Transcript Oscillations in congested traffic

Empirical Measurement of Freeway
Oscillation Characterisitics:
An International Comparision
Benjamin Zielke, Robert L. Bertini and Martin Treiber
87th Annual Meeting of the Transportation Research Board ▪ January 15, 2008
Outline
1. Motivation and Background
2. Illustration of Traffic Oscillations
3. Propagation Velocity
4. Oscillation Period
5. Conclusion and Outlook
2
Motivation
V ( x, t )  Ve  p( x, t )
Speed
Future Traffic Flow
Lighthill-Whitham
Model
Research
Necessary
Oscillations in Congested Regime
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Motivation
Country
A
Driver Behavior
Infrastructure
Vehicle Mix
Driving Rules
Differences
Country
B
Driver Behavior
Infrastructure
Vehicle Mix
Driving Rules
Conclusion
Traffic
Flow
Traffic
Model
Differences
Differences
Traffic
Flow
Traffic
Model
4
Oscillation Defined
Alternating fast/slow driving motions in congested traffic
Space mean speed drops, rises and drops again over time
Traffic is congested
Observed pattern propagates upstream
Hypothetical Oscillation
Amplitude Amplitude
Speed
-
•
•
•
•
Time
5
Oscillation Defined
•
•
•
•
Alternating fast/slow driving motions in congested traffic
Space mean speed drops, rises and drops again over time
Traffic is congested
Observed pattern propagates upstream
Features Examined
• Propagation velocity
• Frequency
• Amplitude: one half of the difference between the
maximum observed speed and minimum observed
speed
6
Causes of Traffic Oscillations
Traffic
oscillations
Lane changing
Car-following
behavior
7
Previous Research
1. Oscillations grow in amplitude while
propagating upstream, impact of ramps
2. Velocity 16 km/h (Germany), 20 km/h (USA)
3. Period 3–8 min (USA), 6–8 min (Canada), 5.5–
20 min (Germany)
Hypothesis
1. Propagation speed of traffic oscillations is
higher in the USA than in Germany
2. Period of traffic oscillations is country-specific
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Velocity Data
Loop detectors
M4
UK
•
•
•
•
7.0 km
No aggregation
No on-/off-ramps
7 days in 1998
OR 217
USA
•
•
•
•
11.2 km
20 s aggregation
Ramp metering
6 days in 2005
A9
Germany
•
•
•
•
14.9 km
60 s aggregation
Variable speed limit
5 days in 2002
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Travel Direction
72nd
99W
Hall
Denney
Allen
B-H Hwy
Canyon
Walker
Wilshire
US 26 EB
Barnes
Greenburg
OR 217
Scholls Fy
Kruse
380 m
1
2
1090 m
1430 m
1190 m
3
4
6
5
1060 m
930 m
920 m
7
1600 m
1070 m
8
9
1000 m 1240 m
12
710 m
1060 m
650 m
820 m
16 15 14 13
1390 m 760 m 1160 m
1000 m 810 m 1480 m
11 10 9
8
7
5
6
4
890 m 990 m
3
2
1
Travel Direction
M4
1000 m
13
11 12
Travel Direction
1480 m
17
400 m
1260 m
10
A9
410 m
Velocity Data
500 m
12
11
500 m
10
500 m
800 m
9
500 m
8
500 m
7
500 m
6
500 m
5
500 m
4
500 m
3
500 m
2
1
Loop detector station
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Methodology
1. Deviation curves for visualization
2. Cross-correlation
3. Autocorrelation
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Identification of Congestion
M4 November 2, 1998
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Identification of Congestion
Transitions
verified with
oblique curves
M4 November 2, 1998
13
Identifying Oscillations
M4 November 2, 1998
14
Identifying Oscillations via Deviation Curves
50 km/h
Traffic speed
Raw velocity over time:
oscillations not always clear
0
18:45
19:00
19:15
Time
[h]
15
Identifying Oscillations via Deviation Curves
Traffic speed
50 km/h
0
18:45
t
19:00
19:15
Time
[h]
16
Identifying Oscillations via Deviation Curves
Traffic speed
50 km/h
0
18:45
t
19:00
19:15
For time t, subtract
green area from red
area for deviation
Time
[h]
Red Area
Green Area
time
t-7,5 min
t
t+7,5 min
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Identifying Oscillations via Deviation Curves
0
18:45
t
19:00
19:15
Time
[h]
Mauch – Deviation [km]
Traffic speed
50 km/h
0
18:45
t
19:00
19:15 Time
[h]
Red Area
Green Area
time
t-7,5 min
t
t+7,5 min
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Deviation Curves
Flow direction
Detector-Position
Deviation [km]
18:45
19:00
19:15
M4 November 2, 1998
Time
[h]
19
Deviation Curves
Flow direction
Detector-Position
Deviation [km]
18:45
19:00
19:15
M4 November 2, 1998
Time
[h]
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Propagation
Velocity Upstream
[mean=14.2 km/h]
Deviation Curves
Flow direction
Detector-Position
Deviation [km]
Amplitude
Increases
18:45
19:00
19:15
M4 November 2, 1998
Time
[h]
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Proportional to
detector distance
Uncertainty Motivates Analytical Tool
Deviation
Uncertainty
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Cross-Correlation Method: Location Pairs
Data discarded for analysis
Data sets
match
Data A
(downstream)
Uncertainty
resulting in
subjective
interpretation
Data B
(upstream)
Data shifted
in time
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Detector-Position,
Deviation [km]
Identification of Propagation Velocity
Time needed
for propagation
Time
M4 November 2, 1998 Detectors 5 and 8
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Determination of Propagation Velocity
Peak 140 s
0,80.8
0.5 km
12.9 km/h
(Detector spacing)
0,60.6
correlation coefficient
Correlation
Coefficient
0,40.4
0,20.2
0,0 0
-0.2
- 0,2
-0.4
- 0,4
-0.6
0
5
5
10
10
15
15
20
20 [min]
Timeshift
25
25
30
30
35
35
40
40
Time shift
[min]
M4 November 2, 1998 Detectors 7 and 8
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Propagation Velocity Results
Analyzed
Literature
Confirmed
M4
(United Kingdom)
A9
(Germany)
OR 217
(USA)
14 km/h
16 km/h
19 – 20 km/h
16 km/h
20 km/h
Upstream Propagation, Increase in Amplitude
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Speed
Oscillation Period: Autocorrelation
Multiple of period
Same data
Time
27
Oscillation Period
Peak every 12 min
1,01
36.0 min
11.7 min
0.6
0,6
47.3 min
24.3 min
0.4
0,4
correlation coefficient
Correlation coefficient
0.8
0,8
Period ≈12 min
0.2
0,2
0,00
- 0,2
-0.2
-0.4
- 0,4
-0.6
- 0,4
-0.8
0
5
5
10
10
15
15
20
20
25
25
30
30
Timeshift [min]
35
35
40
40
45
45
50
50
M4 November 2, 1998 Detector 8
Time shift
[min]
28
Oscillation Period
M4
(United Kingdom)
A9
(Germany)
OR217
(USA)
Analyzed
8 – 12 min
[mean 9.0]
10 – 30 min
[mean 21.8]
3 – 6 min
[mean 4.0]
Literature
–
6 – 20 min
3 – 8 min
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Conclusion/Outlook
Analyzed
Freeway Sections
Generalizations
Propagation Velocity
OR 217 > A9 / M4
USA > Germany
Oscillation Period
A9 > M4 > OR 217
Germany > USA ?
Future Research
•
Additional data from more locations
•
Oscillation periods for other freeway sections
•
Alternative method for determination of oscillation period
•
Oscillation causes
•
Model applications
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Acknowledgments
•
•
•
•
•
•
•
•
•
Stuart Beale, UK Highways Agency
Tim Rees, Transport Research Laboratory, UK
Christian Mayr and Thomas Linder, Autobahndirektion Südbayern
Klaus Bogenberger and Dr. Georg Lerner, BMW Group
Oregon Department of Transportation
National Science Foundation
Steve Boice, DKS Associates
Soyoung Ahn, Arizona State University
Prof. Dirk Helbing, ETH Zürich
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Questions?
Thank You!
www.its.pdx.edu
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