Probe based Arterial Travel Time Estimation and Prediction – A Case Study of Using Chicago Transit Authority Bus Fleet as Probes Jie (Jane) Lin, Ph.D

Probe based Arterial Travel Time Estimation and Prediction – A Case Study of Using

Chicago Transit Authority Bus Fleet as Probes Jie (Jane) Lin, Ph.D.Associate Professor

Department of Civil and Materials EngineeringInstitute for Environmental Science and Policy

University of Illinois at Chicago

September 29, 2009 CTS-IGERT Seminar

National ITS Architecture

Source: RITA, U.S. DOT

ITS ApplicationsType of applications

Advanced Traffic Management System (ATMS)Advanced Traveler’s Information System (ATIS)

Area of applicationsFreewayHighwayArterial/Urban streets

Classification of Applications

Source: RITA, U.S. DOT

The Focus of Today’s TalkIs travel time estimation and prediction.

Travel time data collection/sourcesTraffic sensors, e.g., inductive loop detectorFloating car method/probe vehicleCell phone signals

Travel Time Estimation and Prediction

Unknown traffic conditions

Future time

Estimation

Instantaneous prediction

Short-term prediction Long-term prediction

Past Now

Known traffic conditions

Prediction

1 hour

Travel time Travel timeTravel timeTravel time

Space

Travel Time Prediction

Source: Vlahogianni et al. 2004

Traffic Forecasting Models (source: You and Kim, 2003)

Type Model Advantages DisadvantagesStatistical models

Historical Profile Approaches -Relatively easy to implement-Fast execution speed

-Difficult to respond to traffic incidents

Time series models-ARMA/ARIMA-State Space/Kalman filter

-Many applications-Well-defined model formulation

-Difficult to handle missing data

Nonparametric regression-Dynamic clustering/pattern recognition

-Pattern recognition-No assumption of underlying relationship

- Complexity of search for “neighbors”

Hybrid models-Clustering+linear regression-ARIMA+SOM-Fuzzy logic+GA

-Smaller and more efficient network

-Not yet many implementations

Computer simulation

Traffic simulation -Possible to simulate various situations

- Requires traffic flow prediction in priori

Mathematical optimization

Dynamic Traffic Assignment -Various types of models available and well known

-Not suitable for micro-simulation

Artificial Intelligence

Neural Networks -Suitable for complex, non-linear relationships

-Forecasting in black box-Training procedure

Performance of Forecasting Models

Source: You and Kim, 2003

Historical Profile Approach

Time Series Analysis

Urban Arterial Travel Time PredictionLargely in void because of the challenging

natureComplex urban traffic environmentLack of continuous traffic data/measurementsMost existing applications are focused in the area

of ATMS rather than ATISQualitative versus quantitative measuresOther traffic parameters

Bus Probe Based Arterial Travel Time Estimation and PredictionResearch Questions

Can real-time AVL bus data be used to identify any form of interaction (or relation) between buses and cars in a traffic stream on a signalized urban street? If yes, what is the best way to quantify that?

Is it possible to use real-time incoming bus data to derive concurrent car travel time in recurring or non-recurring traffic conditions?

Is it possible to use bus probes to forecast future car travel time?

Findings in Bus Probe LiteratureLimited research effort – 6 bus probe studiesBuses can be probe vehicles.

On freeway and suburban highway: Real-time AVL buses are used as complementary speed sensors reporting real-time speeds in King County, WA.

On urban street: Statistically significant relationships between archived AVL buses and general vehicles were identified.

Bus stop dwell time is the most significant noise and should be excluded in directly relating bus travel time to general vehicle travel time.

Linear regression is a common method in quantifying bus-car relationship.

Travel Time Prediction Framework

Historical relationships


Past Now Future

Historical bus travel

Historical car travel

Real-time

bus travel

Real-time

car travel

Predicted

bus travel

Predicted

car travel

Historic estimation Instantaneous prediction Future prediction: short-term (15 min) and long term (>1 hr)

Type of Input Data: Archived AVL vs. Real-time AVL

• Real-time AVL data was used in the study

Archived versus Real-time AVL

(a) Archive AVL (b) Real-time AVL

Travel Time versus Speed as Predictor

Bus trip 1 . . . . . .. . . . .. . . . . . . .. . . . . . . . . . . .Bus trip 2 . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . .

P Q

Intrinsic measurement errors

Poll during a bus trip

In Real-time Bus AVL:

In addition, no stop dwell time is available in real-time AVL

Field Study Segment

Peoria S

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N

Aberde

en St.

Throop S

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Morgan S

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Loom

is St.

Lafl in St.

W. MADISON ST.

RA

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AS

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Paul ina S

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Leavi tt S

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0 665 1330 2039 2672 3329 4013 4680 5270 5984 6646 7310 8123 8673Eastbound: Distance into block (feet)

0643149820842780344840144707547261036705737980378695Westbound: Distance into block (feet)

W. MADISON ST.

Signalized intersection

Bus stop

Data CollectionBus: real-time AVL data from Route #20 (Madison)

covering about 4 months from June 1st – September 19th, 2007.

Car: GPS-equipped test vehicle data covering 9 weekdays (September 4th – 14th, 2007), 2 hours a day (10:30am – 11:30am, 5:30pm-6:30pm). The GPS records car speed, location and time every 0.1 seconds.

Street configuration.Bus stop configuration.Intersection control strategy .

Part I: Building Historical Bus–Car Relationship – base model

Historical relationshipHistorical

relationship

Past Now Future



Real-time

bus travel

Real-time

car travel

Predicted

bus travel

Predicted

car travel

Spatial Profiles of Bus and Car Speeds

8,0007,0006,0005,0004,0003,0002,0001,0000

45

40

35

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15

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5

0

BusCar

Distance into block (feet)a) EP

Spe

ed (

mph

)

EB

Three Types of Location (Links)

Number Name Location Relationship between bus speed and car speed

Representativeness of car speed by bus

speed

1 Midblock The portion of street that is outside the influence of a bus stop and/or intersection

1) Vehicles travel at relatively high speeds under normal and undisturbing conditions;2) Cars generally travel faster than buses.

Good, expected similar travel patterns between buses and cars.

2 Bus-stop-only

At posted bus stops where general vehicle traffic is not controlled.

Buses stop upon passengers’ requirements; while general vehicles may travel at normal speeds if not obstructed by buses.

Poor, expected dissimilar patterns between buses and cars.

3 Controlled- intersection

At controlled intersections, with or without a bus stop.

Both buses and cars may experience full stops or low-speed travel.

Most probably not good, hard to tell.

Heuristic Engineering Segmentation

0

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45

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

Sp

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h)

Distance into block (feet)a) EA

Leav

itt

Hoyn

e

Dam

en

Unite

d.Ce

nter

Woo

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Paul

ina

Seni

or A

pt.

Ashl

and

Laflin

Loom

is

Thro

op

Racin

e

Aber

deen

Peor

ia

Mor

gan

Total: EB 29 links + WB 29 links

Three Forecasting Models AppliedWere tried and compared:

Multiple linear regression 2-hour aggregate model 1-hour aggregate models 15-minute models

Seemingly unrelated regression 2-hour aggregate model 1-hour aggregate models 15-minute models

State-space model

(i) Multiple Linear Regression (MLR)y = Xβ + ε

Variable Name Definition or value

y Delta Car speed – Bus speed

X Midblock 1, if a link is midblock link; 0, otherwise.

Signal 1, if a link is signalized intersection link; 0, otherwise.

StopSign 1, if a link is Stop sign-controlled intersection link; 0, otherwise.

BusStopOnly 1, if a link is bus-stop-only link; 0, otherwise.

busBay 1, if a link is bus bay stop link; 0, otherwise.

ParkingArea 1, if a link is within the United Center parking area; 0 otherwise.

Nlane 1 or 2, Number of lanes.

(ii) Seemingly Unrelated Regression (SUR)

yc is car speed, is yb bus speed, Xc and Xb are explanatory variables.

Xc and Xb may not sufficiently explain the variations and some common factors that affect both car speed and bus speed may be omitted. Thus the errors can be correlated.

The SUR model and the associated generalized least square (GLS) estimation will take the correlations among the errors into consideration and may produce better results.

yc = Xcβc + εc

yb = Xbβb + εb

(iii) State Space ModelIn essence, SSM uses the observed trajectory of one object to predict the unknown states of the same or a different object

matrixunity

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matrixn informatioinput

matrixn transitio

n vectorobservatio

vectorstate,

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e

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z

z0Ix

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t

t

t

tt

1tt1t

where

Estimation

zt could be:

, , ,

etc.

VAR

Canonical correlation analysis

Significant correlation

?

Smallest AIC?

State vector z

State equation estimation (F, G, Σ)

Estimates of Z

I (Determine state vector z)

II

III

t

tt C

Bx tz

1t

t

t

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C

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z

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t

t

t

t

C

B

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B

z

Data used in SSMSpatial unit: equal-distance link (10ft, 150ft or 300ft) in

each direction respectively.Temporal unit: average link speed, of 2 hour, 1 hour, and

15 minutes of the nine weekdays.Stationarity is checked first; if nonstationary, differencing

of the original data series is used.

Model TimePeriod N Root

MSE Adj. R-Sq.Parameter Estimates

Intercept BusStopOnly Signal

2-Hour Model 2 hours 58 3.2190 0.6348 5.28 10.91 4.95

1-Hour Model

Pooled 116 4.6685 0.4268 5.83 10.39 4.8510:30am-11:30am 58 5.0027 0.3350 6.37 9.187 4.77

5:30pm-6:30pm 58 4.3720 0.5089 5.28 11.58 4.92

15-Minute Model

Pooled 464 5.9489 0.3412 5.58 10.95 5.3010:30am-10:45am 58 7.2325 0.1578 7.25 8.18 5.21

10:45am-11:00am 58 5.3749 0.3504 5.92 10.43 4.44

… … … … … … …

6:00pm-6:15pm 58 5.2335 0.4438 5.07 12.21 5.28

6:15pm-6:30pm 58 6.6157 0.2568 4.41 9.25 7.02

Base Model Results: (i) Estimation from MLR

Model Time Period

Car travel time (seconds)Eastbound Westbound

Est’d Obs’d Error (%) Est’d Obs’d Error

(%)2-Hour Model 2 Hours 285 289 1.38 285 293 2.73

1- Hour Model

Pooled 277 289 4.15 282 293 3.7510:30am-11:30am 276 290 4.83 283 288 1.745:30pm-6:30pm 279 289 3.46 281 298 5.70

15-Minute Model

Pooled 282 289 2.42 287 293 2.0510:30am-10:45am 257 293 12.29 294 278 5.7610:45am-11:00am 291 302 3.64 273 289 5.5411:00am-11:15am 287 283 1.41 269 284 5.2811:30am-11:45am 280 282 0.71 332 300 10.675:30pm-5:45pm 298 293 1.71 268 289 7.275:45pm-6:00pm 284 297 4.38 289 315 8.256:00pm-6:15pm 289 282 2.48 278 282 1.426:15pm-6:30pm 272 284 4.23 282 302 6.62

Estimated Car Travel Time from MLR

(ii) Estimation of SUR Models

Model Time Period Method Cross

Corr

Parameter Estimates

Intercept MidblockBusStopOnly

ParkingAera Nlane

2-Hour Model

2 Hours OLS 0.4625 14.88 7.53 9.12 4.14 -

SUR 14.83 7.58 9.22 4.15 -

1-Hour Model

Pooled OLS 0.2497 15.31 7.47 8.93 4.41 -

SUR 15.30 7.47 8.95 4.41 -

10:30am-11:30am

OLS 0.2981 17.08 6.54 7.68 - -

SUR 17.08 6.53 7.66 - -

5:30pm-6:30pm

OLS 0.2127 8.54 8.70 10.47 4.76 3.81

SUR 9.06 8.68 10.46 5.00 3.43

Model Time Period

Car travel time (seconds)Eastbound Westbound

Estimated Observed Error (%) Estimated Observed Error

(%)2-Hour Model 2 Hours 286 289 1.04 288 293 1.71

1- Hour Model

Pooled 279 289 3.46 282 293 3.7510:30am-11:30am 277 290 4.48 277 288 3.825:30pm-6:30pm 289 289 0.00 285 298 4.36

15-Minute Model

Pooled 277 289 4.15 280 293 4.4410:30am-10:45am 262 293 10.58 263 278 5.4010:45am-11:00am 276 302 8.61 276 289 4.5011:00am-11:15am 273 283 3.53 273 284 3.8711:30am-11:45am 289 282 2.48 289 300 3.675:30pm-5:45pm 280 293 4.44 283 289 2.085:45pm-6:00pm 291 297 2.02 285 315 9.526:00pm-6:15pm 288 282 2.13 283 282 0.356:15pm-6:30pm 293 284 3.17 285 302 5.63

Estimated Car Travel Time from SUR

(iii) Speed Estimation Results from SSM

33

34

Estimated Car Travel Time from SSM

Segmentation Model Estimated Observed Error (%) Estimated Observed Error (%)

10-feet 2-Hour 289 289 0.00 290 293 1.02

10:30am-11:30am 286 290 1.38 285 288 1.04

5:30pm-6:30pm 287 289 0.69 295 298 1.01

150-feet 2-Hour 292 289 1.04 293 293 0.00

10:30am-11:30am 288 290 0.69 288 288 0.00

5:30pm-6:30pm 296 289 2.42 298 298 0.00

10:30am-10:45am 275 295 6.92 275 278 1.02

10:45am-11:00am 287 293 2.05 287 286 0.21

11:00am-11:15am 288 280 2.97 288 296 2.58

11:30am-11:45am 310 293 5.87 310 300 3.30

5:30pm-5:45pm 300 293 2.37 289 292 1.00

5:45pm-6:00pm 287 297 3.32 305 297 2.53

6:00pm-6:15pm 292 282 3.46 295 304 2.93

6:15pm-6:30pm 290 284 2.11 315 301 4.70

300-feet 2-Hour 291 289 0.69 293 293 0.00

10:30am-11:30am 288 290 0.69 288 288 0.00

5:30pm-6:30pm 295 289 2.08 298 298 0.00

10:30am-10:45am 274 295 7.26 274 278 1.37

10:45am-11:00am 287 293 2.05 287 286 0.21

11:00am-11:15am 287 280 2.62 287 296 2.92

11:30am-11:45am 309 293 5.53 309 300 2.97

5:30pm-5:45pm 299 293 2.03 289 292 1.00

5:45pm-6:00pm 299 297 0.72 306 297 2.87

6:00pm-6:15pm 291 282 3.11 294 304 3.26

6:15pm-6:30pm 289 284 1.76 314 301 4.37

Car travel time (seconds)

Eastbound Westbound

FindingsStatistically significant relationships between bus and car

speeds exist.The variations of the difference between bus and car

speeds can be largely explained by two location dummy variables: “bus-stop-only” and “signal-controlled intersection”.

The SUR model did not gain much efficiency over OLS models. Nonetheless, SUR is a good method to check the correlations among errors.

The most accurate travel time estimation is obtained by using state space models.

Part II: Real-Time Travel Time Prediction



Past Now Future



Real-time

bus travel

Real-time

car travel

Predicted

bus travel

Predicted

car travel

ApproachLinear model

State space model

Updated bus speed

Linearbus-car

relationship

Concurrent car speed

Updated bus speed

Historical car speed

Concurrent car speed

State space model

Bus Speed UpdatingHistorical database

Confidence interval (C.I.)

New bus speed (b)

Is b in the C.I.?

Historical mean

Bayesian updating

Yes

No

Example

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Bus

sp

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(mp

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Link number

Lower 95% conf idence limit Upper 95% conf idence limit Mean speed (10:45am-11:00am,9/11)

Bayesian Updating

Estimated Car Travel Time - WBAM

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Car

tra

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(sec

ond

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Index of 15-minute interval

Observed Linearly estimated State space estimated

WBPM

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EBAM

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EBPM

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360

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Car

tra

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(sec

ond

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Part III: Short-Term Travel Time Prediction



Past Now Future



Real-time

bus travel

Real-time

car travel

Predicted

bus travel

Predicted

car travel

Approach

0

5

10

15

20

25

30

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47

Bus

sp

eed

(mp

h)

Time (15 minutes)

Historical mean Newly observed in a day

A

B

Step 1. Bus speed prediction (State Space Model)Updating --> forecasting --> updating

Step 2. Car speed prediction (linear regression) using predicted bus speeds

Car Travel Time Prediction

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TimePredicted Observed

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Eastbound, September 11th Westbound, September 11th




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Bus Probe Micro-Simulation StudyThree scenarios:

1. Drastic increase in traffic demand2. Road block due to traffic incident.3. Drastic increase in bus ridership along the route

Testbed: Roosevelt Road

0

Eastbound: Distance into block (feet)

Westbound: Distance into block (feet)

423 1270 1733 2379 2954 3279 3951 4434 5330

086011981792233726983390423047395356

Network representation in VISSIM

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travel tim

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Run 9

Run 2Run 1

Run 3 Run 4

Run 5 Run 6

Run 8Run 7

Run 10

Scenario 3 – Large increase in bus ridership: Estimated car travel time

Summary of Major FindingsFirst of its kind, this is a proof-of-concept study of

urban street travel time prediction using real-time bus probes.

This study finds statistically significant relationships between bus travel and car travel.

This study finds bus speed is a better predictor for arterial travel time prediction compared to bus travel time.

Bus-car speed relationship is location-specific, i.e., at midblocks, bus-stop-only location and controlled-intersection location.

Major Findings (cont’d)Difference between bus and car speeds at midblock

is minimal when traffic is either highly congested or very light, and largest when traffic condition is somewhere in between.

Drastic increase of bus ridership has minor impact on the performance of bus probes, suggesting a superiority of a speed-based approach to a travel-time based one.

Future ResearchNeed better base models under various traffic

conditions.Sample size issue should be further investigatedIssues with spatial and temporal coverageThe transferability and scalability of the proposed bus

probe development framework and algorithms should be further investigated.

AcknowledgementsChicago Transit Authority (CTA) and Clever

Devices, Ltd. for generously providing AVL data.American Society of Civil Engineers (ASCE), for

partial financial support via the 2007 Freeman Fellowship.

56

Thank You.

Travel Time

58

Bus travel time (seconds)a) 9 days

1080960840720600480360240

Freq

uenc

y

6

5

4

3

2

1

0

Mean =601.43

Std. Dev. =99.747N =21

Bus travel time (seconds)b) 4 months

1080960840720600480360240

Freq

uenc

y

30

20

10

0

Mean =618.32

Std. Dev. =103.589N =171

Car travel time (seconds)c) 9 days

1080960840720600480360240

Freq

uenc

y

20

15

10

5

0

Mean =289.89

Std. Dev. =24.839N =36

Eastbound Madison Street, 10:30am – 11:30am

Bus stop dwell time is not available from the real-time AVL system

Bus trip 1 . . . . . .. . . . .. . . . . . . .. . . . . . . . . . . .Bus trip 2 . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . .

P Q

Intrinsic measurement errorsPoll during a bus trip

Past Bus Probe Studies

59

Study Objective Bus DataCar Data

ModelFacility Type

Conclusion

Bae (1995) Travel time and speed probe

Field collected, location-driven

Test vehicle

Simple linear regression, ANN

Urban streets Buses can be probes

King County, WA (Dailey et al. 1999-2005)

Speed probe

Real-time AVL, time-driven

Loop detector

Kalman filter, Speed mapping

Freeways and principle arterials

Buses are used as speed probes in reality

Orange County, CA (Hall et al. 1999-2000)

Congestion detection

Self-designed AVL system

GPS floating car

Simple linear regression

Urban streets Buses are imperfect probes

Delaware DOT (Chakroborty and Kikuchi, 2004)

Travel time probe

Field collected, location-driven

Test vehicle

Simple linear regression

Urban arterials

Bus probe is promising

TriMet (Bertini and Tantiyanugulchai, 2004)

Travel time and speed probe

Archived AVL, location-driven

GPS floating car

Simple linear reverse regression

Urban arterials

Buses can be probes

Central Ohio (Coifman and Kim, 2006)

Travel time and speed probe

Real-time AVL, time-driven

Loop detector

Filtering Freeways Bus speeds are consistent with car speeds

Traffic demand surge

60

Departure time (seconds after simulation started)

500045004000350030002500200015001000

Per

cent

age

of e

xist

ing

flow

rat

e (%

)

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50

0

Flow rate


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vel t

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onds

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Bus travel time


500045004000350030002500200015001000

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vel t

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onds

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Car travel time

Estimated car travel time (traffic demand surge)

61

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nd

s)

15-min interval

Simulated Estimated

180

230

280

330

380

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

180

230

280

330

380

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

180

230

280

330

380

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

180

230

280

330

380

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

Run 1

Run 3 Run 4

Run 5 Run 6

Run 8Run 7

Run 10Run 9

Scenario 2 – Road Block

62Departure time (seconds after simulation started)

500045004000350030002500200015001000

Tra

vel t

ime

(sec

onds

)

700

600

500

400

300

200

100

Bus travel time


500045004000350030002500200015001000

Tra

vel t

ime

(sec

onds

)

700

600

500

400

300

200

100

Car travel time


500045004000350030002500200015001000

Inci

dent

(0:

No;

1:Y

es)

1

0

Incident

Estimated car travel

time

63

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

160

210

260

310

360

410

460

1 2 3 4 5

Car

travel tim

e (

seco

nd

s)

15-min interval

Simulated Estimated

Run 9

Run 2Run 1

Run 3 Run 4

Run 5 Run 6

Run 8Run 7

Run 10

ReasonsUpdating algorithm puts too much weight on the historical

averageBus-car relationship

Linear base bus-car model usedNonlinear bus-car relationship in reality

64

Bus speed (mph)

403020100

Del

ta =

car

spe

ed -

bus

spe

ed (

mph

)

40

30

20

10

0

-10

-20

Baseline

Bus speed (mph)

403020100

Del

ta =

car

spe

ed -

bus

spe

ed (

mph

)

40

30

20

10

0

-10

-20

Unexpected incident

Documents

Probe based Arterial Travel Time Estimation and Prediction – A Case Study of Using Chicago Transit Authority Bus Fleet as Probes Jie (Jane) Lin, Ph.D