Yi-Chang Chiu, Ph.D. Chiu, Ph.D.University of Arizona

S. Travis Waller, Ph.D.

University of Texas at Austin

FFREEWAYREEWAY T TRAVELRAVEL T TIMEIME P PREDICTIONREDICTION & D& DETECTORETECTOR C COVERAGEOVERAGE A ANALYSISNALYSIS

Workshop MaterialWorkshop Material

Project 0-5141September 2007

Workshop Overview

• Concept overview

• Software overview Travel Time Prediction Detector Placement Analysis

• Introduction• Motivation• Literature Review

• Travel Time Classification•Summary and conclusions

PART 1: BACKGROUND & TRAFFIC DATABASE

PART 2: INTEGRATED STATISTICAL/SIMULATION MODEL

• Implementation Issues

• Conclusions

• Concept overview

PART 3: N-CURVE MODEL

• Software overview

PART 4: TRAFFIC DATABASE GENERATION

PART 1

Introduction

Introduction

• Providing freeway travel time prediction Helps traveling public make pre-trip/en-route travel

decision Increases perceived benefits of ITS infrastructure

• Travel time prediction is challenging under non-free-flow situations (e.g. peak hours, incidents, work zones, etc.) due to rapidly changing traffic conditions

Motivation

Develop a computationally efficient travel time prediction model

Develop a model to determine the optimal location of sensors

Dynamic: reactive to evolving congestion patterns

Uses counts from dual loop detectors as inputs (most widely used data collection devices)

• Conclusions Many agencies implement naïve estimation methods

• Good results under stable/recurrent conditions, but may introduce large errors otherwise

Prediction is necessary to account for multi-segment trips

Literature Review

State of the Art

State of the practice

Literature Review

Short term travel time predictionTime series, regression, Kalman filtering,

neural networks, simulation

Travel time estimationspeed-based, traffic flow theory

Prediction Approaches

Estimate TT

Predict Input Compute TT

Predict TT

Travel Time ClassificationINSTANTANEOUS

Travel time on sections at 8:00 A.M

tAB(8:00) = tBC(8:00) = tCD(8:00) = 5 min

Instantaneous Travel Time (ITT)

ITTAD= tAB(8:00) + tBC(8:00) + tCD(8:00) = 15 minutes

S1 S2 S3..8:00 A.M.

A B C D

8:05 A.M.

8:10 A.M.

Experienced Travel Time (ETT) ETTAD= tAB(8:00) + tBC(8:00 + tAB(8:00) ) + tCD(8:00 + tAC(8:00))

ETTAD = tAB(8:00) + tBC(8:05) + tCD(8:05+ tBC(8:05))

Notice: ETTAD = ITTAD ONLY if: tBC(8:05)= 5 minutes tCD(8:05+ tBC(8:05))=5 minutes

Predicted Travel Time (PTT) PTTAD(8:05)= tAB(8:05)+tBC(8:05 + tAB(8:05))+tCD(8:05+ tBC(8:05 + tAB(8:05))

Travel Time ClassificationEXPERIENCED & PREDICTED

S1 S2 S3..8:00 A.M.

A B C D

8:05 A.M.

8:10 A.M.

Conditions don’t change

Travel Time ClassificationSUMMARY

TRAVEL TIME

ESTIMATED

PREDICTEDPTTAD(8:00)=tAB(8:05)+tBC(8:05+tAB(8:05))+tCD(8:05+tBC(8:05+tAB(8:05)))

Prediction necessary for all segments

Experienced Travel Time ETTAD(8:00)= tAB(8:00)+tBC(8:00+tAB(8:00))+tCD(8:00+tBC(8:00+tAB(8:00)))

Prediction necessary for downstream segments

Instantaneous Travel Time ITT(8:00) =tAB(8:00) + tBC(8:00) + tCD(8:00)

No Prediction/Forecasting Necessary

Lessons Learned

• Estimating experienced & predicted travel times is much more difficult than determining instantaneous travel times

• Estimation and Prediction involves Forecasting future conditions on the freeway Modeling the temporal & spatial evolution

of congestion in the freeway section

• Implemented models should be able to provide experienced & predicted travel times

PART 2

Integrated Statistical/Simulation

Model

STATISTICAL COMPONENT

Uses a time series (ARIMA) model to forecast future flows in the on ramps

MODEL 1 Integrated Statistical/Simulation Model

SIMULATION COMPONENT

Uses Cell Transmission Model (CTM) to simulate future travel times utilizing forecasted flows

Time Series

• Applied in numerous domains to predict future trends from past trends

• Time series: sequence of data points collected at uniform time intervals

Time Series Model

• Stationary Time Series: Data points vary around a constant mean value

• Non-Stationary time series: Exhibit an upward and downward trend Example: aggregated 5 minute volumes on an on-

ramp tend to go up during congestion building phase

• Non-Stationary time series can be converted to stationary time series by differencing successive terms

11343

232

121

.....,.........

,

,

ttt XXYXXY

XXY

XXY

ARIMA Model

• Effective for predicting non-stationary time series, like traffic counts Non-stationary points converted to stationary

points by differencing • Instead of using traffic counts at time t as variables

(ct), it uses the difference of traffic counts at time t and t-1 (ct=ct-ct-1)

• Differenced stationary points predicted as a function of p past data points and r past errors in prediction ct=b+a1x ct-1+a2x ct-2+…+apxct-p+rer

ARIMA Model

• Coefficients of the ARMA model are calibrated using past data points. Most common way is to choose coefficients which minimize the

sum of square error between model predictions and actual value in the past data set (More information available in handbook)

• Time Series Models are implemented using R, an open source statistical software

• The user may easily adjust the time series model specification (p,r)

• The source code is flexible, and different statistical components may be used instead of ARIMA models, if desired (such as Kalman filtering)

Cell Transmission Model (CTM)

• Mesoscopic Traffic Simulation model developed by Daganzo

• Computationally efficient

• Captures dynamic traffic phenomena like queue formation, shockwave propagation & link spillovers

Cell Transmission ModelBasic Principles

• Freeway segment is converted

to cells interconnected by links

• Time is discretized in intervals

• At each time interval, the model “moves” vehicles from one cell to another, based on traffic flow relationships & cell parameters Length Free flow speed Capacity Jam Density Shockwave propagation speed

• Travel times are computed based on cumulative counts

A B C

Calibrated using traffic data

• Choose Simulation Interval: Common values between 4 and 10s

• Select Free Flow Speed: Estimate the value based on speed limit

• Compute Minimum Cell Length: Length > Free Flow Speed * simulation interval

• Locate Sensors & Ramps

• Divide the segment such that sensors are placed at the beginning of cells, and the minimum cell length is respected

Cell Transmission ModelConverting the Freeway Segment to Cells

0.4 m 0.5 m 0.6 m 0.3m Example:•Free flow speed: 75 mph•Simulation interval: 4sec•Minimum cell length: 440ft•1st Segment: 4 cells of 528•3st Segment: 6 cells of 452 ft • + 1 cell of 456ft•4st Segment: 3 cells of 528

23471220 18

Sink Cell

Merge Cell

Sink Cell

Origin Cell

Gate Cell

1

2223

24

21

MODEL 1Software

• A single software tool can be used for: CTM parameter calibration Travel time prediction Detector location

Software Installation

• Install R – open source statistical software available for free from http://cran.cnr.berkeley.edu/

• Create a Working Folder• Copy files R-Arima.txt,original code.exe

original code.exe.config into the working folder

• Adjust path information in R-Arima.txt to reflect path of working folder

Calibration Process

Run model with estimated values for the input parameters

Compare model outputs with calibration data

Adjust parametersDesired accuracy?

Calibration Completed

NO

YES

Calibration Mode

• Parameters to be calibrated Jam Density Maximum Flow (Capacity) Speed of Backward Moving Shockwave Free Flow Speed

• Calibration options: Based on travel times (only possible if real travel time

measurements are available): minimize the difference between ctual section travel time travel time and travel time predicted by model (read from output.txt)

Based on cumulative counts at sensor locations (always feasible): minimize the difference between cumulative counts at each sensor and counts predicted by the model (read from volumes-calibration.txt)

• The software documentation provides further information about the calibration procedure

Online Travel Time PredictionInput Data

The software documentation provides detailed explanations

• Adjustments to the source code are necessary to adapt the model to the TMC operations characteristics (such as frequency of data provision & travel time computations, desired aggregation)

• Historical data can be used to test the model performance The model will read only a specified

number of data points at the time, and therefore behave as if it was actually working in real time

INPUT DATA

REAL TIME TRAFFIC DATA

LINK DATANETWORK DATA

GUI

Online Travel Time PredictionProcedure

• Prepare Input Files Convert the freeway segment into cells Select & Calibrate Parameters Adjust TMC preferences (such as frequency of

predictions)

• Execute the model

• Analyze output files Travel time predictions per OD pair, at desired

intervals and aggregation levels

• Adjust model options based on performance

Example of possible patterns for 3 sensors

Offline Detector Coverage AnalysisBasic Algorithm & Options

Generate one possible detector deployment pattern or read it from

the input file

Compute travel time prediction error

Are there other possible patterns ?

Analyze Errors and select optimal location

YES

NO

Model optionsAutomatically generate ALL possible patterns

•A threshold for the minimum distance between detectors may be included to reduce the umber of feasible patterns

Feed a set of patterns manually

Offline Detector Coverage AnalysisSome Considerations

• Additional Input data (described in detail in the documentation) Relative position of cells (if deployment patterns are generated

automatically) Possible deployment patterns (if only a set of possible patterns is

analyzed) Real travel times for all the analyzed OD pairs

• Real sensor counts are needed for all possible sensor locations Data should be generated using a microscopic traffic simulator, such

as VISSIM• Output files provide several error measurements for all the analyzed

patterns Global error measurements are indicative of the convenience of a

deployment strategy Selecting an optimal pattern is not straightforward, some patterns may

lead to lower global error, but favor the performance for certain OD pairs

Final decision is based on engineering judgment Specific criteria can be incorporated in the source code

General Software Features & Implementation Issues

• Runs on a standard PC • Relies on count data, easily obtainable using loop detectors• As with any model, model performance will vary depending

on accuracy of data

• Additional layer of data screening and filtering should be incorporated to ensure accurate results Characteristics of the layer are TMC specific Objectives include (more information in the final report):

• Generate input data files compatible with the model in terms of file names, aggregation levels, frequency of updates, etc

• Identify malfunctioning sensors– Exclude them from the simulation– Use some procedure to impute the missing data

• Identify extreme traffic conditions which demand for manual adjustment of model parameters

Conclusions

• Travel time prediction is desirable to help drivers to make informed decisions

• Naïve prediction procedures are not accurate enough during unstable traffic conditions

• The model developed for this project has the potential to improve upon existing methodologies Final adjustment for real-time operation are TMC specific, and need to be

accomplished before deployment Model performance should be monitored, and modifications to the following

components may be used to improve results• Heuristic procedure to re-set initial densities (explained in the final report)• Statistical component• Data filtering layer

• The detector coverage analysis tool provided with this package is useful to evaluate potential detector locations, and consider re-location of existing sensors

• CTM is a powerful methodology to model traffic flows. The software provided for this project can be used to develop and calibrate CTM models for other purposes

PART 3

N Curve Model

Problems Statement

• On a basic freeway segment, given a set of detectors, which are able to provide traffic counts at a fixed frequency, the problem is to provide predicted experience travel time at

any time t from a pre-defined DMS location to a pre-defined prediction target destination at each pre-defined update instance over the pre-defined operational horizon.

Problems Statement (cont’d)• Given #1:

Number and locations of detectors Historical data for each detector (distribution information) DMS and prediction target destination location

• Notations: distance between detector d1 and d2, experienced travel time from d1 to d2 predicted at time t, cumulative traffic counts at detector #1 at time t, cumulative traffic counts at detector #2 at time t,

• Property 1 d1 is upstream of d2

Where

• Property 2 Note: no over-taking is considered Question to be asked, how do we determine the following:

21 ddL

tddL 21

)(1tNd)(

2tNd

21

21

21

)()()(

dd

dddd L

tNtNtK

ttNtN dd 0)()(21

ttT t dd 21 )()(12tNtN dd

)()(22tNtN dd

where

and

Problems Statement (cont’d)

• Given #2 . .

• Notations: mean of vehicle(s) n at sensor i at time t, standard deviation of vehicle(s) n at sensor i at time

t, mean of time t at sensor i for vehicle(s) n, standard deviation of time t at sensor i for vehicle(s)

n, cumulative traffic counts at detector i at time tp, cumulative traffic counts at detector j at time tp,

I ,detector )( ),( iittNorm in

in I ,detector )( ),( iittNorm i

tit

)(tin

)(tin)(nit

)(nit)( pi tN

)( pj tN

Problems Statement (cont’d)• Property 1

Model at time tp (time instance at which prediction is needed) DMS location i Prediction target destination j Question to be asked, how do we find t* such that:

• Model 1 Find t* such that of Predicted travel time interval of Predicted travel time interval

15 %ile

)( ),( ttNorm in

in

tp)(tin)( pj tN

)(*)( pij tNtN

)(*)()( pijpj tNtNtN

%15)( pi tN *)( *),( ttNorm jn

jn

))(( * )),(( * pijtpi

jt tNttNt

PART 4

Traffic Database Generation

Traffic Database

•Contains detector fromTransVISTA 77 detectors 37 miles (11 on El Paso Border Highway)

•An online graphic user interface (GUI) is provided to access sensor data

•Complemented w/some real travel time measurements obtained via GPS

Traffic Database

ONLINE GUI

TTI Database

U of A Database

GUI hosted by U of A

Daily TAR fileSender program PcAnywhere Remote

TxDoT

Daily TAR fileReceiver program PcAnywhere Host

TTI

Modem

TCPIP -JDBC URL

Connection to Postgres

server

Data Transfer Schematic

• Major nodes TxDOT TTI U of A

Data Transfer Description

Timer Task 2Interval – 2 minutes *Task description – Read incremental data and overwrite file source.tar

If source.tar has been modified since last check, invoke PcAnywhere Remote to transfer the file to TTI

Timer Task 2Interval – 2 minutes **Task description – Read incremental data and file destination.tar

If destination.tar has been modified since last check, append to output tar file

TxDOT

** TBD

TTI

U of A Database

Timer Task 2Interval – 3 minutes Task description – Read incremental data and overwrite file source.tar

If source.tar has been modified since last check, invoke PcAnywhere Remote to transfer the file to TTI

Timer Task 2Interval – 3 minutesTask description – Read incremental data and file destination.tar

If destination.tar has been modified since last check, interpret hex messages andwrite to U of A database

TxDOT

TTI

U of A Database

Timer Task 2Interval – 2 minutes *Task description – Read incremental data and overwrite file source.tar

If source.tar has been modified since last check, invoke PcAnywhere Remote to transfer the file to TTI

Timer Task 2Interval – 2 minutes **Task description – Read incremental data and file destination.tar

If destination.tar has been modified since last check, append to output tar file

TxDOT

** TBD

TTI

U of A Database

Timer Task 2Interval – 3 minutes Task description – Read incremental data and overwrite file source.tar

If source.tar has been modified since last check, invoke PcAnywhere Remote to transfer the file to TTI

Timer Task 2Interval – 3 minutesTask description – Read incremental data and file destination.tar

If destination.tar has been modified since last check, interpret hex messages andwrite to U of A database

TxDOT

TTI

U of A Database

Database: FTMS File

• Hex file template

Record 1

Record 2

Record 3

.

.

.

.

Database Objects

• Each of this objects will be populated with data read from the hex file

• Examples Sensor ID Time (hour, minute and

second) Date (day, month and year) Volume, speed and

occupancy

PostGreSQL Database

Database ResultsSpeed

Database Results Volume

Database Results Cumulative Volume

GUI: Sensor Locations

GUI: Sensor Selection

GUI: Information for Selected Sensor

Problems Encountered

• Modem communication Unreliable nature of modem communication Unreliable data transfer Difficulty in running programs together

• Must stop program transfers to address difficulties

When modems do not respond… • Manual intervention at both TxDOT and TTI is required• Programs must be stopped to address difficulties

Problems Encountered (cont’d)

• Midnight transfer Reading of new file at TxDoT Data from TTI has to be inserted into a new table. This switch has been tested but a period of no data

for several hours after midnight has been detected. The problem has been resolved as of last visit to

TransVista