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 Engineering
Institute 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 Applications
 Type of applications
 Advanced Traffic Management System (ATMS)
 Advanced Traveler’s Information System (ATIS)
 Area of applications
 Freeway
 Highway
 Arterial/Urban streets
Classification of Applications
Source: RITA, U.S. DOT
The Focus of Today’s Talk
 Is travel time estimation and prediction.
 Travel time data collection/sources
 Traffic sensors, e.g., inductive loop detector
 Floating car method/probe vehicle
 Cell phone signals
Travel Time Estimation and Prediction
Estimation
Prediction
Instantaneous
prediction
Space
Travel time
Travel time
Known traffic
conditions
Past
Short-term prediction
Travel time
Long-term prediction
Travel time
Unknown traffic
conditions
Now
1 hour
Future time
Travel Time Prediction
Source: Vlahogianni
et al. 2004
Traffic Forecasting Models
(source: You and Kim, 2003)
Type
Model
Advantages
Disadvantages
Statistical
models
Historical Profile Approaches
-Relatively easy to
implement
-Fast execution speed
-Difficult to respond to
traffic incidents
Time series models
-Many applications
-Well-defined model
formulation
-Difficult to handle
missing data
- Complexity of search
for “neighbors”
recognition
-Pattern recognition
-No assumption of
underlying relationship
Hybrid models
-Clustering+linear regression
-Smaller and more efficient
network
-Not yet many
implementations
-ARMA/ARIMA
-State Space/Kalman filter
Nonparametric regression
-Dynamic clustering/pattern
-ARIMA+SOM
-Fuzzy logic+GA
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 microsimulation
Artificial
Intelligence
Neural Networks
-Suitable for complex, nonlinear relationships
-Forecasting in black box
-Training procedure
Performance of Forecasting Models
Historical Profile Approach
Time Series Analysis
Source: You and Kim, 2003
Urban Arterial Travel Time Prediction
 Largely in void because of the challenging
nature
 Complex urban traffic environment
 Lack of continuous traffic data/measurements
 Most existing applications are focused in the area
of ATMS rather than ATIS


Qualitative versus quantitative measures
Other traffic parameters
Bus Probe Based Arterial Travel Time
Estimation and Prediction
 Research 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 Literature
 Limited research effort – 6 bus probe studies
 Buses 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 bus
travel
Real-time
Predicted
bus travel
bus travel
Real-time
Predicted
car travel
car travel
Now
Future
Historical
relationships
Historical car
travel
Past
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
Archived AVL
Structure
Data
Data transmission
Usually location-driven
Useful information
Methodology
Usually time-driven
Upload within the range
Transmit via wireless
of the wireless antenna at cellular modems in
garages
real-time
Inclusive information More detailed
Bus probe
applications
Real-time AVL
Less Detailed
Travel time, travel
Instant speed, time
distance, stop dwell time, stamp, and heading
number of stops made
direction
Travel time based
Speed based
• 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
In Real-time Bus AVL:
Poll during a bus trip
Bus trip 1 . . .
. . .. . . . .. . . . . . . .. . . . . . . . . . . .
Bus trip 2 . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . .
P
Q
Intrinsic measurement errors
In addition, no stop dwell time is available in realtime AVL
Field Study Segment
8695
8037
7379
6705
6103
5472
4707
4014
3448
W. MADISON ST.
7310
8123
AV
E
DE
N
G
O
Peoria St.
6646
Morgan St.
5984
Aberdeen St.
5270
RACINE ST.
4680
Throop St.
4013
Loomis St.
3329
Laflin St.
2672
ASHLAND AVE.
.
Senior Apartment
Wood St.
DAMEN AVE.
Hoyne Ave.
Leavitt St.
Oakley Blvd.
0
2039
1330
665
Eastbound: Distance into block (feet)
N
RACINE ST.
United
Center
Westbound: Distance into block (feet)
2084 1498
643
0
Loomis St.
Paulina St.
W. MADISON ST.
2780
8673
Bus stop
Signalized intersection
Data Collection
 Bus: 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 bus
travel
Real-time
Predicted
bus travel
bus travel
Real-time
Predicted
car travel
car travel
Now
Future
Historical
relationship
Historical car
travel
Past
Spatial Profiles of Bus and Car Speeds
45
EB
40
Car
Bus
35
Speed (mph)
30
25
20
15
10
5
0
0
1,000
2,000
3,000
4,000
5,000
Distance into block (feet)
a) EP
6,000
7,000
8,000
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-stoponly
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
Controlledintersection
At posted bus
stops where
general vehicle
traffic is not
controlled.
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.
45
40
Speed (mph)
35
30
25
20
15
10
5
0
0
1,000
2,000
3,000
4,000
5,000
Distance into block (f eet)
a) EA
Total: EB 29 links + WB 29 links
6,000
7,000
8,000
Peoria
Morgan
Aberdeen
Racine
Throop
Loomis
Laflin
Ashland
Senior Apt.
Paulina
Wood
United.
Center
Damen
Hoyne
Leavitt
Heuristic Engineering Segmentation
Three Forecasting Models Applied
 Were 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 = Xcβc + εc
yb = Xbβb + εb
 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.
(iii) State Space Model
In essence, SSM uses the observed trajectory of one
object to predict the unknown states of the same or a
different object
z t 1  Fz t  Ge t 1

x t  I 0z t
where, z t  state vector
x t  observation vector
F  transitio n matrix
G  input informatio n matrix
e t  error vector
I  unity matrix
VAR
Estimation
Smallest
AIC?
 Bt 
xt   
Ct 
zt
zt could be:
 Bt 
B


t
C 
 Bt 


 t 


z

z

C
z t   Ct  , t  t  , t  B  ,
t 1


 Bt 1 
Ct 1 
C
 t 1 
Canonical correlation
analysis
I (Determine state
vector z)
Significant
correlation?
State vector z
II
State equation estimation
(F, G, Σ)
etc.
III
Estimates of Z
Data used in SSM
 Spatial 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.
Base Model Results: (i) Estimation from MLR
Time
Period
Parameter Estimates
N
Root
MSE
Adj. R-Sq.
2 hours
58
3.2190
Pooled
10:30am11:30am
5:30pm6:30pm
116
15-Minute Pooled
Model
10:30am10:45am
10:45am11:00am
Model
2-Hour
Model
1-Hour
Model
…
6:00pm6:15pm
6:15pm6:30pm
Intercept
BusStopOnly
Signal
0.6348
5.28
10.91
4.95
4.6685
0.4268
5.83
10.39
4.85
58
5.0027
0.3350
6.37
9.187
4.77
58
4.3720
0.5089
5.28
11.58
4.92
464
5.9489
0.3412
5.58
10.95
5.30
58
7.2325
0.1578
7.25
8.18
5.21
58
5.3749
0.3504
5.92
10.43
4.44
…
…
…
…
…
…
58
5.2335
0.4438
5.07
12.21
5.28
58
6.6157
0.2568
4.41
9.25
7.02
Estimated Car Travel Time from MLR
Time Period
Car travel time (seconds)
Eastbound
Westbound
Error
Est’d
Obs’d
Est’d
Obs’d
(%)
Error
(%)
2 Hours
285
289
1.38
285
293
2.73
1- Hour
Model
Pooled
10:30am-11:30am
5:30pm-6:30pm
277
276
279
289
290
289
4.15
4.83
3.46
282
283
281
293
288
298
3.75
1.74
5.70
15-Minute
Model
Pooled
10:30am-10:45am
10:45am-11:00am
11:00am-11:15am
11:30am-11:45am
5:30pm-5:45pm
5:45pm-6:00pm
6:00pm-6:15pm
6:15pm-6:30pm
282
257
291
287
280
298
284
289
272
289
293
302
283
282
293
297
282
284
2.42
12.29
3.64
1.41
0.71
1.71
4.38
2.48
4.23
287
294
273
269
332
268
289
278
282
293
278
289
284
300
289
315
282
302
2.05
5.76
5.54
5.28
10.67
7.27
8.25
1.42
6.62
Model
2-Hour
Model
(ii) Estimation of SUR Models
Model
Time
Period
2-Hour
Model
2 Hours
1-Hour
Model
Pooled
Method
OLS
0.4625
SUR
OLS
0.2497
SUR
10:30am11:30am
OLS
0.2981
SUR
5:30pm6:30pm
OLS
SUR
Parameter Estimates
Cross
Corr
0.2127
Intercept
Midblock
BusStop
Only
Parking
Aera
Nlane
14.88
7.53
9.12
4.14
-
14.83
7.58
9.22
4.15
-
15.31
7.47
8.93
4.41
-
15.30
7.47
8.95
4.41
-
17.08
6.54
7.68
-
-
17.08
6.53
7.66
-
-
8.54
8.70
10.47
4.76
3.81
9.06
8.68
10.46
5.00
3.43
Estimated Car Travel Time from SUR
Car travel time (seconds)
Model
2-Hour Model
1- Hour
Model
15-Minute
Model
Eastbound
Time Period
Westbound
Error
(%)
Estimated
1.04
288
289
3.46
282
293
3.75
277
290
4.48
277
288
3.82
5:30pm-6:30pm
289
289
0.00
285
298
4.36
Pooled
277
289
4.15
280
293
4.44
10:30am-10:45am
262
293
10.58
263
278
5.40
10:45am-11:00am
276
302
8.61
276
289
4.50
11:00am-11:15am
273
283
3.53
273
284
3.87
11:30am-11:45am
289
282
2.48
289
300
3.67
5:30pm-5:45pm
280
293
4.44
283
289
2.08
5:45pm-6:00pm
291
297
2.02
285
315
9.52
6:00pm-6:15pm
288
282
2.13
283
282
0.35
6:15pm-6:30pm
293
284
3.17
285
302
5.63
Estimated
Observed
2 Hours
286
289
Pooled
279
10:30am-11:30am
Observed
293
Error
(%)
1.71
(iii) Speed Estimation Results from SSM
33
34
Estimated Car Travel Time from SSM
Car travel time (seconds)
Segmentation
10-feet
150-feet
Model
Eastbound
Estimated Observed
Error (%)
Westbound
Estimated Observed
Error (%)
2-Hour
289
289
0.00
290
293
1.02
10:30am-11:30am
5:30pm-6:30pm
286
287
290
289
1.38
0.69
285
295
288
298
1.04
1.01
2-Hour
292
289
1.04
293
293
0.00
10:30am-11:30am
5:30pm-6:30pm
288
296
290
289
0.69
2.42
288
298
288
298
0.00
0.00
10:30am-10:45am
10:45am-11:00am
11:00am-11:15am
11:30am-11:45am
5:30pm-5:45pm
5:45pm-6:00pm
6:00pm-6:15pm
6:15pm-6:30pm
275
287
288
310
300
287
292
290
295
293
280
293
293
297
282
284
6.92
2.05
2.97
5.87
2.37
3.32
3.46
2.11
275
287
288
310
289
305
295
315
278
286
296
300
292
297
304
301
1.02
0.21
2.58
3.30
1.00
2.53
2.93
4.70
Findings
 Statistically 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 bus
travel
Real-time
Predicted
bus travel
bus travel
Real-time
Predicted
car travel
car travel
Now
Future
Historical
relationships
Historical car
travel
Past
Approach
 Linear model
Updated
bus speed
Linear
bus-car
relationship
Concurrent
car speed
 State space model
Updated
bus speed
Historical car
speed
State space
model
Concurrent
car speed
Bus Speed Updating
Historical
database
Confidence
interval (C.I.)
New bus speed (b)
Is b in the
C.I.?
No
Bayesian
updating
Yes
Historical
mean
Example
30
Bus speed (mph)
25
20
15
10
5
0
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
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
360
Car travel time (seconds)
340
320
300
280
260
240
1
2
3
4
5
6
7
8
9
10
11
12
Index of 15-minute interval
Observed
Linearly estimated
State space estimated
13
14
15
16
WBPM
360
Car travel time (seconds)
340
320
300
280
260
240
1
2
3
4
5
6
7
8
9
10
11
12
Index of 15-minute interval
Observed
Linearly estimated
State space estimated
13
14
15
16
EBAM
360
Car travel time (seconds)
340
320
300
280
260
240
1
2
3
4
5
6
7
8
9
10
11
12
Index of 15-minute interval
Observed
Linearly estimated
State space estimated
13
14
15
16
EBPM
360
Car travel time (seconds)
340
320
300
280
260
240
1
2
3
4
5
6
7
8
9
10
11
12
Index of 15-minute interval
Observed
Linearly estimated
State space estimated
13
14
15
16
Part III: Short-Term Travel Time Prediction
Historical bus
travel
Real-time
Predicted
bus travel
bus travel
Real-time
Predicted
car travel
car travel
Now
Future
Historical
relationships
Historical car
travel
Past
Approach
Step 1. Bus speed prediction (State Space Model)
Updating --> forecasting --> updating
30
A
Bus speed (mph)
25
20
15
10
5
B
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47
Time (15 minutes)
Historical mean
Newly observed in a day
Step 2. Car speed prediction (linear regression) using
predicted bus speeds
330
Travel time (seconds)
Travel time (seconds)
Car Travel Time Prediction
300
270
240
5:30pm
5:45pm
6:00pm
Time
Predicted
Observed
330
300
270
240
6:15pm
5:30pm
330
300
270
240
5:30pm
5:45pm
6:00pm
Time
Predicted
Observed
6:15pm
Westbound, September 11th
Travel time (seconds)
Travel time (seconds)
Eastbound, September 11th
5:45pm
6:00pm
Time
Predicted
Observed
6:15pm
Eastbound, September 12th
330
300
270
240
5:30pm
5:45pm
6:00pm
Time
Predicted
Observed
6:15pm
Westbound, September 12th
Travel time (seconds)
Travel time (seconds)
330
300
270
240
5:30pm
5:45pm
6:00pm
Time
Predicted
Observed
330
300
270
240
6:15pm
5:30pm
330
300
270
240
5:30pm
5:45pm
6:00pm
Time
Predicted
Observed
6:15pm
Eastbound, September 14th
6:15pm
Westbound, September 13th
Travel time (seconds)
Travel time (seconds)
Eastbound, September 13th
5:45pm
6:00pm
Time
Predicted
Observed
330
300
270
240
5:30pm
5:45pm
6:00pm
Time
Predicted
Observed
6:15pm
Westbound, September 14th
Bus Probe Micro-Simulation Study
 Three scenarios:
1. Drastic increase in traffic demand
2. Road block due to traffic incident.
3. Drastic increase in bus ridership along the route
Testbed: Roosevelt Road
Westbound: Distance into block (feet)
5356
4739
4230
3390
2698 2337
1198
0
4434
5330
N
ve
.
an
dA
Is l
ue
Bl
Union Ave.
Halsted St.
Morgan St.
RACINE ST.
Throop St.
Loomis St.
Laflin St.
ASHLAND AVE.
860
May St.
W. ROOSEVELT AVE.
0
1792
423
1270
1733
Eastbound: Distance into block (feet)
2379
2954 3279
3951
Bus stop
Signalized intersection
Network representation in VISSIM
360
310
260
210
160
2
3
4
Car travel time (seconds)
Car travel time (seconds)
Run 1
410
1
460
Run 2
410
360
310
260
210
160
5
1
15-min interval
Estim ated
460
Run 3
360
310
260
210
160
2
3
4
Run 4
360
310
260
210
160
1
Run 5
360
310
260
210
160
4
360
310
260
210
160
1
310
260
210
160
4
Car travel time (seconds)
Car travel time (seconds)
360
Estim ated
Run 8
360
310
260
210
160
5
1
2
3
Run 9
360
310
260
210
160
4
15-min interval
Estim ated
5
Car travel time (seconds)
Sim ulated
410
Sim ulated
5
410
Estim ated
3
4
4
5
15-min interval
460
2
3
460
15-min interval
1
2
Sim ulated
Run 7
Sim ulated
Estim ated
Run 6
Estim ated
3
5
410
5
410
2
4
15-min interval
460
1
3
460
15-min interval
Sim ulated
2
Sim ulated
Car travel time (seconds)
Car travel time (seconds)
Estim ated
3
Estimated
410
5
410
2
5
15-min interval
460
1
4
460
15-min interval
Sim ulated
3
Simulated
410
1
2
15-min interval
Car travel time (seconds)
Car travel time (seconds)
Simulated
Car travel time (seconds)
Scenario 3 – Large
increase in bus
ridership:
Estimated car travel
time
460
Estim ated
460
Run 10
410
360
310
260
210
160
1
2
3
4
15-min interval
Sim ulated
Estim ated
5
Summary of Major Findings
 First 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 controlledintersection 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 traveltime based one.
Future Research
 Need better base models under various traffic
conditions.
 Sample size issue should be further investigated
 Issues with spatial and temporal coverage
 The transferability and scalability of the proposed bus
probe development framework and algorithms should
be further investigated.
Acknowledgements
 Chicago 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
Eastbound Madison Street, 10:30am – 11:30am
6
30
Mean =601.
43
Std. Dev.
=99.747
N =21
5
4
20
Mean =618.
32
Std. Dev.
=103.589
N =171
Mean =289.
89
Std. Dev.
=24.839
N =36
15
20
3
2
Frequency
Frequency
Frequency
Bus stop dwell time is not available from the real-time AVL system
10
10
5
1
0
0
240
360
480
600
720
840
960
Bus travel time (seconds)
a) 9 days
1080
0
240
360
480
600
720
840
960 1080
Bus travel time (seconds)
b) 4 months
240
360
480
600
720
840
960 1080
Car travel time (seconds)
c) 9 days
Poll during a bus trip
Bus trip 1 . . .
. . .. . . . .. . . . . . . .. . . . . . . . . . . .
Bus trip 2 . . . . . . . . Intrinsic
.. . . . measurement
. . . . . . . . . .. errors
. .. . . . . ..
P
Q
58
Past Bus Probe Studies
Study
Objective
Bus Data
Bae (1995)
Travel time Field
and speed
collected,
probe
locationdriven
King County, WA Speed
Real-time
(Dailey et al. 1999- probe
AVL, time2005)
driven
Orange County,
CA (Hall et al.
1999-2000)
Delaware DOT
(Chakroborty and
Kikuchi, 2004)
Congestion Selfdetection
designed
AVL system
Travel time Field
probe
collected,
locationdriven
TriMet (Bertini
Travel time Archived
and
and speed
AVL,
Tantiyanugulchai, probe
location2004)
driven
Central Ohio
Travel time Real-time
(Coifman and
and speed
AVL, timeKim, 2006)
probe
driven
Car
Data
Test
vehicle
Model
Simple linear
regression,
ANN
Facility
Conclusion
Type
Urban streets Buses can be
probes
Loop
detector
Kalman filter,
Speed
mapping
GPS
floating
car
Test
vehicle
Simple linear
regression
GPS
floating
car
Simple linear
reverse
regression
Urban
arterials
Buses can be
probes
Loop
detector
Filtering
Freeways
Bus speeds are
consistent with
car speeds 59
Simple linear
regression
Freeways
Buses are used
and principle as speed
arterials
probes in
reality
Urban streets Buses are
imperfect
probes
Urban
Bus probe is
arterials
promising
Traffic demand surge
600
Flow rate
Bus travel time
500
150
Travel time (seconds)
Percentage of existing flow rate (%)
200
100
50
400
300
200
100
0
1000 1500 2000 2500 3000 3500 4000 4500 5000
Departure time (seconds after simulation started)
600
1000 1500 2000 2500 3000 3500 4000 4500 5000
Departure time (seconds after simulation started)
Car travel time
Travel time (seconds)
500
400
300
200
100
1000 1500 2000 2500 3000 3500 4000 4500 5000
Departure time (seconds after simulation started)
60
280
230
180
2
3
4
Car travel time (seconds)
Car travel time (seconds)
330
1
Run 2
380
330
280
230
180
5
1
15-min interval
Estim ated
Run 3
330
280
230
180
2
3
4
330
280
230
180
1
330
280
230
180
4
280
230
180
1
230
180
4
Car travel time (seconds)
Car travel time (seconds)
280
Estim ated
280
230
180
1
2
3
4
5
15-min interval
330
280
230
180
4
15-min interval
Estim ated
5
Car travel time (seconds)
Sim ulated
Run 9
Sim ulated
5
330
Estim ated
3
4
Run 8
5
380
2
3
380
15-min interval
1
2
Sim ulated
330
Sim ulated
Estim ated
330
Estim ated
3
5
15-min interval
Run 7
2
4
Run 6
5
380
1
3
380
15-min interval
Sim ulated
2
Sim ulated
Car travel time (seconds)
Car travel time (seconds)
Estim ated
3
Estimated
15-min interval
Run 5
2
5
Run 4
5
380
1
4
380
15-min interval
Sim ulated
3
Simulated
380
1
2
15-min interval
Car travel time (seconds)
Car travel time (seconds)
Simulated
Car travel time (seconds)
Estimated car
travel time
(traffic demand
surge)
Run 1
380
Estim ated
Run 10
380
330
280
230
180
1
2
3
4
5
15-min interval
Sim ulated
Estim ated
61
Scenario 2 – Road Block
1
Incident (0:No; 1:Yes)
Incident
0
1000 1500 2000 2500 3000 3500 4000 4500 5000
Departure time (seconds after simulation started)
700
700
Bus travel time
600
Travel time (seconds)
Travel time (seconds)
600
500
400
300
500
400
300
200
200
100
100
1000 1500 2000 2500 3000 3500 4000 4500 5000
Departure time (seconds after simulation started)
Car travel time
1000 1500 2000 2500 3000 3500 4000 4500 5000
Departure time (seconds after simulation started)
62
Run 1
410
360
310
260
210
160
1
2
3
4
Car travel time (seconds)
Car travel time (seconds)
Estimated car travel
460
460
Run 2
410
360
310
260
210
160
5
1
15-min interval
Run 3
410
360
310
260
210
160
2
3
4
Run 4
360
310
260
210
160
1
Run 5
360
310
260
210
160
4
360
310
260
210
160
1
310
260
210
160
4
Car travel time (seconds)
Car travel time (seconds)
360
Estim ated
Run 8
360
310
260
210
160
5
1
2
3
Run 9
360
310
260
210
160
4
15-min interval
Estim ated
5
Car travel time (seconds)
Sim ulated
410
Sim ulated
5
410
Estim ated
3
4
4
5
15-min interval
460
2
3
460
15-min interval
1
2
Sim ulated
Run 7
Sim ulated
Estim ated
Run 6
Estim ated
3
5
410
5
410
2
4
15-min interval
460
1
3
460
15-min interval
Sim ulated
2
Sim ulated
Car travel time (seconds)
Car travel time (seconds)
Estim ated
3
Estimated
410
5
410
2
5
15-min interval
460
1
4
460
15-min interval
Sim ulated
3
Simulated
Car travel time (seconds)
Car travel time (seconds)
Estim ated
460
1
Car travel time (seconds)
time
Simulated
2
15-min interval
Estim ated
460
Run 10
410
360
310
260
210
160
1
2
3
4
15-min interval
Sim ulated
Estim ated
5
63
Reasons
 Updating algorithm puts too much weight on the historical
average
 Bus-car relationship
 Linear base bus-car model used
 Nonlinear bus-car relationship in reality
40
Baseline
Delta = car speed - bus speed (mph)
Delta = car speed - bus speed (mph)
40
30
20
10
0
-10
-20
Unexpected incident
30
20
10
0
-10
-20
0
10
20
Bus speed (mph)
30
40
0
10
20
Bus speed (mph)
30
40
64