probe based arterial travel time estimation and prediction – a case study of using chicago transit...
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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
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
t.
N
Aberde
en St.
Throop S
t.
Morgan S
t.
Loom
is St.
Loom
is St.
Lafl in St.
W. MADISON ST.
RA
CIN
E S
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AS
HLA
ND
AV
E.
DA
ME
N A
VE
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Paul ina S
t.
Wo
od St.
UnitedCenter
Hoyne
Av e.
Leavi tt S
t.
Oa
kley Blv d.
OG
DEN AVE.
RA
CIN
E S
T.
Senior Apartment
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
Historical bus travel
Historical car travel
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
30
25
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15
10
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
eed
(mp
h)
Distance into block (feet)a) EA
Leav
itt
Hoyn
e
Dam
en
Unite
d.Ce
nter
Woo
d
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
orerror vect
matrixn informatioinput
matrixn transitio
n vectorobservatio
vectorstate,
I
e
G
F
x
z
z0Ix
GeFzz
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
t
B
C
B
z
1t
t
t
t
C
C
B
z
1
1
t
t
t
t
t
C
B
C
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
Historical relationships
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
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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Bus
sp
eed
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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
vel t
ime
(sec
ond
s)
Index of 15-minute interval
Observed Linearly estimated State space estimated
WBPM
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360
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Car
tra
vel t
ime
(sec
ond
s)
Index of 15-minute interval
Observed Linearly estimated State space estimated
EBAM
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360
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Car
tra
vel t
ime
(sec
ond
s)
Index of 15-minute interval
Observed Linearly estimated State space estimated
EBPM
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360
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Car
tra
vel t
ime
(sec
ond
s)
Index of 15-minute interval
Observed Linearly estimated State space estimated
Part III: Short-Term Travel Time Prediction
Historical relationships
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
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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5:30pm 5:45pm 6:00pm 6:15pm
Trav
el t
ime
(sec
ond
s)
TimePredicted Observed
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Trav
el t
ime
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TimePredicted Observed
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el t
ime
(sec
ond
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TimePredicted Observed
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5:30pm 5:45pm 6:00pm 6:15pm
Trav
el t
ime
(sec
ond
s)
TimePredicted Observed
Eastbound, September 11th Westbound, September 11th
Eastbound, September 12th Westbound, September 12th
Eastbound, September 13th Westbound, September 13th
Eastbound, September 14th Westbound, September 14th
240
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330
5:30pm 5:45pm 6:00pm 6:15pm
Trav
el t
ime
(sec
ond
s)
TimePredicted Observed
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300
330
5:30pm 5:45pm 6:00pm 6:15pm
Trav
el t
ime
(sec
ond
s)
TimePredicted Observed
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300
330
5:30pm 5:45pm 6:00pm 6:15pm
Trav
el t
ime
(sec
ond
s)
TimePredicted Observed
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270
300
330
5:30pm 5:45pm 6:00pm 6:15pm
Trav
el t
ime
(sec
ond
s)
TimePredicted Observed
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
160
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410
460
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
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310
360
410
460
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
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210
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310
360
410
460
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
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210
260
310
360
410
460
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
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210
260
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360
410
460
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
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410
460
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
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360
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460
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
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360
410
460
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
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360
410
460
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
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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
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 (%
)
200
150
100
50
0
Flow rate
Departure time (seconds after simulation started)
500045004000350030002500200015001000
Tra
vel t
ime
(sec
onds
)
600
500
400
300
200
100
Bus travel time
Departure time (seconds after simulation started)
500045004000350030002500200015001000
Tra
vel t
ime
(sec
onds
)
600
500
400
300
200
100
Car travel time
Estimated car travel time (traffic demand surge)
61
180
230
280
330
380
1 2 3 4 5
Car
travel tim
e (
seco
nd
s)
15-min interval
Simulated Estimated
Run 2
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
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
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
Departure time (seconds after simulation started)
500045004000350030002500200015001000
Tra
vel t
ime
(sec
onds
)
700
600
500
400
300
200
100
Car travel time
Departure time (seconds after simulation started)
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