely powerful tool to assist transit operators in developing the necessary data to make operations and investment decisions. GIS provides a current, spatial, interactive visual representation of transit operations. It is a type of computerized database management system in which geographic databases are related to one another via a common set of location coordinates (USDOT 2000). This allows users to make queries and selections of database records based on geographic proximity and attributes. With respect to the transfer coordination problem GIS technology can be used to determine the exact location of the connecting buses on transit routes map based upon the data transmitted from the AVL technologies and it can calculate how much time is left for the vehicles to reach the transfer station based on average link speeds. The data transmitted from the APCs technologies can be used for ridership analysis inside the GIS platform to take decisions on whether the existing transfer demand is sufficient to hold buses at a transfer stop. In conclusion, whereas GIS technology provides significant improvement in the ability to see and understand an entire fixed route transit system, the integration of GIS, AVL, APC and communication technologies makes the system dynamic, demand responsive and a fully functional tool in planning, scheduling, and dispatching.

2.4. Conclusions

Based upon the discussion conducted in this chapter (See 2.1 and 2.2) the following remarks and conclusions were observed and drawn;

• Except for Salzborn 1981, all the models reviewed are analytical models and the solutions for these models are obtained through mathematical optimization

• Analytical solutions for the optimization models formulated can be obtained only under deterministic arrivals of buses to the transfer terminals (Lee and Schonfeld 1991). Assuming other types of vehicle arrivals, only numerical results can be obtained (Lee and Schonfeld 1991), (Knoppers and Muller 1995) and (Chowdhury 2000).

• A total Cost objective function that minimizes the both the passengers and the operators costs is formulated in (Lee and Schonfeld 1991) and (Chowdhury 2000). Knoppers and Muller (1995) minimize the transfer time and bookbinder minimizes a passenger's inconvenience objective function.

• Lee and Schonfeld (1991) deals only with the optimization of slack times added to the schedule of the connecting vehicle assuming that the connecting vehicles are operating under a common headway. Chowdhury (2000) finds the optimal common headway and slack times added to the schedule of the connecting vehicles

It was found that Chowdhury (2000) is the best transfer coordination model to be adapted to the present study for the following reasons;

1) The model follows exactly the same reasoning and analytical formulation used for public transport design (See 2.1.3)

2) The model is based on the optimization of a total cost objective function that includes both the passengers and the operator's costs. The total cost objective function is used in most of the public transport design models as it considers the conflicting objectives of the three stakeholders involved (See 2.1.3)


25

3) The model is dealing with the two decision variables of the transfer coordination problem namely the headway and the slack times (See 2.2.2)

4) The model assumes stochastic arrivals of buses to the stations, which is a realistic assumption under the fluctuating and unreliable urban traffic conditions.

5) The model incorporates all the passengers and operators cost components that are sensitive to the transfer coordination (i.e. waiting, transfer, in-vehicle and operators), giving the model more credibility and applicability. (See 2.2.3)

In the fourth Chapter of this research the model is adapted to the problem of the study area, formulated and solved.

Based upon the discussion of the this chapter (See 2.3) it was found that the deployment of APTS fleet management technologies specifically GPS, APC, GIS and Communication systems can play a significant role in dealing with the dynamic aspects of the transfer coordination problem namely the passengers demand and buses location with accordance to their schedules. Knowing the real-time passengers demand and the exact buses location can potentially improve and facilitate coordinated transfer making the bus system more dynamic and demand responsive In the fifth chapter of this research the integration issues between the above mentioned APTS technologies in a GIS platform will be discusses and the expected benefits and improvements in handling the transfer coordination problem in case of technology deployment.


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3. Case Study Location, Data Collection, and Current Situation Analysis

This chapter aims at giving a detailed description of the data collection process and the existing situation analysis. It starts with a brief description of the case study location and the way it was selected. Then it gives a general overview of the data collection process and the process of selecting the routes to be assessed and coordinated. Finally the current transfer times between the selected connecting bus routes is calculated based on fieldwork data collection and the results are translated into financial losses at the stop during the peak hours using the estimated transfer demand and the value of passengers waiting time.

3.1. Asia Jaya – Stop Selection

Due to the limited fieldwork duration, a comparison study between a numbers of potential transfer stops to select the most suitable stop for the present research could not be carried out. The suitability of the stop is dependent on many aspects such as the transfer passengers' volumes and the service frequency. Instead, the following procedure was followed to select the study location.

3.1.1. Expert Knowledge

After several meetings with the academic staff of the transportation department in the Malaysian University of Science and Technology (M.U.S.T) and some of the transportation consultants on the study area, they suggested having a meeting with one of the public transit experts in the study area. The expert has over 15 years of experience in public transit modelling in the Klang valley region. The expert suggested two different potential locations to conduct the proposed research.

3.1.2. Quick Overview

A quick overview of the two-selected stop was done through a short visit to the suggested locations with the consultant. Based upon field observation it was found that Asia Jaya stop is the more suitable location for the proposed for the following reasons:

• High passengers' volumes can be observed at both the stage and the feeder bus stops. • The bus service frequency at the stop is ranging from 20 to 30 minute, which is a suitable

frequency for a coordination study. • Large passengers' waiting times can be observed at both the stage and the feeder bus stops. • Passengers' movements between the stage and the feeder bus stops can also be observed.


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3.1.3. Brief Description of the Stop Location

Figure �3-1 Asia Jaya Stop Location

Klang, Subang Airport and Shah Alam. An LRT station is also located on the intersection, it is one of the stations of the PUTRA LRT high frequency line linking the eastern and western suburbs of Kuala Lumpur and passing through the city centre. The LRT station is complemented with two feeder buses servicing the passengers of the LRT and the stage buses seeking to commute to the areas surrounding the stop and vice versa. The areas surrounding the stop have mixed land uses ranging from residential to industrial, commercial and institutional.

3.2. Data Collection

The data collection process took place at the study are during the month of September 2004.The secondary data was collected in first two weeks of the field work period through some of the Malaysian government organizations and transportation consultants. In the last two weeks the primary data were collected at the stop location and the buses selected. The next two subsections gives an overview of both the primary and the secondary data collected

3.2.1. Primary Data Collection

Passengers Questionnaire / Interview

With a group of six students from M.U.S.T a sample size of 150 passengers, 50 at AM Peak, 50 at PM Peak and 50 at Non-Peak Hours were interviewed using a preset questionnaire. Due to time limitations and lack of language skills the sample size was decided empirically as 150 passengers, this was found to be the minimum sample needed to understand and evaluate the passengers' movements at the stop. A number of 50 passengers were interviewed each time, 30 passengers on the stage bus stop and 20 passengers at the feeder bus stop. Because of the limited sample size, the results for the three periods were accumulated and analyzed. The questionnaire was conducted to measure the passengers transfer movement at the selected location, the regularity of their trips and to identify the routes between which the transfer movement takes place. More detailed information about the passenger's trips such as the average waiting time, their preference and the order of importance when it comes to bus

ASIA JAYA STOP

LOCATIO

Asia Jaya stop is located in Petaling Jaya municipal council, one of the municipalities of Klang Valley region. The stop is about 11 km away from the Kuala Lumpur central business district (KL CBD) on the intersection of the Federal Highway with Jalan Barat and Jalan Utara. The Federal Highway is one of the six major public transit corridors in the study area servicing the South-western part of the Klang Valley region. There are 12 stage bus routes passing Asia Jaya stop mostly originating from Kuala Lumpur city centre and heading to different destinations on the west and southwest periphery of the region such as


28

services, a stated preference survey comparing decreasing passenger's waiting time and increasing the fees was collected. The data collected from the questionnaire is used to identify the most suitable routes for the coordination study and to measure the percentage of transfer passengers to other types of passengers at the stop. The questionnaire results were accumulated for the three periods AM, PM and Non-Peak hours in order to strengthen the statistical correlations. Table �3-1 Data Survey Methds - Passengers Questionnare

Survey Method Advantages Disadvantages

Questionnaire/ Interview

1- Less time is needed 2-Cost-effective

Less detailed

Stop Monitoring

After conducting, the passengers’ survey three potential stage bus routes along with the two feeder buses servicing the stop were selected for the coordination study. The headway deviation of those bus routes at the stop was measured two times, one time at the AM Peak hour (7-10) AM and the other at PM Peak hour (5-8) PM. At the same time, the number of passengers boarding and alighting from the selected buses at the satiation was calculated. The results are used to estimate the overall passengers demand at the stop and the headway deviation of the selected buses at the stop. They are used for the current situation analysis and as an input for the optimization model.

GPS & APC Survey

A GPS survey was conducted for the selected bus routes. The movement of the selected buses were tracked along its routes from the origin to the destination and back again to the origin. The data extracted from the GPS survey is an (X, Y) coordinate and the average speed of the bus every thirty seconds for the entire bus trip. The survey was conducted three times for each of the selected bus routes at AM Peak Hour, PM Peak Hour and Non-Peak Hour. The Survey was also complemented with a manual APC survey from inside the bus by counting the number of passengers boarding and alighting the bus at each stop. Some of the results are used as input for the optimization model such as the average speed and the rest can be used to assist in developing the proposed APTS based methodology.

3.2.2. Secondary Data Collection

GIS Data

The following date were obtained from the ministry of federal Territory of Malaysia in GIS shape file format

• The road network of the entire Klang valley Region • The routes for the selected stage buses passing hotel armada stop • A hard copy of the selected feeder bus routes with its stops

The GIS data will be used to extract some information required as an input for the optimization model such as the routes length. Moreover, the data collected will be used for visualization as will as assisting the development of the proposed APTS based methodology.


29

Governmental Reports

Three governmental transportation studies carried out for the region were obtained; • JICA study (1999) on integrated urban transportation strategies for environmental

improvement in Kuala Lumpur. The study has some valuable related information on the problems of the public transportation system on the region, the passenger's movements around the region, the modal splits and the financial analysis of the public transport system.

• Special Task Force study (2003) on an integrated bus routing system on the Klang Valley. The study includes valuable related information on the problems of the bus systems in the region, the demand for both rail and bus transport in the region, some passengers surveys and Bus service characteristics in the region (e.g. frequencies, fleet size...)

• PADGLK study (2004) on integrated urban transportation systems on the Klang Valley region. The study includes valuable information on the public transport network on the region and passengers surveys on the current situation.

The data extracted from the studies will be used in the developing the optimization model and strategy and to back up any assumptions made about the study area.

3.3. Present Situation Analysis

A selection of the stage bus routes to be coordinated with the two feeder bus routes is made. The feasibility and desirability of such coordination depends on the variability of traffic conditions and stopping times, service frequencies, fractions of users involved on the transfers and relative costs of vehicle delays and user times (Lee and Schonfeld 1991). Accordingly and for the coordinated routes selection and current situation analysis, the following network and travel demand criteria were tested.

3.3.1. Network Analysis

Service Headway

As discussed in the second chapter the minimum service headway for a suitable coordination study is 13 minutes (Okrent 1974). Based on the secondary data collected (PTK 2004) it was found that all the stage buses operating on the stop have a service frequency of 20 to 30 minuets on peak hours and up to 45 minutes in non-peak hours. The feeder buses are also operating on a 30 minutes peak hour frequency and 45 minutes non-peak hour frequency. Thus, and as shown in table (3-2) a coordination study is suitable for any of stage buses with the two feeder buses servicing the stop. Table �3-2 Selected buses operating headway (Source PTK 2004)

Bus line Peak Hour

Headway (Min) Non Peak Hour Headway (Min)

13 30 45 47 25 45

338 25 45 904A 30 45 904B 30 45

Origins and destination

It can be clearly seen from figure (3-2) that the selected stage buses are covering areas in the outbound direction that are not accessible through the PUTRA LRT service available at the Asia Jaya


30

stop. This would make the selected stage buses the only available direct alternative for passengers seeking to commute from Asia Jaya to those areas and vice versa.

Figure �3-2 The Service Area of The Slected Bus Routes

Figure �3-3 Feeder Bus Route 904A & 904B (Source: PUTRA LRT)


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3.3.2. Transfer Demand Percentage

As expected the suitability of coordination study is also dependent on the passengers' volumes transferring between the routes to be coordinated. The higher the transfer passengers' volume between the routes the more suitable the coordination would be. The results of the passengers' questionnaire mentioned earlier (see 4.2.1.1) were used to estimate the percentage of passengers transferring between the stage and the feeder buses at the stop.

Stage Bus Stop Passengers Survey

It was found that the percentage of transferring passengers from the feeder buses to stage buses at the stage bus stop is 31% while the remaining 69% are passengers originated at the stop using other available modes of transport. It was also found that Stage buses number 13, 338 and 47 have the highest passengers demand with a percentage of 19 %, 11% and 11 % respectively.

Overall Stage Buses Passengers Demand

0.00%

5.00%

10.00%

15.00%

20.00%

4 13 10 99 33

337B 33

8

33D

337C 47 22

2 63

Bus Line

Pass. %

Figure �3-4 Overall Stage Bus Passengers Demand at Asia Jaya stop – Survey Results

Percentage Of Transfer Passengers

0%

20%

40%

60%

80%

100%

13 47 338

Bus Line

Pass. %Transfer

Non Transfer

Figure �3-5 Percentage of Transfer to Non Transfer

Passengers for Buses with The Highest Demand Moreover, and from the passengers survey it was also found that more than 90 % of the transfer passengers interviewed do the same trip on a daily basis.

The same three stage buses were found to have the highest passengers transfer demand from the feeder buses as well. The percentage of the transfer passengers waiting for each of the four routes is determined. Bus number 13 has 70 % of the passengers originating at the stop while 30% are transferring from feeder buses. Buses number 47 and 338 have 60 % of the passengers originating at the stop while 40 % are transferring from feeder buses. For buses number 13 and 338 the transfer passengers are split to 50% originating from feeder bus 904A and 50% originating from bus 904B. For bus number 47 the split is 75% to 25 %.


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Feeder Bus Stop Passengers Survey

The results of the passenger's survey at the feeder bus stop showed that 17% passengers are transferring from stag buses coming from Klang to Kuala Lumpur CBD direction while the remaining 83% are passengers transferring from the PUTRA LRT line. Among those 17% transfer passengers, the demand is split into 50% for each of the two feeders 904A and 904B. From the passengers survey it was also found that 90 % of the bus transfer passengers interviewed do the same trip on a daily basis.

3.4. Selected Routes Passenegrs' Demand Calculations

Based upon the survey results it was found that Stage bus routes number 13,338 and 47 have the highest transfer demand from the feeder buses in the outbound direction and vice versa in the inbound direction. It was also proved that those transfers are directional, from the feeder buses to the stage buses in the outbound direction and from the stage buses to the feeder buses in the inbound direction. The next step was to estimate the overall passengers demand for the stage and the feeder buses at Asia Jaya stop.

3.4.1. Stage Buses Passengers Demand

The selected stage buses were monitored in the outbound direction during the AM Peak Hours (7:00 - 10:00) and the PM Peak Hours (17:00 - 20:00). The number of passengers boarding the selected stage buses was calculated. Then the number is averaged for each of the selected buses to obtain the overall passengers' demand per hour. Table �3-3 Overall Selected Stage Bus Passengers Demand - Asia Jaya Stop

Bus line AM Passengers

Demand (Pass/hr) PM Passengers

Demand (Pass/hr)

13 34 40 47 28 32

338 30 34

Accordingly, the passengers transfer demand can be generated as a percentage from the overall demand based on the data collected in the passengers' survey (See 4.5.2.1) Table �3-4 Transfer Demand - Selected Stage Buses to Feeder Buses

Bus Line Transfer Demand

Percentage

AM Passengers Transfer

Demand(pass/hr)

PM Passengers Transfer

Demand(pass/hr) 904A 904B 904A 904B

13 30% 5 5 6 6 47 40% 9 3 9 4

338 40% 6 6 7 7


33

3.4.2. Feeder Buses Passengers Demand

The same calculations were also done for the two feeder buses at the feeder bus stop during the AM and the PM Peak hours. Then the number of boarding passengers was also averaged for each of the feeder buses to obtain the overall passengers' demand per hour. Table �3-5 Overall Passengers Demand for Feeder Buses – Asia Jaya Stop

Bus AM Passengers

Demand (Pass/hr) PM Passengers

Demand (Pass/hr) 904A 120 106 904B 116 96

The stages buses transfer passengers are also derived from the overall demand data and the passenger survey results. Table �3-6 Stage to Feeder Bus Transfer Demand

Bus

Stage Bus Transfer Demand

Percentage

AM Transfer Passengers Demand

(Pass/hr)

PM Transfer Passengers Demand

(Pass/hr)

904A 17% 21 18 904B 17% 20 17

It was assumed that the transfer demand percentage from the selected stage buses to the two feeder buses in the inbound direction is equal to the transfer demand percentage from the two feeder buses to the selected stage buses in the outbound direction. Accordingly, the selected stage to feeder buses demand was estimated (See. Table3.7) Table �3-7 Transfer Demand - Selected Stage Buses to Feeder Buses

Bus Line AM Passengers Transfer

Demand(pass/hr) PM Passengers Transfer

Demand(pass/hr)

13 47 338 13 47 338 904A 5 4 4 4 3 3 904B 4 3 3 3 3 3


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3.5. Headway Devation

Based upon the headway monitoring survey conducted at the stop it was found that the recorded headway deviation for the selected stage buses in the inbound direction is larger than that recorded in the outbound direction. This is mainly because the part of the route from the origin in the city centre to the stop is shorter in length than the rest of route. Also the buses terminate at the city centre in a control terminal and are being dispatched according to the schedule headway unlike the situation at the destination where buses doesn’t terminate and continue its route back to the city centre causing larger headway losses in the inbound direction. Figure (3-6) and (3-7) shows the recorded AM Peak headway deviations at Asia Jaya Stop for stage bus number 47 which is operating on a 25 minutes headway in both the inbound the outbound directions.

Headway Deviation - Bus 47 - AM Peak - Outbound Direction

20

22

24

26

28

30

N1 N2 N3 N4 N5 N6Sequence

Hea

dw

ay D

iff.(M

in)

Figure �3-6 Headway Deviation – Stage Bus 47 - PM Peak – Outbound Direction

Headway Deviation - Bus 47 - AM Peak - Inbound Direction

202224262830323436

N1 N2 N3 N4 N5 N6Sequence

Hea

dw

ay D

iff.(M

in)

Figure �3-7 Headway Deviation – Stage Bus 47 - PM Peak – Outbound and Inbound Direction

For the feeder buses, the recorded headway deviations at the stop were found to be close to the actual headway and less fluctuated. This is mainly because the feeder bus routes are much shorter than the stage bus routes and the traffic conditions inside the area surrounding the stop are much more stabilized and less congested. Figure (3-8) shows the recorded headway deviations at Asia Jaya Stop in the AM Peak hours for Feeder buses number 904A and 904B respectively. Both buses are operating in 30 minutes headway


35

Headway Deviation - Bus 904B - AM Peak

25

27

2931

33

35

N1 N2 N3 N4 N5 Sequence

Hea

dw

ay D

iff.

(Min

)

Figure �3-8 Headway deviation – Feeder Bus 904B - AM Peak

Headway Deviation - Bus 904A - AM Peak

2527

2931

3335

N1 N2 N3 N4 N5 Sequence

Hea

dw

ay D

iff.

(Min

)

Figure �3-9 Headway deviation – Feeder Buse 904A - AM Peak

Since the average headway is not a reliable measure for the variation, the standard deviation of the headway was calculated and the results are shown in table (3-7) and (3-8) for the selected stage and feeder buses respectively. It was found that the deviation is larger in the inbound direction than the outbound direction due to the route length and the termination reasons discussed above. Also the existing headway deviations for both the stage buses and the feeder buses is between 4.5 % and 14.8 % from the average headway at the stop as shown in table. This indicates the usefulness of the optimization study since the deviation of the headway from the average headway is not large enough (larger than 40 % - (Knoppers and Muller 1995)) to result in an optimal long transfer time which might not be cost effective for the operator. Although the deviation from the average headway is not so large but it can not be neglected making the synchronization study alone not sufficient and giving the room for the implementation of holding strategies to control the dispatching of the buses involved in the transfer operation at the transfer stop. Table �3-8 Headway Standard Deviation / Mean Headway - Selected Stage Buses - Asia Jaya Stop

Headway STD / Headway Mean

AM Peak (Hr)

Headway STD / Headway

Mean PM Peak (Hr)

Bus Line

Outbound Inbound Outbound Inbound

13 0.0279 / 0.5066 0.0767 / 0.52 0.263 / 0.5166 0.0431 / 0.5366


36

47 0.03861 / 0.4305 0.0534 / 0.444 0.036 / 0.427 0.0486 / 0.45

338 0.01948 / 0.4305 0.0560 / 0.4566 0.0272 / 0.411 0.0547 /0.4566

For the feeder buses, the average headway is much closer to the scheduled headway as shown in table (3-9). This should be reasonable since the route of the feeder buses covers the inner area surrounding the stop away from the high congestion levels of the Federal Highway and also because the routes lengths of the feeder buses are much shorter than those of the stage buses. Table �3-9 Headway Standard Deviation - Feeder Buses -Asia Jaya Stop

Headway STD / Headway Mean (Hr) Bus Line

AM Peak PM Peak

904A 0.03979 / 0.5033 0.0345 / 0.49

904B 0.048 / 0.5066 0.0302 / 0.506

3.6. Transfer Time Analysis

It is well recognized that transit riders have a negative perception of transfers because of their inconvenience and this is often referred to as a transfer penalty. Understanding what affects the transfer penalty can have significant implications for a transit authority. It can help identify which types of improvement to the system can most cost-effectively reduce this penalty, thus attracting new customers, and helping determine the value of improvements to key transfer facilities. It should also lead to potential improvement in ridership forecasting models (Guo and Wilson 2004). The transfer penalty is composed of many elements such as transfer waiting time, transfer walking time and transfer cost. It is also affected by some important factors such as the topography, the weather and the surrounding land use. Since the proposed research is concentrating on the management and the coordination of the selected routes to minimize the transfer time at Asia Jaya stop, the Analysis will pay attention to the time components of the transfer penalty only.

3.6.1. Passengers Transfer Times and Transfer Time Appreciation

Passengers Transfer Time

20%

60%

20%

Less than 15 Min

(15 -30) Min

Over 30 Min

Figure �3-10 Average transfer time at Asia Jaya Stop

In the same passengers survey conducted with passengers at the stop, passengers were asked to indicate their average waiting time at the stop. The results of the questionnaire were accumulated for transfer passengers since the waiting time for them at the stop is considered as the transfer time.The questionnaire results indicated that 60% of the passengers have waiting times of (15-30) minutes while the remaining 40% are split equally between over 30 minutes and less than 15 minutes. The results of the questionnaire are shown in figure (3-10)


37

Moreover, passengers were asked to state their preference while assessing the bus services. The quality service indicators used in the assessment are comfort, waiting time, in-vehicle time and fare. The results of the survey were also accumulated for the transfer passengers since the waiting for them is considered as the transfer time. The results of the questionnaire indicated that more than 60% of the passengers consider the transfer time as their first preference and more than 25% consider it as their second preference and around 5% consider it as their third preference. The questionnaire results shows that transfer time is most highly appreciated quality of service indicator among the passengers interviewed.

Passengers' Preference

0%

20%

40%

60%

80%

100%

1st 2nd 3rd 4th Preference

% P

asse

nger

s

Comfort

Fare

In- vehicleTimeTransfer Time

Figure �3-11 Bus Passengers Preference

3.6.2. Transfer Time Fluctuation

The transfer time between the selected stage and feeder buses at Asia Jaya stop was calculated in both the inbound and the outbound directions based on the recorded arrival times of the selected buses while monitoring the headways at the stop. The results shows that transfer times are unstable and fluctuating. This is can be explained, as the service is uncoordinated between the feeder and the stage buses. In addition, the operating headway of buses 338 and 47 is different from the operating headways of the feeder bus which would also contribute to the variation of the transfer time.

Transfer Time Fluctuaion - 904A & 47 - AM Peak - Outbound Direction

0

5

10

15

20

25

N1 N2 N3 N4 N5 N6Transfer No.

Tran

sfer

Tim

e (M

in)


38

Transfer Time Fluctuaion - 904A & 47 - AM Peak - Inbound Direction

0

5

10

15

20

25

30

N1 N2 N3 N4 N5 N6 N7

Transfer No.

Tran

sfer

Tim

e (M

in)

Figure �3-12 Transfer Time - 47 and 904A - AM Peak - Outbound and Inbound Direction

Transfer Time Fluctuaion - 904B & 47 - AM Peak - Outbound Direction

0

5

10

15

20

25

30

N1 N2 N3 N4 N5 N6Transfer No.

Tran

sfer

Tim

e (M

in)

Transfer Time Fluctuaion - 904B & 47 - AM Peak - Inbound Direction

0

5

10

15

20

25

30

N1 N2 N3 N4 N5 N6 N7

Transfer No.

Tran

sfer

Tim

e (M

in)

Figure �3-13 Transfer Time - 47 and 904B - AM Peak - Outbound and Inbound Direction

3.6.3. Value of Time

The value of time for bus passengers at the study area was derived based on Employment Household Income (monthly) in Study Area and bus system average occupancy rates (Source: Socio Economic Survey by Consultant Team, 1999 – See Appendix A). According to the study, the value of In-Vehicle time (In-Bus) was found to be equal to 3.33 RM/ hr (0.95 $/hr). The value of the waiting time and


39

transfer time is assumed equal to three times and twice the value of In-vehicle time respectively as discussed in the chapter 2 (See 2.2.3). Consequently, the value of waiting time is 10 RM/hr (2.85 $/hr) and the value of the transfer time is equal to 6.66 RM/hr (1.90 $/hr).

3.6.4. Transfer Time Losses

From the data collected while monitoring the performance of the selected routes at Asia Jaya stop in the AM and PM peak hours the arrival times of the three stage buses at the stop inbound and outbound direction were recorded as well as those for the two feeder buses. The transfer time from the two feeder buses to the three stage buses in the outbound direction was calculated from these recorded arrival times. In addition, the transfer time from the three stage buses in the inbound direction to the two feeder buses was calculated adding 10 minutes extra walking transfer penalty from the stage bus stop to the feeder bus stop. The results are accumulated for the AM peak Hours and the PM peak Hours to show the transfer time loss in minutes encountered by one passenger for all possible combination of transfer between the selected stage buses and the two feeder buses in the inbound and the outbound direction.

13 47 338

904-A904-B0

50

100

150

Time Lost (Min)

S. Bus line

F. Bus Line

Passengers Transfer Time Penalty AM PEAK - Inbound Direction

904-A

904-B

13 47 338904-A

0

50

100

Time Lost (Min)

S. Bus line

F. Bus Line

Passengers Transfer Time Penalty AM PEAK - Outbound Direction

904-A

904-B

Figure �3-14 Transfer Time Loss - Asia Jaya stop - AM Peak - Outbound Direction and Inbound Direction

13 47 338904-A

020406080

100120

Time Lost (Min)

S. Bus line

F. Bus Line

Passengers Transfer Time Penalty PM PEAK - Inbound Direction

904-A

904-B

13 47 338

904-A904-B0

20406080

100120

Time Lost (Min)

S. Bus line

F. Bus Line

Passengers Transfer Time Penalty PM Peak - Outbound Direction

904-A

904-B

Figure �3-15 Transfer Time Loss -Asia Jaya stop -PM Peak –Outbound and Inbound Direction


40

3.6.5. Transfer Time Financial Losses

The transfer time losses are then multiplied by the derived transfer demand and the value of passengers waiting time for the study area obtained from a consultant study (6.66 RM/hr) to translate the time losses into financial losses at the stop location. The average total transfer time financial losses during the AM & PM peaks added up to 600 (160 $) RM per Hour Per working day.

13 47 338

904A0100200300400500

Money Lost (RM)

S. Bus line

F. Bus Line

Transfer Time Financial Losses AM PEAK

904A

904B

13 47 338904A0

100200300400500

Money Lost (RM)

S. Bus line

F. Bus Line

Transfer Time Financial Losses PM PEAK

904A

904B

Figure �3-16 Transfer Time Financial Losses - Asia Jaya Stop -AM Peak & PM Peak

3.7. Conclusions

Based upon the conducted analysis it was found that passengers transfers between the feeder and the stage buses exists at Asia Jaya stop with 31% of the overall demand for the stage buses and 17% of the overall demand of the feeder buses. It was also found that the transfers between the feeder and the stage buses at Asia Jaya stop are directional. The transfers are from the feeder buses to the stage buses in the outbound direction and vice versa in the inbound direction. The stage buses with the highest transfer demand from the feeder buses in the outbound direction are bus lines number 13, 47 and 338. In the inbound direction the same situation exists by assuming that the highest transfer demand to the two feeder buses comes from stage buses 13, 47 and 338. In conclusion the daily working day financial losses emerging from the uncoordinated service between the stage and the feeder buses at the stop are 600 (160$) RM/hr during the AM and PM Peak hours. This is hourly financial losses resulting from uncoordinated transfers at one bus stop between three stage buses and two feeder buses only. For a bus network serving a metropolitan city like Kuala Lumpur if all beneficial transfers are coordinated a huge financial gain can be expected per hour which highlights the benefits of coordinated transfers


41


42

4. ASIA JAYA - OPTIMIZATION OF TRANSFER COORDINATION

This chapter aim is to obtain the optimal values of the transfer coordination problem (Headway and Slack times) following a mathematical optimization based approach. A 3-step procedure is followed to obtain the optimal values of the decision variables. Firstly, the optimal buses headways are determined without any coordination and compared to the current operating headways. Secondly, the optimal combination from the selected buses to be synchronized is also determined with its optimal operating headway. Thirdly, a method is suggested to obtain the optimal holding time added to the schedule of the coordinated buses to increase the probability of a successful connection. All three steps are conducted following an optimization procedure that minimizes both the passengers and the operators' costs at the stop. A sensitivity analysis is also conducted to measure the effect of the involved parameters on the optimal values of the optimization model decision variables. All the conducted analysis in this chapter is based on the data collected for the AM peak hours.

4.1. Problem Identification

In the previous chapter the passenger transfer time between the stage buses and the feeder buses at Asia Jaya stops were evaluated. The evaluation of the passengers transfer time was carried out for the stage buses with the highest demand for transfer to and from the feeder buses at the stop at both the AM and PM peak hours. The transfer time loses were converted into financial losses based on the available information on the value of passengers time and the bus operational costs in the study area. An optimization procedure is followed to determine the optimal values of the decision variables of the transfer coordination problem (Headways and Slack Times). The formulation of the optimization model objective function is based upon the minimization of the passengers and the operator costs. In that respect the costs considered in the optimization model are the time costs encountered by both the passengers (Waiting, Transfer and In-vehicle) and the Operator (route operational cost). The mathematical formulation of the both the passengers and the operator costs in this chapter is guided by the mathematical formulation used in Chowdhury (2000) and discussed in second chapter (See 2.5)

4.2. Model Assumptions

To simplify the mathematical formulation of the optimization model and to overcome the limitations of the data collection the following assumptions was made

1) The passengers demand for each of the selected stage buses is assumed uniform along the whole route and equal to the demand evaluated at Asia Jaya stop. This assumption can be relaxed by evaluating the passengers demand at each individual stop along the selected routes.

2) The passengers demand is assumed fixed and independent of the service quality. In reality the

passengers demand is dependent on the quality of transit service provided. The relationship between demand and service quality is expected to be positively reinforcing. The increase in passenger demand will cause service quality to deteriorate due to more highly variable


43

boarding and alighting activity. Bus routes characterized by poor service quality will likely suffer patronage declines over time or have difficulty attracting new riders because passengers are inconvenienced by unpredictable service. The overall effect is that the initial increase in demand due to increased service provision will be partially offset by a demand decrease due to adverse impacts on bus performance.(Kimpel 2001)

3) All the system parameters involved in the formulation of optimization model such as routes

length, value of passengers time, operating costs and average operating speeds are fixed and given or collected during the fieldwork duration.

4) The total travel time of passengers regarding a door-to-door trip is composed of Access time,

waiting time, in vehicle time, transfer time and egress time. Since the transport facilities such as the bus stops and the routes are considered fixed and given in the current study only the waiting time, transfer time and in vehicle time will be considered as the passengers travel time costs.

5) Buses arrivals at the stop are stochastic due to traffic conditions. A normal distribution of

buses arrival at the stop is used. The normal distribution of buses arrival has considerable theoretical and empirical support and permits numerical solutions (Lee and Schonfeld 1991). In reality and with an extensive data collection on the distribution of buses arrival an actual empirical distribution can be formulated to over come the unrealistic negative tail of the normal distribution.

6) Passenger's arrivals at the stop are random and the average waiting time is assumed equal one-

half of the headway. Although the service headway for all the selected buses are considerably high this assumption may, still no bus schedules are available for the stop.

7) Passengers transferring from the LRT to the feeder buses are not considered as transfer

passengers since the operating headway of the LRT service in the peak hours is around two minutes, which is too small, compared to the feeder buses headway proving that the coordination between the two services will not be of any value.

8) The optimization model has no constraints on buses capacity since the maximum utilization

ratio of buses operating on the Federal Highway is 77% which means that buses operating on that route are under utilized and there is no need for setting capacity constraints (PTK 2004).


44

4.3. Rationale of The Optimization Model

Figure �4-1 Stages of the Optimization Model

As shown in fig (4-1), in the first stage a total cost objective function is formulated that represents both the passengers costs (waiting time costs, transfer time costs and In-vehicle time costs) and the operator cost. The objective function is minimized for each one of the stage and the feeder buses independently. The optimal operating headway is obtained for each bus and the corresponding total costs. The optimal operating headway obtained is then compared with the existing operating headway. The financial gains resulting from the optimization are determined for each of the passengers and the operator costs components as will as for the total costs. In the second stage, a total cost objective function is formulated that represents both the passengers costs (waiting time costs, transfer time costs and In-vehicle time costs) and the operator cost. The objective function is minimized for all possible combinations of stage and feeder buses schedule synchronization. The optimal common headway for the coordinated group is obtained while the other uncoordinated buses are considered to be operating on the headways obtained from the first stage. The corresponding total costs are determined and compared with the existing total costs and the total costs obtained from the first stage. The financial gains are also obtained and the best group of buses for schedule synchronization is identified. In the third stage, the transfer is fully coordinated for the best group of buses obtained from the second stage. A total cost objective function is formulated that represents both the passengers costs (transfer time costs and In-vehicle time costs) and the operator cost. The objective function is minimized to determine the optimal slack times added to the schedule of the connected buses.


45

4.3.1. Transfer Direction

It was found in the last chapter that the transfers in the outbound direction is totally directional from the two feeder buses 904A and 904B to the three stage buses 13,338 and 47. In the inbound direction, the situation is exactly the opposite as transfers are from the stage buses 13,338 and 47 to the feeder buses 904A and 904B. Figure (4-2) shows a schematic representation of the direction of transfers in both the outbound and the inbound directions.

Figure �4-2 Passengers Transfer Movement at Asia Jaya Stop- Outbound and Inbound Directions


46

4.4. Demand Functions Formulation

The bus passengers' demand at Asia Jaya stop is the summation of the transfer demand between the stage and the feeder buses and the other forms of passengers demand originating at the stop. The demand is formulated for the stage and the feeder buses respectively in the following subsections.

4.4.1. Stage Bus Passengers Demand

The selected stage bus passengers' demand at Asia Jaya stop is the summation of the transfer demand from the selected feeder buses and the other passengers demand originating at the stop. As mentioned before the passengers demand at the stage bus stop will be calculated only for the outbound direction since the demand for the stage buses at the inbound direction is very small and can be neglected.

1

ikn

ijk ijok

ijD D D =

= +� (�4-1)

Dij Demand for stage bus (j) at stop (i) in the outbound direction Dijk Transfer Demand from feeder bus (k) to stage bus (j) at stop (i) Dijo Other passengers demand for stage bus (j) at stop (i) nik The number of connecting feeder buses (k) connecting at stop (i)

4.4.2. Feeder Bus Passengers Demand

The selected Feeder bus passengers' demand at Asia Jaya stop is the summation of the transfer demand from the selected stage buses and the demand from the LRT at the stop. Since the feeder bus routes are circular (no inbound and outbound directions), the passengers demand has only one direction

1

ijm

ikj iktj

ikD D D =

= +� (�4-2)

Dik Demand for feeder bus (k) at stop (i) Dikj Transfer Demand from stage bus (j) to feeder bus (k) at stop (i) Dikt Transfer Demand from LRT (t) to feeder bus (k) at stop (i) mij The number of connecting stage buses (j) connecting at stop (i)

4.5. Building Blocks of The Optimization Model

In the following subsections, the building blocks of the passengers and the operator costs are identified for each stage of coordination and its corresponding mathematical formulation in terms of the problem decision variables and parameters. The total cost objective function representing each stage is formulated as well.

Stage (1) – Headway Evaluation

In the first stage, the optimal operating headway for the selected stage and feeder buses is obtained based on the optimization model formulated for uncoordinated services. The results of the optimization procedure are evaluated and compared with the current operating headways. Figure (4-3) and (4-4) shows the steps followed in the optimization model and the structure of the passengers and the operator costs respectively.


47

Figure �4-3 Steps of the Optimization Model – Stage (1)

Figure �4-4 Total Cost Structure - Stage (1) i) Passengers Travel Time Costs Formulation

The passengers travel time costs are composed of the waiting, transfer and In-vehicle travel time costs. The Passengers travel time costs is formulated for the stage and the feeder buses respectively in the following subsections.

� Waiting Time Cost

The waiting time cost can be defined as the product of the average waiting time, passengers demand and the value of the passengers waiting time.


48

a) Stage Bus For the stage bus and since the passenger's arrivals at the stop are random, the average waiting time is considered one-half of the headway.

= wij ij ijo1CW H *D *U 2

(�4-3)

CWij Waiting time cost for stage bus (j) at stop (i) - (RM) Hij Headway of stage bus (j) at stop (i) - (hr) Dijo Other passenger demand for stage bus (j) at stop (i) - (Pass/hr) Uw Value of passengers waiting time - (RM) b) Feeder Bus For the feeder bus and since the passengers waiting at the feeder bus stop are mainly originating from the LRT service which follows a uniform pattern of passengers arrival to the stop the transfer time can be obtained using the formula of Weldings (1957).

( )= + ikt

ik ikwik

ik

H Var HCW *D *U

2 2 H[ ][ ][ ][ ] (�4-4)

CWik Waiting time cost for stage bus (k) at stop (i) - (RM) Hik Headway of stage bus (k) at stop (i) - (hr)

Var(H ik) The variance of the headway of stage bus (j) at stop (i) Dikt Transfer Demand from LRT (t) to feeder bus (k) at stop (i) - (Pass/hr)

Uw Value of passengers waiting time - (RM)

� Transfer Time Cost

The transfer time cost can be defined as the product of the average transfer time, transfer demand and the value of the passengers waiting time. In the case of uncoordinated service and assuming uniform pattern of transfer passengers’ arrivals at the stop, the transfer time can be obtained using the formula of Weldings (1957). a) Stage Bus

( ) ikNC

n

k=1

ij ijtijk ijk

ij

H Var HCT * D * U

2 2 H[ ][ ][ ][ ]= + � (�4-5)

NCijkCT Uncoordinated transfer time cost for stage bus (j) at stop (i) - (RM)

Hij Headway of stage bus (j) at stop (i) - (hr) Dijk Transfer Demand from feeder bus (k) to stage bus (j) at stop (i) - (Pass/hr) Ut Value of passengers Transfer time - (RM) Var(H ij) The variance of the headway of stage bus (j) at stop (i) b) Feeder Bus

( ) ijNC

m

j=1

ik iktikj ikj

ik

H Var HCT * D * U

2 2 H[ ][ ][ ][ ]= + � (�4-6)

NCikjCT Uncoordinated transfer time cost for stage bus (k) at stop (i) - (RM)

Hik Headway of stage bus (k) at stop (i) - (hr) Dijk Transfer Demand from feeder bus (j) to stage bus (k) at stop (i) - (Pass/hr)


49

Ut Value of passengers Transfer time - (RM) Var(H ik) The variance of the headway of stage bus (k) at stop (i)

� In-vehicle Time Costs

The In-vehicle time cost can be defined as the product of the average In-vehicle time, the corresponding passengers demand and the value of the passengers' In-vehicle time. The In-vehicle time is composed of the bus moving time and the bus dwelling time. The bus moving time is equal to the bus route length divided by the average operating speed. The bus dwelling time is equal to the product of the bus headway, the number of stops, the average boarding and alighting rate and the average time needed for the boarding/alighting of one passenger. The total in-vehicle time is divided by two to represent that each passenger will travel only half of the route length. a) Stage Bus Since the passengers’ demand is assumed uniform over the stage bus route then the average boarding and alighting rate is equal to the passengers demand at Asia Jaya stop (Dijo).

*[ ]* *ijj

vij ijj

12ij H *n*

L D D U SCV ΨΨΨΨ++++==== (�4-7)

CVij In-vehicle time cost for stage bus (j) at stop (i) - (RM) Lj The Length of stage bus route (j) - (Km) Hij Headway of stage bus (j) at stop (i) - (hr) Sj The average speed of stage bus (j) - (Km/hr) Dij Overall passenger demand for stage bus (j) at stop (i) - (Pass/hr) n The number of stops � The boarding/alighting time needed for one passenger - (hr) Uv Value of passengers in-vehicle time - (RM) b) Feeder Bus In the case of the feeder bus, the demand at Asia Jaya is much larger than the demand at other stops of the feeder bus routes mainly because of the passengers demand resulting from the LRT service. Consequently, the boarding and alighting rate cannot be assumed equal to the passengers demand at Asia Jaya stop. Instead, the boarding and alighting rate was recorded a number of times for each stop in the feeder bus routes during the GPS survey. The obtained boarding and alighting rate was averaged (qk) and used to determine the feeder bus dwelling time. The dwelling time at Asia Jaya Feeder bus stop is calculated separately as the product of the service headway, the overall passengers demand at the stop and the average time needed for the boarding/alighting of one passenger.

**[ ]* *ik ikk

vk ik ikk

1 *2ik H q *n* H

L D D U SCV Ψ + ΨΨ + ΨΨ + ΨΨ + Ψ++++==== (�4-8)

CVik In-vehicle time cost for stage bus (k) at stop (i) - (RM) Lk The Length of stage bus route (k) - (Km) Hik Headway of stage bus (k) at stop (i) - (hr) Sk The average speed of stage bus (k) - (Km/hr) qk The average boarding and alighting rate - (Pass/hr)


50

Dik Overall Passengers Demand to feeder bus (k) at stop (i) - (Pass/hr) n The number of stops � The boarding/alighting time needed for one passenger - (hr) Uv Value of passengers in-vehicle time - (RM)

ii) Operator Cost Formulation The bus operating costs is defined as the product of the fleet size and the bus operating cost. The fleet Size is the number of on-line vehicles required to provide service in the selected route, which is the total round-trip time divided by the service headway. The total round-trip time is composed of the moving time. The bus moving time is equal to the bus route length divided by the average operating speed. The bus dwelling time is equal to the product of the bus headway, the number of stops, the average boarding and alighting rate and the average time needed for the boarding/alighting of one passenger. The moving and dwelling time is formulated the same way as the in the formulation of the In-vehicle time cost.

a) Stage Bus

j j ij ij

ijb

( L / S ) H * D *n*H

NCij UCO [ ]*+ Ψ+ Ψ+ Ψ+ Ψ==== (�4-9)

NCijCO Operator cost for stage bus (j) – (RM)

Lj The Length of stage bus route (j) - (Km) Hij Headway of stage bus (j) at stop (i) - (hr) Sj The average speed of stage bus (j) - (Km/hr) Dij Overall Passengers Demand to feeder bus (k) at stop (i) - (Pass/hr) n The number of stops � The boarding/alighting time needed for one passenger - (hr) Ub Bus operation costs - (RM/hr)

b) Feeder Bus

k k ik k ik ik

ikb

( L / S ) H * q *n* H * D *H

NCik UCO [ ]*+ Ψ + Ψ+ Ψ + Ψ+ Ψ + Ψ+ Ψ + Ψ==== (�4-10)

NCikCO Operator cost for stage bus (j) – (RM)

Lk The Length of stage bus route (k) - (Km) Hik Headway of stage bus (k) at stop (i) - (hr) Sk The average speed of stage bus (k) - (Km/hr) qk The average boarding and alighting rate - (Pass/hr) Dik Overall Passengers Demand to feeder bus (k) at stop (i) - (Pass/hr) n The number of stops � The boarding/alighting time needed for one passenger - (hr) Ub Bus operation costs - (RM/hr)

iii) Total Cost Objective Function Formulation A total cost objective function is formulated that represents both the passengers' and the operators' costs. The decision variable of the objective function in case of the uncoordinated service is the


51

service headway, Hij in case of the stage bus and Hik in case of the feeder bus. The objective function is formulated and minimized once for each of the stage and feeder bus routes selected to obtain the optimal operating headway.

a) Stage Bus NC NC

ij ik

ij

ij

( ) ijk ijfor : i 1 , 1 j m , 1 k n

NCij ijH

Subject to : H 0

TC CW CT CV CO+ + ++ + ++ + ++ + +

≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤>>>>

==== (�4-11)

( )NCijTC H Total passengers and operator costs of bus route (j) at stop (i) under

uncoordinated service – (RM) CWij Waiting time cost for stage bus (j) at stop (i) - (RM) NC

ijCT Uncoordinated transfer time cost for stage bus (j) at stop (i) - (RM) CVij In-vehicle time cost for stage bus (j) at stop (i) - (RM)

NCijCO Operator cost for stage bus (j) – (RM)

b) Feeder Bus

NC NC

ik ij

ik

ik

( ) ikj ikfor : i 1 , 1 k n , 1 j m

NCik ikH

Subject to : H 0

TC CW CT CV CO+ + ++ + ++ + ++ + +

≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤>>>>

==== (�4-12)

( )N C

ikT C H Total passengers and operator costs of bus route (k) at stop (i) under

uncoordinated service – (RM) CWik Waiting time cost for stage bus (k) at stop (i) - (RM) NC

ikCT Uncoordinated transfer time cost for stage bus (k) at stop (i) - (RM) CVik In-vehicle time cost for stage bus (k) at stop (i) - (RM)

NCikCO Operator cost for stage bus (k) – (RM)


52

iv) Optimization Model Solution and Discussion of Results The first stage determines the optimal headway for each of the selected buses individually without any coordination. First, the results are discussed for each of the cost components involved in the total cost objective function formulation with respect to the optimization model decision variable (operating headway). Then the total cost objective function is discussed. Route 13 results are used for illustration of results.

Figure �4-5 The Headway - Passengers Cost Relationship

From figure (4-5), it can be clearly seen that the relationship between the operating headway (H) and the waiting time is strictly a linear relationship. The larger the operating headway the larger the passenger waiting time and consequently the waiting time financial cost will be larger. In case of the relationship between the service headway and the passengers, transfer cost the situation is different. It can be seen that for very short headways the transfer time cost is unexpectedly higher. This is ought to the fact that very short headways are normally associated with service irregularities that might result in values for the transfer time and consequently larger transfer time costs. With the increase of the service headway the transfer, time costs starts to decrease non-linearly until it reaches an optimal value then it starts to increase again linearly with the increase of the service headway.

The relationship between the in-vehicle time cost and the operating headway is strictly linear. The larger the headway the larger the number of passengers boarding and alighting the bus at each stop and consequently the larger the time the passengers have to spend inside the vehicle and the larger this will cost. The constant part represent the moving time, which is not a function of the headway.


53

Figure �4-6 The Headway-Operators Cost Relationship

For the operator cost, the relationship is a non-linear and inversely proportional relation. In figure (4-6) for very small headways and as expected, the operational costs are very high since the required fleet size for the operations will be large. Then with the increase of the operating headway the operators costs starts to decrease. The non linear relationships stems from the fact that although the headway increase will result in a fleet size decrease and lower operational cost, still with the increase of the headway the stoppage time will increase because of the higher passengers loads resulting in higher operational costs.

Figure �4-7 The Headway -Total Cost Relationship

Form the previous discussion of the various cost components involved in the formulation of the total cost objective function it can be seen that the passengers and the operators costs are conflicting. In


54

general, the passengers' costs are less with smaller headways and the operators costs are less with longer headways.

Figure (4-7) shows that the total costs starts to decrease non-linearly with the increase of the headway until it reaches an optimal value of the headway where its starts to increase again with any increase in the headway. In the first part of the curve and with the increase of the headway the total costs are decreasing, the decrease in the operators' costs is more influential in the total costs minimization. After reaching the optimal value of the headway and although the operators costs are still decreasing the passengers costs starts to be more influential in the total cost minimization process resulting in a linear increase in the total cost.

In conclusion, the results of the first stage shows that the current operating headways of the stage buses are near to the optimal values obtained from the optimization models for buses number 338 and 13. For bus number 47 the results show that the current operating headway is smaller than the optimal headway. This can be explained by the lower passenger demand and the high value of the headway variance at the stop. For the two feeder buses the optimization model results suggest to decrease the current operating headway, this also can be explained by the higher demand from the LRT station resulting in higher waiting and transfer passengers costs at the stop under the current situation.

In the first stage the optimal headway for the three selected stage buses and the two feeder buses serving Asia Jaya stop are optimized individually. The total cost function in that case is purely a function of the each route headway.

a) Stage Bus Taking the first derivate of the total cost objective function with respect to (Hij)and setting it equal to zero, the analytical relation for the headway of bus route (j) at stop (i) is obtained and shown in equation (4-13) and the results are shown in table (4-1).

j t ijk ij v ijo w b j ijk t j ij

ijk t j ij v j ijo w jij

1.414* (S *(2.*U*D +D ^2*n* *U +2.*D *U )*(2.*U *L +D *U*S *VarH )=

2.*D *U*S +D ^2*n* *U *S +2.*D *U *S H ΨΨΨΨ

ΨΨΨΨ (�4-13)

Table �4-1Optimal headway of stage buses - stage (1) Stage Bus 47 Stage Bus 13 Stage Bus 338

Dij 28 34 30 Dijk 12 10 12 Dijo 16 24 18

VarHij 0.001490741 0.000777778 0.00037963 Lj 56 53 48 Sj 22 25 30 � 0.001166667 0.001166667 0.001166667 n 84 88 96

Uw 10 10 10 Uv 3.33 3.33 3.33 Ut 6.66 6.66 6.66 Ub 26.4 30 24

Hij (hr) 0.60 0.50 0.42

( )N CijT C H (RM/hr) 354.22 418.03 301.88


55

b) Feeder Bus The same procedure is followed to obtain the feeder bus headway (Hik) using equation (4-14) and the results are shown in table (4-2).

k ikt w t ikj k v ik v ik b k ikj t k ik

ikikt w k ikj t k ik v k k ik v k

= S *(D *U +U*D +n*q *U*D * +2*U*D 2̂* )*(2*U*L +D *U*S *VarH )D *U *S +D *U*S + *D *U*S *q *n+2* *D 2̂*U*S )H Ψ Ψ

Ψ Ψ (�4-14)

Table �4-2 Optimal headway of feeder buses - stage (1)

904A 904B

Dik 120 116 Dikj 21 20 Dikt 99 96

VarHik 0.001583333 0.002305556 Lk 11.5 10 Sk 15 15 qk 10 12 � 0.001166667 0.001166667 n 24 16

Uw 10 10 Uv 3.33 3.33 Ut 6.66 6.66 Ub 25 25

Hik(hr) 0.172163802 0.167085038

ik( )N C HT C (RM/hr) 396.7271205 352.327279

Table (4-3) shows a comparison between the headways obtained from the optimization model with their corresponding total costs and the current operating headways with their corresponding total costs.

Table �4-3 Financial gains from resulting from stage (1)

Bus Headway

(Hr) Stage

Waiting Time Cost

(RM/hr)

Transfer Time Cost

(RM/hr)

In-vehicle Time Cost

(RM/hr)

Operator Costs

(RM/hr)

Total Costs (RM/hr)

0.42 Current Values 33.28 16.77 85.94 233.98 369.97

0.60 Stage (1) 48.38 24.26 98.01 183.57 354.22 47

Gain (RM) 15.75 0.50 Current Values 60.00 16.70 109.41 231.92 418.03 0.50 Stage (1) 60.28 16.78 109.64 231.32 418.03 13

Gain (RM) 0.00 0.42 Current Values 37.44 16.66 74.87 172.95 301.92 0.42 Stage (1) 38.14 16.97 75.52 171.25 301.89 338

Gain (RM) 0.03 0.17 Current Values 249.07 35.19 209.12 48.83 542.21 0.50 Stage (1) 89.77 12.68 172.44 121.83 396.73 904A

Gain (RM) 145.48 0.17 Current Values 242.21 33.61 176.53 42.32 494.67

0.50 Stage (1) 86.82 12.05 144.72 108.73 352.33 904B

Gain (RM/hr) 142.34

Total gain (RM/hr) 303.61


56

For the stage buses, 13 and 338 the headways (Hij) obtained from the optimization model are the same as the current operating headways. Consequently, the corresponding total costs are the same. For the stage bus 47 the headway obtained from the optimization model is smaller than the current operating headway resulting in lower total costs. This can be explained by one of two reasons. The first possible explanation is that the headways of the buses are determined by the operator in another way rather than using mathematical optimization of the passengers and the operator total costs. The second possible explanation is that although the operator might be using the same total cost optimization model to determine the operating headway still the results would be different since the current model assumes a fixed passenger's demand all over the bus routes equal to the passengers demand at Asia Jaya stop. Since the bus route headway should be designed on the maximum passengers demand, another stop on route 47 with higher passengers demand might exist resulting in a lower operating headway. For the feeder buses, 904A and 904B the headways (Hik) obtained from the optimization model are much smaller than the operating ones and hence the there is a larger gap in the total costs. This is mainly because of the high passengers' volumes coming from the high frequency LRT service available at Asia Jaya stop and waiting for the feeder buses and consequently resulting in a higher value of the waiting time cost. The large existing operating headways are ought to the limited fleet size of the feeder bus operator as explained in the TTF report (2004).

In conclusion, a total financial gain of approximately 300 RM/hr is obtained when comparing the total costs resulting from the optimization model of the five stage and feeder buses involved with thee existing total costs. Almost 90% of the financial gain is ought to the change of the headways of the two feeder buses at the stop.


57

Stage (2) – Headway Synchronization In the second stage, all possible combinations of schedule synchronization between the stage and the feeder buses at Asia Jaya stop are tested. The optimal common headway for the synchronized group is obtained and the corresponding total cost. The optimal headway and the corresponding total costs for the buses not involved in the synchronization process is obtained separately based on the results of stage (1).



58

Figure �4-9 Total Cost Structure - Stage (2)

i) Passengers Travel Time Costs Formulation The passengers travel time costs are composed of the waiting, transfer and In-vehicle travel time costs. The waiting time cost and the In-vehicle time as well as the operators cost will have the same formulation as in stage (1). The only cost component that differs after synchronization is the transfer time cost.

� Transfer Time Cost The transfer time cost can be defined as the product of the average transfer time, transfer demand and the value of the passengers transfer time. A normal distribution of buses arrival at the Asia Jaya stop is assumed to derive the transfer time value for both successful and missed connection under synchronized services. In the following subsections, the value of transfer time cost is derived for both stage and feeder buses respectively. In the case of synchronized services, the transfer time is calculated based on a joint normal probability density function of both pick up vehicle and delivery vehicle arrivals to the stop. Two types of transfer time exist under coordinated service depending on the stage and the feeder buses arrival time at the stop. The first type is the successful connection transfer time, which contains two possible scenarios depending on the time of arrival of both the stage and the feeder buses to the stop. The second type is the missed connection transfer time, which contains two possible scenarios depending also on the time of arrival of both the stage and the feeder buses to the stop. The following are the mathematical formulation of the transfer time for both the stage and the feeder buses under successful and the missed connection types.


59

Successful Connection � Scenario (1) The first scenario occurs when the delivery vehicle arrives before or at schedule and the pick up vehicle arrives after or on schedule. a) Stage Bus In figure (4-10), the first scenario shows that the delivery vehicle (feeder bus) on route (K) arrives before the scheduled time (area A) and the pick up vehicle (stage bus) on route (j) arrives on or after the scheduled time (area B). Therefore the delivery vehicle arrival time ranges between the common headway of the two vehicles (-H) to the scheduled time (0), while the pick up vehicle arrival time ranges between the scheduled time (0) to the common headway (H).

( ) ( )H

sijk ik ik ij ij

Hf t dt f t dtT

−� �= 0

1

0

(�4-15)

sijkT 1

b) Feeder Bus Similarly, and using figure (5-8) the same results can be obtained for the feeder bus.

( ) ( )H

sikj ij ij ik ik

Hf t dt f t dtT

−� �= 0

1

0

(�4-16)

sikjT 1

� Scenario (2) The second scenario occurs when both the delivery and the pick vehicles arrive after schedule but the delivery vehicle arrives first. a) Stage Bus In figure (4-10), the second scenario shows that the delivery vehicle (feeder bus) on route (K) arrives after the scheduled time (area E) and the pick up vehicle (stage bus) on route (j) arrives on or after the delivery vehicle arrives (area F). Therefore, the delivery vehicle arrival time ranges between the common headway of the two vehicles (0) to (tik), while the pick up vehicles arrival time ranges between the (tik) to the common headway (H).

( ) ( )ik

ik

t Hs2

ijk ik ik ij ijt

f t dt f t dtT � �=0

(�4-17)

s2ijkT


( ) ( )ij

ij

t Hs2

ikj ij ij ik ikt

f t dt f t dtT � �=0

(�4-18)

s2ikjT

Transfer time from feeder bus (k) to stage bus (j) at stop (i) under the first scenario – Outbound direction- (hr)

Transfer time from stage bus (j) to feeder bus (k) at stop (i) under the first scenario – Inbound direction - (hr)

Transfer time from feeder bus (k) to stage bus (j) at stop (i) under the second scenario – Outbound direction- (hr)

Transfer time from stage bus (j) to feeder bus (k) at stop (i) under the second scenario – Inbound direction - (hr)


60

Figure �4-10 Joint Probabilty of successful Connection – Stage 2 -Outbound Direction

Figure �4-11 Joint Probabilty of successful Connection – Stage 2 - Inbound Direction


61

Missed Connection � Scenario (3) The third scenario occurs when the delivery vehicle arrives after schedule and the pick up vehicle arrives before or on schedule. a) Stage Bus In figure (4-12), the second scenario shows that the delivery vehicle (feeder bus) on route (K) arrives after the scheduled time (area A) and the pick up vehicle (stage bus) on route (j) arrives before or on the scheduled time (area B). Therefore, the delivery vehicle arrival time ranges between the common headway of the two vehicles (-H) to the scheduled time (0), while the pick up vehicles arrival time ranges between the scheduled time (0) to the common headway (H).

*( ) ( )[ ]*H

mijk ik ik ij ij

Hf t dt f t dtT H

−� �= 0

1

0

(�4-19)

m

ijkT 1


*( ) ( )[ ]*H

mikj ij ij ik ik

Hf t dt f t dtT H

−� �= 0

1

0

(�4-20)

mikjT 1

� Scenario (4) The fourth scenario occurs both the delivery and the pick vehicles arrive after schedule but the pick up vehicle arrives first. a) Stage Bus In figure (4-12), the second scenario shows that the delivery vehicle (feeder bus) on route (K) arrives after the scheduled time (area A) and the pick up vehicle (stage bus) on route (j) arrives before or on the scheduled time (area B). Therefore, the delivery vehicle arrival time ranges between the common headway of the two vehicles (-H) to the scheduled time (0), while the pick up vehicle arrival time ranges between the scheduled time (0) to the common headway (H).

*( ) ( )[ ]*ij

ij

tHm

ijk ik ik ij ijt

f t dt f t dtT H� �=2

0

(�4-21)

mijkT 2


( ) ( )[ ]*ik

ik

H tm

ikj ij ij ik ikt

f t dt f t dtT H� �=2

0

(�4-22)

mikjT 2

Transfer time from feeder bus (k) to stage bus (j) at stop (i) under the third scenario – Outbound direction- (hr)

Transfer time from stage bus (j) to feeder bus (k) at stop (i) under the third scenario – Inbound direction- (hr)

Transfer time from stage bus (j) to feeder bus (k) at stop (i) under the fourth scenario – Inbound direction- (hr)

Transfer time from feeder bus (k) to stage bus (j) at stop (i) under the fourth scenario – Outbound direction- (hr)


62

Accordingly, the total transfer time is the summation of the transfer time calculated from the four generated scenarios. a) Stage Bus

( ) *ik ik

Cn n

s 1 s 2 m 1 m 2

k=1 k=1tijk ijk ijk ijk ijk ijkCT T T T T D * U = + + +� � (�4-23)

CijkCT

Dijk Transfer Demand from feeder bus (k) to stage bus (j) at stop (i). (Pass)

Ut Value of passengers Transfer time - (RM) b) Feeder Bus

( ) *ij ij

Cm m

s 1 s 2 m 1 m 2

j=1 j=1tikj ikj ikj ikj ikj ikjCT T T T T D * U = + + +� � (�4-24)

CikjCT

Dikj Transfer Demand from feeder bus (k) to stage bus (j) at stop (i). (Pass) Ut Value of passengers Transfer time - (RM)

Figure �4-12 Joint Probabilty of Missed Connection – Stage 2 - Inbound Direction

Transfer time cost from feeder bus (k) to stage bus (j) at station (i) in the outbound direction under synchronized service. (RM)

Transfer time cost from stage bus (j) to feeder bus (k) at station (i) in the inbound direction under synchronized service. (RM)


63

Figure �4-13 Joint Probabilty of successful Connection- Stage 2 - Inbound Direction

ii) Total Cost Objective Function Formulation A total cost objective function is formulated that represents both the passengers' and the operators' costs. The decision variable of the objective function in case of the synchronized service is the service common headway (H). The objective function is formulated and minimized for all possible combinations of schedule synchronization between the stage and the feeder buses at Asia Jaya stop. Exactly 21 combinations are possible for the synchronization of the three selected stage buses and the two feeder buses at Asia jaya stop. The corresponding total cost for the synchronized group is obtained from the objective function formulated in equation (4-25) while for the uncoordinated group the corresponding total costs are obtained based on the objective function formulated for first stage (see equation (4-11) and (4-12) for the stage and feeder buses respectively.

ij ik ijikC NC C NC

( ) ij ijk ij ij ik ikj ik ikk 1 j 1j 1 k 1

ij ik

C Hm n mn

( CW CT CV CO ) ( CW CT CV CO )

for : i 1 , 1 j m , 1 k nSubject to : H 0

TC ++++

= == == == == == == == =

+ + + + + ++ + + + + ++ + + + + ++ + + + + +

≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤>>>>

� �� ====� �� (�4-25)

( )C HTC

iii) Optimization Model Solution Because of the normal distribution probability density function introduced in the transfer time formulation of the second stage, the objective function formulated in not analytically tractable anymore. Instead, the objective function is minimized numerically using the built-in MatLab

Total passengers and operator costs of synchronized stage and feeder bus routes at stop (i) – (RM)


64

minimization function fminbnd. The function is Scalar bounded nonlinear minimization function. The algorithm of the function is based on golden Section search and parabolic interpolation. For the uncoordinated group the total costs and the operating headway are obtained based on the results of the first stage. Then the cost of the coordinated group is added to the cost of the uncoordinated group to obtain the final total costs. The results of the second stage are shown in table (4-4) It was found from the second stage results that the best group to be coordinated are buses 338 and 904B which results in the minimum total costs of 1923.88 RM/hr and a common headway of 0.25 hr. Compared to the results obtained from first stage under uncoordinated service (1823.4 RM/hr) which is less than the value obtained under coordinated service. This result implies that stage and feeder bus coordination at Asia Jaya stop is not a suitable solution under the same common headway. This is can be explained by the high passengers volumes (much larger than the bus transfer passengers) coming from the LRT service available at the stop and waiting for the feeder bus. Applying a common headway for the stage and the feeder bus at the stop through coordination will result in longer waiting time for those passengers since the optimal common headway is much larger than the optimal headway obtained for the feeder buses under uncoordinated services in stage (1) and consequently it will diminish any value of the coordination. If the results are compared with the total costs obtained under the existing situation (2126.79 RM/hr) we can still see from table (4-4) that not only the coordination between buses 338and 904B will result in a lower total costs but a few other coordination's as well. This can be explained by the fact that under the existing situation the feeder buses are operating in headways that is much larger than the optimal ones obtained in stage (1).


65

Table �4-4 Total Costs Under Coordinated Service (RM) - Stage (2)

Tota

l Cos

ts o

f Coo

rdin

ated

an

d U

ncoo

rdin

ated

gro

up

(RM

/hr)

2020

.93

1959

.95

2111

.81

2043

.55

1978

.18

2138

.51

1980

.35

1923

.88

2055

.65

2066

.21

2024

.95

2043

.45

1992

.81

1958

.65

1973

.95

2194

.79

2128

.72

2153

.43

2064

.93

1986

.33

2210

.60

Tota

l Cos

t of

Unc

oord

inat

ed

Gro

up (R

M/h

r)

1008

.43

1052

.83

656.

11

1072

.24

1116

.64

719.

91

1124

.58

1168

.98

772.

25

654.

21

706.

55

770.

35

698.

61

750.

95

814.

75

301.

89

354.

22

418.

03

352.

33

396.

73

Unc

oord

inat

ed

Gro

up

47&

338&

904B

47&

338&

904A

47&

338

13&

338&

904B

13&

338&

904A

13&

338

13&

47&

904B

13&

47&

904A

13&

47

338&

904B

47&

904B

13&

904B

338&

904A

47&

904A

13&

904A

338

47

13

904B

904A

Tota

l Cos

ts o

f C

oord

inat

ed

Gro

up (

RM

/hr)

1012

.50

907.

11

1455

.70

971.

31

861.

54

1418

.60

855.

78

754.

90

1283

.40

1412

.00

1318

.40

1273

.10

1294

.20

1207

.70

1159

.20

1892

.90

1774

.50

1735

.40

1712

.60

1589

.60

2210

.60

Com

mon

H

eadw

ay

(hr)

0.28

0.29

0.24

0.30

0.31

0.25

0.24

0.25

0.21

0.35

0.30

0.33

0.36

0.33

0.33

0.29

0.26

0.27

0.36

0.32

0.29

Coo

rdin

ated

Gro

up

13&

904A

13&

904B

13&

904A

&90

4B

47&

904A

47&

904B

47&

904A

&90

4B

338&

904A

338&

904B

338&

904A

&90

4B

13&

47&

904A

13&

338&

904A

338&

47&

904A

13&

47&

904B

13&

338&

904B

338&

47&

904B

13&

47&

904A

&90

4B

13&

338&

904A

&90

4B

338&

47&

904A

&90

4B

13&

47&

338&

904A

13&

47&

338&

904B

13&

47&

338&

904A

&90

4B

Itera

tion

1 2 3 4 5 6 7 8 9 10

11

12

13

14

15

16

17

18

19

20

21

OPTIMIZING BUS TRANSFER COORDINATION

67

Stage (3) – Full Coordination

In the third stage, a slack time is added to the schedule of the coordinated stage and feeder buses determined from the second stage. The optimal slack time for the each bus in the coordinated group is obtained and the corresponding total cost.


Figure �4-15 Total Cost Structure - Stage (3)


68

i) Passengers Travel Time Costs Formulation The passengers travel time costs are composed of the waiting, transfer and In-vehicle travel time costs. The waiting time is formulated in the same way as stage (1). The other Passengers travel time costs are formulated in the following subsections

� Transfer Time Cost In the case of coordinated services the transfer time is calculated based on a joint normal probability density function of both stage (pick up vehicle) and feeder bus (delivery vehicle) arrivals at the stop. Two types of transfer time exist under coordinated service depending on the stage and the feeder buses arrival time at the stop. The first type is the successful connection transfer time, which contains three possible scenarios depending on the time of arrival of both the stage and the feeder buses to the stop. The second type is the missed connection transfer time, which contains two possible scenarios depending also on the time of arrival of both the stage and the feeder buses to the stop. The following are the mathematical formulation of the transfer time for both the stage and the feeder buses under successful and the missed connection types. Successful Connection � Scenario (1) In the first scenario, the transfer time is equal to the slack time (a) added to the schedule of the stage bus to increase the probability of a successful connection. a) Stage Bus

13ijk a T = (�4-26)

13ijkT

a

b) Feeder Bus Similarly for the feeder bus, the transfer time is equal to the slack time (b) added its schedule to increase the probability of a successful connection.

13ikj b T = (�4-27)

13ikjT

b

� Scenario (2) In the second scenario, the delivery vehicle arrives on or before its schedule and the pick up vehicle arrives after its schedule. a) Stage Bus In figure (4-16), the first scenario shows that the delivery vehicle (feeder bus) on route (K) arrives before the scheduled time (area A) and the pick up vehicle (stage bus) on route (j) arrives after the scheduled time (area B). Therefore the delivery vehicle arrival time ranges between the common headway of the two vehicles (-H) to the slack time

Transfer time from feeder bus (k) to stage bus (j) at stop (i) under the first scenario- Stage 3 - Outbound direction- (hr) Slack time added to the schedule of stage bus (j) at stop (i) in the outbound direction. (hr)

Transfer time from stage bus (j) to feeder bus (k) at stop (i) under the first scenario- Stage 3 - Inbound direction- (hr) Slack time added to the schedule of feeder bus (k) at stop (i) in the inbound direction. (hr)


69

added to the schedule of the pick up vehicle (a), while the pick up vehicles arrival time ranges between the slack time added to its schedule (a) to the common headway (H).

( ) ( )a H

23ijk ik ik ij ij

H af t dt f t dtT

−� �= (�4-28)

23ijkT


( ) ( )b H

23ikj ij ij ik ik

H bf t dt f t dtT

−� �= (�4-29)

23ikjT

� Scenario (3) In the third scenario, both the delivery and the pick up buses arrive after schedule but the feeder bus arrives before the stage bus. In figure (4-15), the second scenario shows that the delivery vehicle (feeder bus) on route (K) (area C) arrives before the pick up vehicle (stage bus) on route (j) (area D). Therefore, the delivery vehicle arrival time ranges from (a) to the common headway (H) and the pick up vehicle arrival time ranges between the delivery vehicle arrival times (tik) to the common headway (H) a) Stage Bus

( ) ( )ik

H H

ijk ik ik ij ija t

f t d t f t d tT � �=33 (�4-30)

ijkT 33


( ) ( )ij

H Hs

ikj ij ij ik ikb t

f t d t f t d tT � �=33 (�4-31)

ikjT 33

Transfer time from feeder bus (k) to stage bus (j) at stop (i) under the second scenario- Stage 3 - Outbound direction- (hr)

Transfer time from stage bus (j) to feeder bus (k) at stop (i) under the second scenario- Stage 3 - Inbound direction- (hr)

Transfer time from feeder bus (k) to stage bus (j) at stop (i) under the third scenario- Stage 3 - Outbound direction- (hr)

Transfer time from stage bus (j) to feeder bus (k) at stop (i) under the third scenario- Stage 3 - Inbound direction- (hr)


70

Figure �4-16 Joint Probabilty of successful Connection - Stage 3 - Outbound Direction

(Based on Chowdhury 2000)

Figure �4-17 Joint Probabilty of successful Connection –Stage 3 - Inbound Direction



71

Missed Connection � Scenario (4)

In the fourth scenario, the pick up vehicle arrives before or in schedule and the delivery vehicle arrives after the end of the slack time of the pick up vehicle.

a) Stage Bus In figure (4-18), the third scenario shows that the pickup vehicle arrives early or in schedule (area E) and the delivery vehicle arrives late (area F). Under this situation the pick up vehicle ranges between (-H) to (b) and the delivery vehicle ranges between (b) to (H).

( ) ( )H a

43ijk ik ik ij ij

a Hf t dt f t dt HT

−

� �� = (�4-32)

43ijkT


( ) ( )H b

43ikj ij ij ik ik

b Hf t dt f t dt HT

−

� �� = (�4-33)

43ikjT

� Scenario (5) In the Fifth scenario, both the delivery vehicle and the pick up vehicle arrive after the slack time of the pick up vehicle has ended but the delivery bus arrives after the pick up vehicle.

a) Stage Bus In figure (4-18) the fourth scenario shows that both vehicles arrives late but the pick up vehicle arrives first (area G) and the delivery vehicle arrives later (area H). Under this situation the pick up vehicle ranges between (a) to (tik) and the delivery vehicle ranges between (tik) to (H)

ik

ik

tH53

ijk ik ik ij ijat

f ( t )d t f ( t )d t HT� �� ==== ( �4-34)

53ijkT


ij

ij

tH53

ikj ij ij ik ikbt

f ( t )dt f ( t )dt HT� ��

� �� ==== (�4-35)

53ikjT

Transfer time from feeder bus (k) to stage bus (j) at stop (i) under the fourth scenario- Stage 3 - Outbound direction- (hr)

Transfer time from stage bus (j) to feeder bus (k) at stop (i) under the fourth scenario- Stage 3 - Inbound direction- (hr)

Transfer time from feeder bus (k) to stage bus (j) at stop (i) under the fifth scenario- Stage 3 - Outbound direction- (hr)

Transfer time from stage bus (j) to feeder bus (k) at stop (i) under the fifth scenario- Stage 3 - Inbound direction- (hr)


72

Figure �4-18 Joint Probabilty of Missed Connection – Stage 3- Outbound Direction


Figure �4-19 Joint Probabilty of Missed Connection – Stage 3 - Inbound Direction –



73

Hence, the transfer time cost under full coordination can be derived as the summation of the transfer time under the above mentioned scenarios five scenarios, the transfer demand and the value of passengers transfer time. a) Stage Bus

( ) *FCtijk ijk

13 23 33 43 53ijk ijk ijk ijk ijk+ + + D * UC T T T T T T= + ( �4-36)

FC

ijkCT

Dijk Transfer Demand from stage bus (j) to feeder bus (k) at stop (i). (Pass) Ut Value of passengers Transfer time - (RM)

b) Feeder Bus

( ) *FCtik j ik j

13 2 3 3 3 43 53ik j ik j ik j ik j ik j+ + + D * UC T T T T T T= + ( �4-37)

FCikjCT

Dijk Transfer Demand from stage bus (j) to feeder bus (k) at stop (i). (Pass) Ut Value of passengers Transfer time - (RM)

� In-vehicle Time Cost

The In-vehicle time cost is derived in the same way as stage (1).The only difference is adding the slack time (a) added to the schedule of the stage bus (j) at stop (i) to the In-vehicle time encountered by the In-vehicle passengers while travelling. Similarly, the In-vehicle time cost of the feeder bus passengers can be derived. a) Stage Bus

F Cij

jvij ij

j

12ij H * n * a

L D D U SC V Ψ +Ψ +Ψ +Ψ +++++==== *[ ]* * (�4-38)

FC

ijCV

Lj The Length of stage bus route (j) - (Km) Hij Headway of stage bus (j) at stop (i) - (hr) Sj The average speed of stage bus (j) - (Km/hr) Dij Overall passenger demand for stage bus (j) at stop (i) - (Pass/hr) n The number of stops � The boarding/alighting time needed for one passenger - (hr)

a Slack time added to the schedule of stage bus (j) at stop (i) in the Outbound direction. (hr)

Uv Value of passengers in-vehicle time - (RM)

b) Feeder Bus

Transfer time cost from feeder bus (k) to stage bus (j) at station (i) in the outbound direction under fully coordinated service. (RM)

Transfer time cost from stage bus (j) to feeder bus (k) at station (i) in the inbound direction under fully coordinated service. (RM)

In-vehicle time cost for stage bus (k) at stop (i) under fully coordinated services - (RM)


74

FCik ik

kvk ik ik

k

1*

2ik H q *n* H bL D D U SCV Ψ + Ψ +Ψ + Ψ +Ψ + Ψ +Ψ + Ψ +++++==== **[ ]* * (�4-39)

FC

ikCV

Lk The Length of stage bus route (k) - (Km) Hik Headway of stage bus (k) at stop (i) - (hr) Sk The average speed of stage bus (k) - (Km/hr) qk The average boarding and alighting rate - (Pass/hr) Dik Overall Passengers Demand to feeder bus (k) at stop (i) - (Pass/hr) n The number of stops � The boarding/alighting time needed for one passenger - (hr)

b Slack time added to the schedule of feeder bus (k) at stop (i) in the outbound direction. (hr)

Uv Value of passengers in-vehicle time - (RM) ii) Operator Cost Formulation

The operator cost is derived also the same way as stage (1).The only difference is adding the slack time (a) added to the schedule of the stage bus (j) at stop (i) to the total trip time. Similarly, the Operator cost of the feeder bus can be derived.

a) Stage Bus

j j ij ijFC

ijb

( L / S ) H * D *n* aHij UCO [ ]*+ Ψ ++ Ψ ++ Ψ ++ Ψ +==== (�4-40)

F C

ijC O Operator cost for stage bus (j) under fully coordinated service – (RM)

Lj The Length of stage bus route (j) - (Km) Hij Headway of stage bus (j) at stop (i) - (hr) Sj The average speed of stage bus (j) - (Km/hr) Dij Overall Passengers Demand to feeder bus (k) at stop (i) - (Pass/hr) n The number of stops � The boarding/alighting time needed for one passenger - (hr)

a Slack time added to the schedule of stage bus (j) at stop (i) in the outbound direction. (hr)

Ub Bus operation costs - (RM/hr) b) Feeder Bus

FC k k ik k ik ik

ikb

( L / S ) H * q *n* H * D * bHik UCO [ ]*+ Ψ + Ψ ++ Ψ + Ψ ++ Ψ + Ψ ++ Ψ + Ψ +==== (�4-41)

F C

i kC O Operator cost for feeder bus (k) under fully coordinated service – (RM)

Lk The Length of stage bus route (k) - (Km) Hik Headway of stage bus (k) at stop (i) - (hr) Sk The average speed of stage bus (k) - (Km/hr) qk The average boarding and alighting rate - (Pass/hr) Dik Overall Passengers Demand to feeder bus (k) at stop (i) - (Pass/hr) n The number of stops � The boarding/alighting time needed for one passenger - (hr)

b Slack time added to the schedule of feeder bus (k) at stop (i) in the

In-vehicle time cost for stage bus (j) at stop (i) under fully coordinated services - (RM)


75

outbound direction. (hr) Ub Bus operation costs - (RM/hr)

iii) Total Costs Objective Function Formulation A total cost objective function is formulated that represents both the passengers' and the operators' costs. The decision variable of the objective function in case of the fully coordinated service is the slack time added to the schedule of the coordinated bus. The objective function is formulated and minimized to obtain the slack time added to the schedule of the stage bus to wait for the feeder bus in the outbound direction and vice versa in the inbound direction

a) Stage Bus F C F C F C F C

ij ik

( a ) i j k ijfo r : i 1 , 1 j m , 1 k n

i j i j

S u b j e c t t o : 0a

T C C W C T C V C O+ + ++ + ++ + ++ + +

≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤>>>>

==== (�4-42)

FC( a)TC

b) Feeder Bus

FC FC FC FC

ik ij

( b ) ik j ikfor : i 1 , 1 k n , 1 j m

ik ik

S u b j ect t o : b 0

T C C W C T C V C O+ + ++ + ++ + ++ + +

≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤≥ ≤ ≤ ≤ ≤>>>>

==== (�4-43)

FC ( b )TC

iv) Optimization Model Solution The total cost objective function for the third stage is also optimized numerically using the same non linear minimization function fminbnd. The optimization procedure is carried out for each of the coordinated buses individually, once for each pair of coordinated buses. The results shows that both the slack time added to the schedule of bus number 338 to wait for bus 904B in the outbound direction (a) and the slack time added to the schedule of bus 904B to wait for bus 338 in the inbound direction (b) tends to be equal to zero. This is mainly ought to the small volume of transfer passengers when compared to the other passengers volumes involved in the optimization procedure

4.6. Conclusions

In this chapter a 3 stage optimization model was formulated to obtain the optimal value of the decision variables (Headway & Slack time) of the transfer coordination problem. The first stage aimed at evaluating the existing operating headways of the selected buses, it was found that the stage buses are operating on headways almost similar to those obtained from the optimization model and consequently there was almost no gain in the total costs from the optimization process. On the other hand it was found that the feeder buses are operating on headways much larger than the optimum ones and consequently a large financial gain will be achieved (292 RM/hr) if the operating headways are shifted to the optimum ones.

Total passengers and operator costs of fully coordinated service for stage bus (j) at stop (i) – (RM)

Total passengers and operator costs of fully coordinated service for feeder bus (k) at stop (i) – (RM)


76

The second stage aimed at testing and evaluating the financial benefits of coordinating the service of the selected stage and feeder buses at Asia Jaya stop through schedule synchronization by imposing a common headway in the coordinated group. It was found that the coordination is not suitable when compared with the total costs obtained from the first stage because of the high passengers' volumes coming from the LRT service and waiting for the feeder buses which implies a higher frequency. When compared to the total costs under the current existing situation it was found that the best group to be coordinated are buses 338 and 904B. The third stage aimed at estimating the optimal slack time to be added to the schedule of the coordinated buses 338 and 904B at Asia Jaya stop to increase the probability of a successful connection the stop. It was found that the slack time added to both schedules tends to be equal to zero. This was explained by the relatively small volume of transfer passengers when compared with the other volumes involved in the optimization procedure. Finally it can be concluded based on the results of the optimization model that coordination between the stage and the feeder buses at Asia Jaya stop through a common headway is not an attractive solution if the feeder bus company have no constraints on the fleet size and can operate its fleet according to the optimum headways obtained from stage (1). Instead other sorts of coordination can be tested and evaluated such as operating the stage buses on double or three times the operating headway of the feeder buses to avoid the large waiting time encountered by the LRT passengers at the stop in the case of coordinated service under a common headway. In case of fleet size constraints that forces the feeder bus operator to keep operating its fleet on the same headways, a number of coordinated groups was found to result in a lower total costs than the existing one. See table (4-4). Adding a slack time to the schedule of the connecting vehicle is not a suitable solution under the relatively small transfer passengers' volume.


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5. APTS Provision – Potential Role in the Transfer Coordination Problem

In the previous chapter optimal combination of stage-feeder bus coordination at Asia Jaya stop was found with the common operating headway and slack times added to the schedule to increase the probability of a successful connection (See 4.5). The main shortcoming of such a model that it will be implemented blindly and based upon the average data collected for a period of time about the transfer passengers demand volumes and the pattern of arrivals of the connecting buses to the stop. In other words, the bus drivers of the connecting vehicles do not communicate during their trip to coordinate their arrivals to the transfer stop. Also if one of the bus drivers arrives first to the stop, he has to wait for the static period of the slack time added to the bus schedule to wait for the other connecting bus without having any idea whether it will arrive during the slack time or even if there are any passengers seeking this connection. The discussion in chapter 2 established that the deployment of APTS fleet management technologies in general and specifically GPS, APC, GIS and communication system can play an important role in overcoming this shortcoming and making the system more dynamic and demand responsive (See2.3). This chapter aims at exploring and emphasising the potential role of those specific APTS fleet management technologies can play to improve the handling of the transfer coordination problem in the real-time context. It starts with a description of the real-time data output from the GPS and APC technologies and the fixed route data available in the GIS format, the description is supported by data available from the conducted fieldwork. A brief discussion on how these real-time data can be integrated with the other fixed route data available on the bus network under a GIS platform is conducted in the third section. Finally, possible real-time and long run improvements to the way the transfer coordination problem is handled under the deployment of the technology is discussed and emphasised.

5.1. Technology Data Output

A number of APTS fleet management technologies were discussed in the second chapter (see 2.3). These technologies can play a significant role in enhancing the efficiency of coordinated bus transfers in the real-time context. In the next two subsections, the data output from the GPS and APC technologies are discussed. GPS and APC technologies are of most important with respect to the transfer coordination problem as they provide the transit agency with the real-time data on the passengers' buses location and corresponding passengers demand. The discussion is supported by samples of the data collected at the fieldwork from the study area for the selected buses.

5.1.1. GPS Data Output

GPS receiver provides the transit agency with real-time bus position information in the form of latitude and longitude on the surface of the earth. The position data collected from the GPS on the buses location can be directly transformed to any local coordinated system. Differential GPS can be used to enhance positional accuracy to about ±5 m (with 95% confidence) under almost all conditions (Taylor et al 2000). In addition to the data on the latitude and longitude the GPS provides data on the date, the exact time the location was recorded, the accumulative distance travelled since the start of


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the trip, the accumulative time since the start of the trip and the instantaneous speed at the time the coordinate was recorded. In the present research and since buses at the study area is not equipped with GPSs; a number of GPS units were used from inside the bus instead to track the movement of the selected buses while traversing their routes. Unfortunately, the accuracy of the collected data could not be enhanced through a DGPS since the data is collected through stand-alone GPSs. Table (5-1) shows a sample from the GPS data collected from bus route 13 at the AM Peak hour Table �5-1GPS survey – Bus 13 – AM Peak

ID EASTING NORTHING DATE TIME Accumulative

Time(Sec) Accumulative Distance(m)

SPEED (m/sec)

1 799912 348057 10/4/2004 7:20:18 AM 0 0 0 2 799914 348061 10/4/2004 7:20:49 AM 31 4 0.1 3 799905 348062 10/4/2004 7:21:19 AM 61 13 0.3 4 799889 348056 10/4/2004 7:21:49 AM 91 31 0.6 5 799808 348044 10/4/2004 7:22:20 AM 122 112 2.6 6 799721 347904 10/4/2004 7:22:51 AM 153 277 5.3 7 799721 347768 10/4/2004 7:23:21 AM 183 414 4.6 8 799717 347772 10/4/2004 7:23:51 AM 213 419 0.2 9 799650 347755 10/4/2004 7:24:21 AM 243 489 2.3 10 799605 347741 10/4/2004 7:24:52 AM 274 536 1.5 11 799608 347720 10/4/2004 7:25:22 AM 304 557 0.7 12 799587 347586 10/4/2004 7:25:53 AM 335 692 4.4 13 799605 347508 10/4/2004 7:26:24 AM 366 773 2.6 14 799569 347346 10/4/2004 7:26:55 AM 397 939 5.4 15 799568 347068 10/4/2004 7:27:26 AM 428 1216 9 16 799508 346733 10/4/2004 7:27:57 AM 459 1557 11 17 799252 346579 10/4/2004 7:28:28 AM 490 1855 9.6 18 799136 346338 10/4/2004 7:28:58 AM 520 2123 8.9 19 799050 346180 10/4/2004 7:29:29 AM 551 2302 5.8 20 798785 345986 10/4/2004 7:30:00 AM 582 2631 10.6

5.1.2. APC Data Output

When passengers' activity occurs, the APCs count the total number of boarding and alighting passengers, which are then recorded in two separate fields. The APCs should be installed at both the front and the rear doors and is activated only if the doors are open. Having the data on both the passengers boarding and alighting the bus, the real-time In-vehicle passengers' demand can be continuously calculated. As for the transfer passengers demand and as explained by Dessouky (1999), it can only be counted accurately if passengers register their destination, either directly (e.g. a mobile data terminal accessible to passengers) or indirectly (the driver asks passengers where they are going, and registers this information for them). In the present research and since buses at the study area are not equipped with APCs, manual passengers counting survey was conducted from inside each of the selected buses while they are traversing their routes. Unfortunately, data on the transferring passengers could not be collected


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because of high passengers' volumes and passengers not welling to cooperate. Table (5-2) shows a sample from the manual passengers counting survey conducted on stage bus 13 at the AM peak hour Table �5-2 Manual Passengers Counting - Bus 13 - AM Peak

Stop ID No Of Passengers

Boarding No of passengers

Alighting Net No of Passengers

on Board 1 38 38 2 4 42 3 2 44 4 1 45 5 4 49 6 4 53 7 1 1 53 8 5 1 57 9 2 1 58

10 4 2 60 11 1 2 59 12 1 60 13 1 61 14 1 60 15 4 17 47 16 1 8 40 17 1 39

5.1.3. GIS Data

As previously mentioned in second chapter (Se 2.3), GIS provides significant improvement in the ability to see and understand an entire fixed route transit system. In conventional models of public transport systems each transit line is typically represented by a set of links between stops that that particular line visits (Ortuzar 1994). Figure (5-1) gives a simple illustration of this representation where two bus lines 1 and 2 serves seven stops in all. Line 1 starts at A, ends at E and visits the stops B, C and D. Line 2 starts at I, ends at H and also visits the stops B, C and D. The representation is not directed, each line on the figure and accordingly in the model represents both directions of that line. To represent the two transit lines in the figure, eight links are needed in the model.

Figure �5-1 Traditional way of modeling public transport in a transport mode (Source: Thorlacius 1998)


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Individual stop locations can be identified by means of point coordinates of the same coordinate system used for the base street network (Figure 5.2). The coordinates can be acquired through digitizing existing stop maps, on-screen designing or an automatic data collection device such as GPS. Those stops and links have feature attributes attached to it in a relational database;

� Link (Link ID, from stop, to stop, length, Average Speed,…) � Stop (Stop ID, stop name, X coordinate, Y Coordinate…)

In conclusion, a conventional public transit GIS model should be able to provide the fixed route spatial data in the form of links and stops data, this data can be linked to any with any other data such as average speeds and traffic volumes through a relational data base. The next section describes briefly how can the output data from the GPS and APC data be integrated with links and stops data to make use of the analytical capabilities of the GIS.

5.2. GPS and APC Output Data Integration within a GIS Platfom

As discussed in (5.1.1) the main data out put from the GPS is giving the bus location (x, y) with a time stamp and its average speed while traversing its route every fixed time interval. As expected and shown in figure (5-3) the coordinated measured by the GPS will not coincide exactly over the fixed bus route data available in the GIS format.

Figure �5-2 GPS data collected for stage bus 13 - AM Peak

To be able to know the bus location and its expected time of arrival at the transfer stop, the coordinate data collected through the GPS should be firstly related to the GIS fixed route data. Linear referencing Systems (LRS) are used to achieve this task. A linear referencing method is a mechanism for finding and stating the location of an unknown point along a network by referencing it to a known point (Vohderobe et al 1997). The known point in this case is the nearest ahead or before bus stop. Linear referencing systems LRS supports the storage and the maintenance of information on events that occur within a transportation network. An event object represent an occurrence that takes place in an instant or over a period of time that changes the state of a transportation feature ( after Fletcher et al.1995). A LRS typically consists of a transportation network, a location referencing method (LRM), and a datum. The LRM determines an unknown location within the transportation network using a defined path and an offset distance along the path from some known location. This provides the basis for maintaining event data within the network. The datum is a set of objects with known (directly


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measured) geo-referenced locations, which ties the LRS to the real world. When locating the GPS point data collected along routes, the route and measure information of each point feature is computed and written to a point event table. To be located successfully, the features must be located on or within a specified radius tolerance of the routes. The specified tolerance will depend on the accuracy of the GPS equipment used, the higher the accuracy the lower the tolerance needed. As shown in figure (5-4), the GPS equipment in the bus transmits its position, speed and other related information to the control centre by some means of data communication. The point N (Xi, Yi) is the actual position of the bus. Using the above-mentioned tolerance function, the point N is projected to the nearest link on the bus network between stops S1(X1, Y1) and S2 (X2, Y2) and exactly on the point M (Xj, Yj), which is the orthogonal projection of N on the link S1S2. After locating the point M (Xj, Yj), the distance D from the point M to the stop S1 can be easily located and the bus location is successfully referenced with respect to the stop S1.

Figure �5-3 Schematic representation of relating the GPS data to the bus network data using (LRS)

Knowing the bus location with respect to the stop S1 and the average speed of the bus which is attached to the bus network links data, the time of arrival of the bus to any of the stops ahead can be easily predicted and compared with the scheduled time of arrival. The count of passengers boarding and alighting the bus as well as the transfer passengers is transmitted from APC equipment and the mobile data terminal at every bus stop and can be linked directly to the stop file to show the in-vehicle passengers demand and the transfer passengers demand. In conclusion both the GPS location data and the APC passengers demand data can be accommodated and analyzed inside a GIS platform. However, The data model must be able to represent objects and events in the form of dimension in which they occur in the real world. In the real world these dimensional objects are dynamic, that is, they change over time and are referenced by their state in


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time. Therefore, a true comprehensive location referencing system (LRS) data model must incorporate the forth dimension, time (Koncz et al 2002)

5.3. Potential Improvements in Coordinating Bus Transfers and limitations

With the integration of the bus location data and the passengers’ in-vehicle and transfer demand data in GIS platform the transit agency can control and manage its bus fleet in the real time context. Potential improvements are as follows;

Real-time improvement

• Through the communication systems available and monitoring the connecting vehicles

locations with respect to their schedule directions can be sent to drivers to speed up or slow down in order to protect the connection.

• In some systems and if traffic lights can be controlled the movement of the connecting buss can be adjusted with respect to the schedule. If the bus is behind schedule and is expected to miss the connection the traffic lights can be affected to allow the late bus to catch up with its schedule and vice versa

• A real-time control strategies can be applied at the transfer stop if one of the connecting buses arrived and the others are late. The strategies are based upon the location of the late bus, its forecasted time of arrival and the evaluated transfer demand. A number of criterion is then tested using this information such as whether or not the forecasted arrival time of the late bus is within the slack time and whether or not the number of connecting passengers exceeds a minimum set by the transit agency and whether or not the savings in the transfer time cost will compensate the losses in the waiting and the in-vehicle time costs for the non-transfer passengers. Based on these data a decision to dispatch the bus which arrived on time or hold it indefinitely or hold it up to a maximum time can be made

• Also a dynamic dispatching model that determines the optimal slack time based upon the actual demand data and the late bus location can be developed and ran within a tine step to obtain a dynamic slack time

Long term improvements

• Bus trajectories can be analyzed to identify the bottlenecks in the network and optimize schedule time over the network segments and over time

• Through the analysis of boarding and alighting patterns the stoppage time can be better modelled and best location for bus stops and buses connections can be determined

Limitations

• Although the integration of GPS and APC technologies within a GIS platform can significantly improve the quality of service in general and the quality of coordinated transfers in particular, still and as stated by Thill (2000), real-time data storage , retrieval, processing,


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and analysis are presently not meeting the needs of society when it comes to geo-referenced data. Quicker access data models, and more powerful, accurate and faster algorithm are needed to make use of the real time information and allows the agency to make real-time decisions to improve the service

5.4. Conclusions

In this chapter the form of the output data of the GPS and APC technologies was shown and discussed. Then the integration of theses data with a conventional public transport GIS model was briefly discussed. It was found that the output data of both GPS and APC technologies can be integrated within a GIS public transport model with the help of the linear referencing systems (LRS) capability inside the GIS. Finally a number of potential improvements to improve the quality of coordinated transfers in the real-time context and in the long run were identified and elaborated. Finally the main limitation of the technology is identified, it was elaborated that the speed in which this real-time integration and analysis takes place is a crucial and important factor in achieving the desired results.


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6. Conclusions and Recommendations

6.1. Introduction

The main objective of the present research was to evaluate and assess the benefits of coordinated transfers between the different bus operators at the study area through a pilot coordination study between the stage bus operator (main bus lines) and the feeder bus operator (secondary bus lines). The research also aimed emphasising the role that APTS technologies can play to support the desired coordinated transfers. To achieve this objective the research was conducted in three portions. Firstly, a transfer stop was selected based upon expert knowledge and a quick overview of the stop. Afterwards, a detailed survey was conducted at the stop to determine the actual passengers’ volumes transferring between the stage and the feeder buses at the stop and their preference while using the service. Accordingly, the stage and the feeder bus routes that are more suitable for coordination were selected and monitored and the existing transfer time losses between them where determined. Moreover, those transfer time losses were translated into hourly financial losses based on the value of time for the study area available from a previous study. Secondly, a coordination study was conducted between the selected stage and feeder buses at the selected stop. A 3-stage optimization procedure was used to determine the optimal status of coordination between the selected buses based upon the minimization of a total passenger’ and operator costs objective function. Thirdly and finally the role that that APTS fleet management technologies can play in facilitating and improving the efficiency of the desired coordinated transfers at the stop was discussed, emphasised and elaborated.

6.2. Results against research outline

The correspondence of results with the study objectives and the research questions stated in the first chapter of this research will be the evidence in order to draw the general conclusions of the present research. Consequently, the study objectives with their corresponding research questions will be briefly evaluated in the light of the findings of the present research. • To assess the current transfer situation between the selected bus routes in the study area 1- How important is the transfer time as one of the quality service indicators for the passengers at

the selected stop?

It was found the transfer time is most highly appreciated quality of transit service indicator among transfer passengers at the selected transfer stop when compared with other important quality of service indicators namely, the bus fare, the in-vehicle time and the comfort of the trip. More than 60% of the transfer passengers sample interviewed at the stop indicated that transfer time is their first preference when using the bus system (See 3.6.1)


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2- How long is the transfer time between connecting buses at the study area under the current

situation and what are the equivalent financial losses to the lost time in transferring at the selected location?

Monitoring the selected stage and feeder buses arrivals at the stop during the AM Peak (7:00 -10:00) and PM Peak (17:00 - 20:00) hours it was found that transfer time between the selected stage and feeder buses at the stop is totally unstable and significantly fluctuating during both (See 3.6.4).Consequently the transfer time losses were accumulated for the AM Peak and the PM peak hours for each pair of stage and feeder buses at the stop (See 3.6.5). Moreover, those transfer time losses were converted into the equivalent financial losses at both the AM and the PM peak hours using the value of time for bus passengers at the study area available from a previous study (See Appendix A). The results showed that around 600 (160$) RM/ hr is lost at the stop because of uncoordinated transfers at the stop between the selected stage and feeder buses (See 3.6.5).

• To optimize the transfer coordination between the selected bus routes in the study area

3- What are the major objectives (costs and benefits) of the passengers and the operators?

The discussion in the second chapter established the basic elements of the transfer coordination problem as one of the intermodal public transport network design problems. The major stakeholders involved in the problem were identified with their main objectives (costs and benefits). (See 2.1)

4- How can those objectives be formulated the in a mathematical form that is suitable for the

optimization model? The mathematical formulation of the passengers and the operator objectives is carried out in the fourth chapter of this research for a 3- stage optimization procedure (see 4.5). Several previous models dealing with the transfer coordination problem were discussed with their advantages and disadvantages in the second chapter of this research. The mathematical formulation of the passengers and the operator objectives was done based on the model developed by Chowdhury (2000) discussed in the second chapter of this research (See 2.2.2).

5- What is the approach for evaluating the optimal value of the optimization model decision

variables? A 3-stage optimization procedure was formulated and discussed in the fourth chapter of this research. In the first stage the operating headways of both the stage and the feeder buses are optimized under uncoordinated service, the corresponding total cost is also obtained and compared with the total costs under the current existing situation (See 4.1, 4.2 and 4.3). In the second stage all possible combinations of stage-feeder bus coordination at the stop are tested and corresponding total costs cost of each combination is also obtained. The results of the


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second stage are compared with the existing situation results as well as the first stage results and the coordinated combination resulting in the minimum total costs is identified. In the third and last stage the optimal slack time added to the schedule of the coordinated buses to increase the probability of a successful connection and overcome the stochastic arrivals of buses to the stop under the varying traffic conditions.

6- What are the optimal values of the decision variables after solving the optimization problem and their corresponding financial gains?

In the first stage of the optimization procedure the optimal value of the headway under uncoordinated services (decision variable of the first stage) for the selected stage and feeder buses was determined with their corresponding total costs (See table 4.1 and 4.2). The results of the first stage was compared to the existing headways and it was found that; for the stage buses the optimal headway resulting from the first stage of the optimization procedure is almost similar to the operating headways. For the feeder buses it was found that the optimal headways obtained from the first stage of the optimization procedure is much smaller that the operating ones indicating that a significant increase in the number of buses operating on the feeder bus routes is needed from 2 buses/ hr to almost 6 buses/ hr for each of the selected feeder buses, this can be explained by the high passengers volumes originating from the LRT service available at the stop and seeking the feeder bus service. It was found that when comparing the total first stage with existing situation a total financial gain of 300 RM/ hr is obtained if buses are operated under the optimal headways obtained from the first stage. More than 90% of this gain is resulting from the change in the operating headways of the feeder buses since that the significant change in the headway occurred to the feeder buses after the first stage of the optimization. In the second stage of the optimization procedure all possible combinations of selected stage-feeder buses service coordination through schedule synchronization is tested. The optimal common headway under coordinated service is obtained (decision variable of the second stage) with the corresponding total costs (See table 4.4). The results of the second stage are compared with both the results of the first stage and the existing situation. It was found that when compared with the first stage there were no financial gains from the proposed coordination study, moreover the total costs (RM/hr) resulting from any combination of coordination between the stage and the feeder buses are relatively higher from the total costs obtained from first stage under uncoordinated service. This is mainly ought to the fact that although there some savings on the transfer time costs resulting from the coordination, still there a much higher loss on the feeder bus waiting time costs because of the large volumes of passengers originating from the LRT service that has to wait much more time for the feeder buses if the stage-feeder bus service is coordinated. However, when the results of the second stage were compared with the total costs under the existing situation it was found that there is a financial gain in the total costs of the operations under some combinations of coordination as shown in table (4-4). This can be explained by the fact that under the existing situation the feeder buses are already operating on relatively large headways. Hence, the LRT passengers waiting at the stop for the feeder buses are already encountering large waiting times and consequently a large waiting time costs.


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Therefore the savings in the transfer time costs becomes significant. The best group to be coordinated was found to be stage bus 338 and feeder buses 904A and 904 B with an optimal common headway of 0.25 hr. Buses number 13 and 47 are kept operating on the existing headways which is 0.5 and 0.416 hr respectively. The savings in the total costs under such coordination when compared with the existing situation is 350 RM/hr. In the third and final stage of the optimization procedure the optimal value of the slack time added to the schedule of the coordinated buses (338, 904A and 904B) to overcome he stochastic arrivals of buses at the stop because of the varying traffic conditions and to increase the probability of a successful connection is obtained. It was found that the slack time tends to be equal to the zero. This can be explained by the fact that although some savings on the transfer time costs occur, still the losses in the in-vehicle time costs and the operator costs are higher because of the relatively low transfer passengers’ volumes and the higher values of the standard deviation of buses arrival time at the stop.

• To explore, investigate and emphasis the role that APTS technologies can play to facilitate, control and improve the efficiency and of the desired coordinated bus transfers

7- What are the relevant APTS technologies that can play a role in facilitating, controlling and

improving the efficiency of handling the transfer coordination problem in the real-time context?

The discussion in the second chapter identified the APTS technologies that can play a role in facilitating, improving the efficiency and controlling the coordinated transfers (See 2.3). It was found that Global Positioning Systems (GPS) technology can play a significant role in identifying the exact location of the buses in the real-time context and consequently controlling the buses movements to facilitate transfers and predicting its arrival times to the stop. Automatic passengers’ counters (APC) with mobile data terminals can play a significant role in identifying the in-vehicle passengers demand and the transfer demand in the real-time context. Geographical Information systems GIS can play a significant role with being the main platform integrating and visualizing the data transmitted from GPS and APC technologies with the other fixed route data such as stop locations and schedules to allow the operator to perform real-time analysis and make real-time decisions. Finally communication systems play a significant role in transmitting the orders and direction from the operations room to the drivers and vice versa.

8- How to integrate these technologies to solve the transfer coordination problem? A discussion on the integration of output data of the GPS and APC technologies in a GIS platform is presented in the fifth chapter of the research supported by examples form the GPS and the manual APC survey conducted for the selected routes in the fieldwork period (See 5.1.2 and 5.1.3). A simple method for integrating the GPS and APC data with the conventional fixed rout public transit model is proposed as the main aim of this part of the study is not to develop an accurate and sophisticated model for the integration of these technologies but to emphasis and explain the benefits and the improvements that can occur to


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the handling of the transfer coordination problem in the real-time context if these technologies are deployed and implemented by the transit agency (See 5.2).

9- How can the transit agency make use of the integrated data available from to facilitate the

coordinated transfers in both the real-time context and the long term? Finally a number of strategies that can be implemented and employed by transit agency to improve the handling of the transfer coordination problem are identified (See 5.3). Those strategies make use of the integrated data and allows for real-time improvements as well as long term improvements.

6.3. General Conclusions

A number of general conclusions can be drawn based upon the analysis conducted in the present research; • Coordinating transit routes becomes beneficial when the increase the in-vehicle and waiting time

costs can be compensated by the savings in the transfer time costs. • Full coordination of transfers through the addition of a slack time (holding time) at the transfer

stop to the schedule of the coordinated buses is only beneficial when there is a large number of transferring passengers and standard deviation of buses arrival to the stop is not so large. If the standard deviation of buses exceeds a certain value the slack time tends to get smaller till it reaches zero. In that case the savings in the missed connection cost is not enough to compensate for the losses in the in-vehicle time cost and the operator costs.

• Among the various benefits that can be gained through the deployment of APTS fleet management technologies to monitor and control the buses operations, the technology can play a significant role in enhancing and facilitating coordinated transfers. The output data from the relevant APTS technologies can be continuously used in the real-time context to determine the added value of coordinated transfers based on the data available on the passengers transfer demand, exact buses location and other static data such s bus schedules. Furthermore, the output data can be archived and then analyzed for certain periods of time to perform various analyses such as identifying the bottlenecks in the transit network and measuring ridership levels which can be used to update the system scheduling and improve the quality of service provided to attract more passengers to use the system.

6.4. Study area Recommendations

• It is recommended to increase the frequency of the feeder buses services at Asia Jaya stop to meet the existing high passengers demand originating from the LRT service. If the feeder bus operator have no constraints on their fleet size and can implement the operating headways obtained from the first stage of the optimization procedure the coordination study with the stage buses under a common headway will not be beneficial as previously discussed (See 6.2). Instead, the coordination between the feeder and stage buses can still be done but under simple integer ratios (e.g. 1:2, 1:3). In that case the LRT passengers are satisfied and the transfer passengers between the stage bus will also be satisfied but they have to schedule their arrivals at the stop at the time when the stage and the feeder buses are connecting to avoid waiting for long times at the stop to catch their connecting bus.


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• In case there are fleet size constraints that might prevent the feeder bus operator from implementing the operating headways obtained from the first stage of the optimization procedure the coordination between the stage and the feeder buses at Asia Jaya stop will be an attractive solution since the LRT passengers waiting at the stop are already encountering long waiting times at the stop and consequently larger waiting time cost. In that case the savings in the transfer time costs will compensate some of the loses of the waiting time costs.

• A general observation on the study area that can be generalized over the whole Klang valley region that no schedules are available at the buses or at the bus stops and consequently passengers arrivals to the stops are completely random. It is proposed that nodes identified as transfer points should be equipped with facilities that allows for proper coordination among the connecting routes. The information on buses schedules can be integrated with the real-time information on buses location and its expected time of arrival to the stop available through the deployment of APTS technologies. It is proposed that intermodal nodes should be equipped with displays or information kiosks through which passengers can know exactly the waiting time till the next service is available. The intermediate stops should be provided with route maps showing the connections with other services and its timings

• Also it was observed that the bus dispatchers at buses terminals are not following strictly the operating headway. In order for any coordination to be successful the dispatching of buses from their terminating stop must be followed strictly to increase the probability of a successful connection. Also the operator of the stage buses is different that the operator of the feeder buses. No coordination exists what so ever between the two operators and consequently it will be so hard if not impossible to coordinate the services under the present situation. It is proposed to establish a main control and operations room that monitors the fleet of the different bus operators. Having such a control room will improve the quality of service provided and allows for better coordination between the different operators.

6.5. Further Research Recommendations

Because of time and fieldwork data limitations a number of assumptions have been made while pursuing the present research. Possible areas of extension for the present research are summarized below; • While formulating the present coordination model, it was assumed that passengers demand is

fixed and independent of the service quality (See 4.2). In reality the passengers demand is dependent on the quality of transit service provided. The increase in passenger demand will cause service quality to deteriorate due to more highly variable boarding and alighting activity. Bus routes characterized by poor service quality will likely suffer patronage declines over time or have difficulty attracting new riders because passengers are inconvenienced by unpredictable service. The overall effect is that the initial increase in demand due to increased service provision will be partially offset by a demand decrease due to adverse impacts on bus performance (Kimpel 2001). An optimization model that takes into consideration the elasticity of passengers demand and iteratively optimizes the coordination between connecting busses is desirable extension of the present research.

• It was assumed in the present research that the transfer demand is fixed (See 6.2). The suitability of desired transfer coordination is highly affected by the real- time transfer demand and the exact location of the connecting buses with respect to their schedules. A model that incorporates the


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data available through the APC and AVL technologies on the passengers demand and buses location to evaluate the suitability of transfers in the real-time context and generate different strategies to be followed accordingly will make the system more dynamic and demand responsive.

• It was assumed that buses arrivals at the transfer stop are stochastic and follows the pattern of normal distribution (See6.2). In reality buses arrival to the stop does not follow exactly theoretical distributions. A model that uses the real empirical distributions of buses arrivals to the stop is a desirable extension of the present research. The empirical distribution can be easily generated if AVL technology is deployed to monitor the movement of the buses. However this sort of distributions is normally analytically intractable and requires sophisticated numerical approaches in order to be solved.

• In the present research no constraints were introduced while formulating the optimization model due to data limitations. In future research constraints on buses capacity or fleet size or minimum frequency can be considered.

• In the present research the coordination study assumed the coordinated buses will be operating under the same common headway. An optimization model that uses simple integer ratios (e.g. 1:2, 1:3) to compensate for the high passengers volumes seeking the feeder buses and originating from the LRT services is a desirable extension of present research.

• The present study used a value of passengers’ time that is derived for the whole Klang valley region based on the average annual income. A comprehensive and more precise study on the value of time for the bus system passengers is required.

• A total cost objective function was formulated and minimized in the present research for the coordination study (See 4.5). Other objective functions such as social welfare maximization can be considered in future research.

• Although transfer time is the most crucial factor affecting quality of transfers other factors still needs to be considered to make the coordination between different operators more successful such as the integration of fares, transfer stops locations and integrating bus routing to avoid competition over the same routes

• In general and if successful service coordination should have significant effect on the increase of ridership levels and consequently lower congestion levels, less pollution and lower fuel consumption. In future models these factors should be somehow taken into consideration


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Appendix (A): Value of time Calculation for the study Area

Value of Time (Work and Non-Work Time) Calculation of Value of Work Time (RM) 1. Employment Household Income (monthly) in Study Area 1450.00 (Source: Socio Economic Survey by Consultant Team,1999) 2. Assume average no. of workers per household is 1.7, 852.94 therefore income per worker 3. Average worker spends 180 hrs / month, 4.74 therefore cost of worker per hour 4. Adding employers’ cost of 60%, which takes into account 7.58 EPF, SOCSO and other hidden costs Therefore the cost of work time is 7.58 Calculation of Value of Non-Work Time This is valued at 30% of household income 2.27 Therefore the cost of non work time is 2.27 Value of Time Work Time 7.58 Non Work Time 2.27 Type of Vehicle Car Taxi Van M/Lorry Lorry Bus M/cycle Occupancy Rate 2.15 2.76 2.66 2.12 1.96 28 1.29 Type of Vehicle Car Taxi L/Truck Lorry Bus M/cycle Occupancy Rate 2.15 2.76 2.39 1.96 28 1.29 Description Car Taxi L/Truck Lorry Bus M/cycle Work Time (%) 50 100 100 100 20 40 Non Work Time (%) 50 0 0 0 80 60 Description Car Taxi L/Truck Lorry Bus M/cycle Value of Time(RM) 10.60 20.93 18.12 14.86 93.41 5.67


96

Appendix (B): Passengers Questionnaire

age ( below 20 / 21- 60 / over 60 ) sex ( Male/ female )

origin ( other place / this bus stop ) coming from bus line waiting for bus line

average waiting time (min) ( <15 / 15-30 / >15 ) regularity of the trip ( daily / weekly / monthly )

What are the most important factors in your own opinion when using the

bus system?

Please put them in order of

importance

waiting time fare comfort In vehicle time

If the waiting time is reduced to 5 minutes or less but the fare is increased

by 50 % will you still use the bus system?

(yes/no)


97

Appendix (C): MatLab Script

Stage (2) Sunchronization of stage bus 338 and feeder bus 904B

Declaration of the function and the variables:

function [TC

,C338,C

904B,C

W338,C

T338,C

V338,C

O338,C

W904B

,CT

904B,C

V904B

,CO

904B]=

synchro(H,D

i338o,Di338k,D

i338,Uw

338,Ut338,U

v338,Uo338,L

338,S338,n338,psi338,Di904B

t,Di904B

j,Di904B

,VarH

i904B,U

w904B

,Ut904B

,Uv904

B,U

o904B,L

904B,S904B

,n904B,q904B

,psi904B)

%B

us338 Data

CW

338=0.5*H.*D

i338o.*Uw

338; C

T338=((norm

pdf(.506666666666667,.480162009696265e-1)*H)*(norm

pdf(.456666666666667,.560257877132379e-1)*H

)+(normpdf(.506666666666667,.480162009696265e-1)*H

)*(normpdf(.456666666666667,.560257877132379e-1)*H

))*Di338k*U

t338; C

V338=(L

338./(4*S338)+(H.*D

i338.*n338.*psi338./4)).*Di338.*U

v338; C

O338=((L

338./S338)+ (H.*D

i338.*n338.*psi338./1)).*Uo338/H

; C

338=CW

338+CT

338+CV

338+CO

338; %

Bus 904B

Data

CW

904B=((H

./2)+(VarH

i904B./(2*H

))).*Di904B

t.*Uw

904B;

CT

904B=((norm

pdf(.456666666666667,.560257877132379e-1)*H)*(norm

pdf(.506666666666667,.480162009696265e-1)*H

)+(normpdf(.456666666666667,.560257877132379e-1)*H

)*(normpdf(.506666666666667,.480162009696265e-1)*H

))*Di904B

j*Ut904B

; C

V904B

=(L904B

./(2*S904B)+(H

.*q904B.*n904B

.*psi904B./4)+(H

.*Di904B

.*n904B.*psi904B

./4)).*Di904B

*Uv904B

; C

O904B

=((L904B

./S904B)+ (H

.*q904B.*n904B

.*psi904B./1)+(H

.*Di904B

.*n904B.*psi904B

./1)).*Uo904B

/H;

C904B

=CW

904B+C

T904B

+CV

904B+C

O904B

; T

C=C

338+C904B


98

Running Fminbnd to solve the function:

%Bus 338 Data Di338o=16; Di338k=6; Di338=30; Uw338=10; Ut338=6.66; Uv338=3.33; Uo338=24; L338=48; S338=30; n338=96; psi338=0.00117; %Bus 904B Data Di904Bt=96; Di904Bj=3; Di904B=116; VarHi904B=0.00231; Uw904B=10; Ut904B=6.66; Uv904B=3.33; Uo904B=25; L904B=10; S904B=15; n904B=16; q904B=12; psi904B=0.00117; [H,TCval] = fminbnd(@synchro,0.1,100,[],Di338o,Di338k,Di338,Uw338,Ut338,Uv338,Uo338,L338,S338,n338,psi338,Di904Bt,Di904Bj,Di904B,VarHi904B,Uw904B,Ut904B,Uv904B,Uo904B,L904B,S904B,n904B,q904B,psi904B);

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