SIMULATION MODELLING

FINAL PROJECT

STADIUM QUEUE SIMULATION

Professor: David Kelton

Created By: Aditya Singh

M-Number: M10574606

Chapter 1

Introduction and Problem Statement

1.1 Introduction

The Nippert Stadium is UC’s Football and Soccer Stadium. It has a capacity of 35,000.

There are 6 entrances through which fans enter the stadium during games. Most fans are

passionate and regulars at the stadium and on an average, we get attendances of over 20

thousand per game. This project simulates fans entering the stadium from the Main Street

Entrance, Gate 6 (Near the Recreation Center) on the 18th of November during the UC

Bearcats vs Memphis Football game. The idea of this project is to analyze the current

model and based on the current metrics, develop a better working simulation model using

Arena Software so that the average waiting time of the fans in the queues reduces.

1.2 Motivation and Objective

I visit the Nippert stadium very often during games and I have always been interested in

understanding how queues function at the stadium entrances. Through this project, I

want to understand the rate of arrival of fans and the time spent by them in queues

before entering the stadium. On Several occasions, I have been stuck in long queues and

missed the beginning of the game. The objective of this project is to reduce the total time

spent by each fan in the queues before entering the stadium and to optimize the number

of resources in the parallel queues.

Chapter 2

Data Collection and Model Fitting

2.1 Data Collection and Fitting to Distributions

1) For this model, the input data was the arrival schedule of the fans every five

minutes from 7:30PM to 8:30PM. The game began at 8:00PM. This data was fed

into an arrival schedule in Arena.

2) The Number of fans carrying bags were observed in the one hour period.

3) It was observed that 11.5% of the fans throughout the one hour period had bags

which were searched.

4) The individual scanning time of each fan was difficult to record and therefore I

counted the number of fans which passed the scanning process after completing

the bag check for a period of 30 seconds. I repeated this process 10 times to get

data points to obtain a distribution in the input analyzer.

The table above gives a better picture of how I obtained data points for the

scanning time. This data was fed into an input analyzer and the following

distribution was fit:

Distribution: Beta, Expression: 0.62+0.38 * BETA(1.61,1.33)

5) The time taken for searching bags was recorded for 66 fans since it was difficult to

observe the bag search time for every fan. This Data was fed into an input analyzer

and the following distribution was fit:

Distribution: Gamma

Expression: GAMM(2.51,4.4)

2.2 Assumptions in the Model

Certain assumptions were made as collecting data for every scenario was complex.

1) It was observed that 11.5% of the fans in the one hour period had bags. Only

people with significantly large bags have been considered. I have not taken ladies

with clutches and small bags into account.

2) The arrival rate of fans carrying bags entering every five minutes is uniform

throughout the one hour period.

3) Fans carrying bags choose one of lanes 1,2 and 3 with equal probabilities (0.33,0.33

and 0.34).

4) A bigger percentage of fans without bags enter the express lane (48%) and the

remaining are enter lane 1,2 and 3 with equal probabilities (0.18,0.17 and 0.17).

Chapter 3

Arena Model

3.1 Modeling the System

The Procedure that any fan follows while entering the stadium is divided into the

following steps:

Fans Arrive.

Fans Choose which lane to enter.

Fans wait in queue to get bags searched.

Fans wait in queue to get tickets scanned.

Fan leaves the System.

There are certain decision modules which decide the path of the fans in the model.

There are four lanes in total and there have been probabilities assigned to fans

using Assign Modules to choose the lanes. One of the four lane’s is an express lane

where only fans without bags can enter. This lane has only the Scanning Process

where as the other three lanes has the Bag Search Process as well.

The following is an overview of all the model parameters:

The following is the Snapshot of the Model in Arena:

The model parameters and logic have been explained in detail:

1) A Create Model was created using Arena for fans arriving at the Stadium Entrance

2) For this model, the input data is the arrival schedule of the fans every five minutes

from 7:30PM to 8:30PM. The game began at 8:00PM. This data was fed into an

arrival schedule in Arena.

The above snapshot shows how fans arriving every five minutes are fit into a

schedule in Arena.

3) This model has two types of fans entering the stadium:

Fans carrying bags

Fans without bags

The probabilities are assigned using an Assign Module in Arena in the following

way

4) A Decide Process Module is used in Arena to check if fan has a bag or not

5) The fans can enter the stadium via four parallel lanes. The fourth lane is an express

lane where only fans without bags can enter. Probabilities with which the fans

choose the lanes have been assigned using the Assign Module in Arena in the

following ways:

6) A Decide Process Module is then used to split the fans into four lanes.

The first three lanes contain two processes as follows:

7) The following Process Modules are Created in the first Three Lanes:

Bag Search- If a fan has a bag his bag is searched before he/she goes on to the

next process. While his bag is being searched, the fan standing behind him

irrespective of whether he/she has a bag or not has to wait until his bag is

searched. There is one resource in each lane (bag search person) who searches

bags.

The expressions for bag search time has been created in the following way:

Process Module for Bag Search

The figure above shows the created expression Frisking Time(With_Bags).

When With_Bags is False then Frisking Time will be equal to zero.

Ticket Scanning – Every fan must get his/her ticket scanned before entering

the stadium. There is one resource in each lane who scans tickets.

An Expression has been created for Scanning time

The Process Module for Scanning is below:

The fourth lane is an Express Lane where only fans without bags can enter. This

lane has one process- scanning of tickets.

8) A Dispose Module is placed at the end of the model through which all the fans

depart the lanes and enter the Nippert Stadium.

3.2 Simulating the Model

The Model was simulated using Arena for one hour. The Replication Parameters are given

below:

CHAPTER 4

Results

After running the model for 150 replications, it was found that the number out for the

fans was 2586. The Average time in system and Average Work in Progress are as follows:

The average time in system is found to be 2.77 minutes and the average WIP is found to

be 120.44 fans. We want to reduce these quantities to improve the system.

Arena gives us the Waiting time and Number of Entities waiting for each queue in the

model.

The utilization of the resources is given below:

It can be observed that the Bag Search Person is used up for maximum time while the

utilization of the person in charge of scanning is very less comparatively.

Chapter 5

Improving the System

5.1 Suggestion for Improvement

The new system has been improved by reducing the average total time spent per fan in

the system. Also, the WIP average has been reduced.

This has been achieved by removing one of the resources and converting lane 3 into an

express lane. Only people without bags can enter this express lane. Now, our model has

2 express lanes and 2 regular lanes. Here 50% of fans carrying bags go into lane 1 and lane

2. The fans without bags enter lane 1, lane 2, lane 3 and lane 4 with probabilities

0.15,0.15,0.35 and 0.35 respectively.

The new model is shown below:

5.2 Comparing the Results

The two models were run for 150 replications each and were compared using the tool,

process analyzer. The .p files of both the models were added as scenarios in the process

analyzer tool. The average total time and average WIP were added as the input response

and scenarios were run. The values found are shown below:

The input charts for both the responses were plotted in the form of box and whisker plot

and the best scenario was depicted in each using the “smaller is better” criteria and

keeping the error tolerance as zero. The charts are listed below:

Both charts depict that the recommended model scenario is the best scenario with

smaller values for average work in progress and average total time in system.

Chapter 6

Conclusion

The queues at the Gate 6 Entrance of Nippert Stadium was modeled in Arena Simulation

software and the results about the relevant parameters were generated. After

performing an analysis, it was observed that the overall time spent by each fan in the

system was close to 3 minutes. A new model was developed to reduce average fan time.

The new model was compared statistically for the average wait fan time in the system

using a software called Process Analyzer and it was found that the new, suggested model

has a statistically significant decrease in the Average Fan time and WIP as compared to

the original model. The new model also, has one less resource as compared to the original

model. Hence, with these suggested changes, more number of fans can enter through

gate 6 and spend less time in the system before heading to their seats.

References

1. Content-

Simulation with Arena 6/e- W. David Kelton- University of Cincinnati, Randall P.

Sadowski, Nancy B. Zupick, Rockwell Automation