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Traffic Jamboree: Factors Contributing to Phantom Jams
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Traffic Jamboree: Factors Contributing to Phantom Jams Jamie Ye, Eva Reyes, Brooks Wilding, Jack Lance, Zack Shen, Benjamin Nesselrodt, Stefan Joseph
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Traffic Jamboree: Factors Contributing to Phantom Jams. Jamie Ye, Eva Reyes, Brooks Wilding, Jack Lance, Zack Shen, Benjamin Nesselrodt , Stefan Joseph. Classic Scenario. - PowerPoint PPT Presentation
Transcript of Traffic Jamboree: Factors Contributing to Phantom Jams
Traffic Jamboree: Factors Contributing to Phantom Jams
Jamie Ye, Eva Reyes, Brooks Wilding, Jack Lance, Zack Shen, Benjamin Nesselrodt, Stefan Joseph
Stuck in a Jam? The Science behind Traffic. Digital Image. Evidence Based Living. Cornell University, n.d. Web. 29 July 2014
Classic Scenario
History
Car industry revolutionized lives of Americans Came with many negatives Traffic rules and regulations evolved with growth of
transportation industry Greenshields study in 1930s
Why it Matters
Cost Environment Public Health
Various Models
Microscopic Car-Following Models Macroscopic Models Gas-Kinetic Models Cellular Automaton Models
Nagel-Schreckenberg
Freeway Traffic Four Steps Slow-to-Start Variant
Time (min)
Car locations when vmax = 135 km/h, ρ = 8.67 cars/km, and prob(slow) = 0.5
Po
sitio
n (
km)
7.5
5.0
2.5
25 500
0
75 95 115 135 155 175 195 215 235 255 2756.5
7
7.5
8
8.5
9
9.5
10
10.5
11
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Density-Velocity Phase Diagram at P = 0.5
Velocity (km/h)
De
nsi
ty (
cars
pe
r ki
lom
ete
r)
Velocity (km/hr)
Den
sity
(ca
rs p
er k
ilom
eter
)
80 100 120 140 160 180 200 220 2406
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
Phase Diagram Intermediate Transition Points
Den
sity
(ca
rs p
er k
ilom
eter
)
Velocity (km/h)
80
60
40
20
0 20 40 60 80 100 120
--- P = 0.25
P = 0.50
--- P = 0.75
Combined Phase Diagram
2 3 4 5 6 7 8 9 10 110
5
10
15
20
25
Mean Flux vs. Density P = 0.25
81108135162189216243270
Car Density (cars per kilometer)
Me
an
Flu
x (c
ars
pe
r m
inu
te)
MaximumVelocity(km/h)
80 100 120 140 160 180 200 220 240 2600
5
10
15
20
25
Mean Flux vs. Velocity at P = 0.25
6.677.3388.679.331010.67
Velocity (km/h)
Me
an
Flu
x (c
ars
pe
r m
inu
te)
Highway Density
(cars/km)
2 3 4 5 6 7 8 9 10 110
2
4
6
8
10
12
14
16
18
Mean Flux vs. Density at P = 0.50
81108135162189216243270
Density (cars per kilometer)
Me
an
Flu
x (c
ars
pe
r m
inu
te)
MaximumVelocity(km/h)
80 100 120 140 160 180 200 220 240 2600
2
4
6
8
10
12
14
16
Mean Flux vs. Velocity at P = 0.50
6.677.3388.679.331010.67
Velocity (km/h)
Me
an
Flu
x (c
ars
pe
r m
inu
te)
Highway Density
(cars/km)
6.5 7 7.5 8 8.5 9 9.5 10 10.5 110123456789
10
Mean Flux vs. Density at P = 0.75
81108135162189216243270
Density (cars per kilometer)
Me
an
Flu
x (c
ars
pe
r m
inu
te)
Maximum Velocity(km/h)
80 100 120 140 160 180 200 220 240 2600
2
4
6
8
10
Mean Flux vs. Velocity at P = 0.75
6.677.3388.679.331010.67
Velocity (km/h)
Me
an
Flu
x (c
ars
pe
r m
inu
te)
Highway Density
(cars/km)
Slow-to-start model
Po
sitio
n (
km)
Time (min)
2 3 4 5 6 7 8 9 10 110
5
10
15
20
25
30
Mean Flux vs Density for Slow-to-Start Model
81108135162189216243270
Density (cars per kilometer)
Me
an
flu
x (c
ars
pe
r m
inu
te)
Maximum Velocity(km/h)
80 100 120 140 160 180 200 220 240 2600
5
10
15
20
25
30
Mean Flux vs Velocity for Slow-to-Start Model
6.677.3388.679.331010.67
Velocity (km/h)
Mea
n flu
x (c
ars
per
min
ute)
Highway Density
(cars/km)
75 95 115 135 155 175 195 215 235 255 2756.5
7
7.5
8
8.5
9
9.5
10
10.5
11
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Density vs. Velocity Phase Diagram for Slow-to-Start Model
Velocity (km/h)
De
nsi
ty (
cars
pe
r ki
lom
ete
r)
1. Before vc , ρc : vmax = flux , density = flux . At or beyond vc , ρc : unstable, jams, variance
2. For slow-to-start vc ≈ 180 km/h for all ρ, so for vmax < vc : vmax = flux
3. Pushing vmax to unrealistic levels (>200 km/h): no benefit
Conclusions:The Five Commandments of Traffic Jams
4. As P(slow) increases, vmax and ρ show less effect on flux
The Five Commandments of Traffic (continued)
100 120 140 160 180 200 220 240 260 2800
20
40
60
Propagation Velocity of Traffic Jam vs. Speed Limit
Speed Limit (km/h)
Jam
Vel
oci
ty (
km/h
) 5. vmax has no apparent effect on speed of jam propagation
Relevance
London M25 Motorway
Boston Central Artery/Tunnel Project
De
nsi
ty (
cars
pe
r ki
lom
ete
r)
Velocity (km/h)
80
60
40
20
0 20 40 60 80 100 120
--- P = 0.25
P = 0.50
--- P = 0.75
Combined Phase Diagram
Sources
Stuck in a Jam? The Science behind Traffic. Digital Image. Evidence Based Living. Cornell University, n.d. Web. 29 July 2014
Hicks, Mark A. Stone Tablets – Clip Art Gallery. Digital Image. Stone Tablets – Clip Art Gallery. Discovery Education, n.d. Web 30 July 2014.
Acknowledgements
Pennsylvania Department of Education
PGSS Corporate Sponsors: EQT, AT&T, Teva Pharmaceuticals, PPG, Alcoa, Westinghouse
PGSS Private Sponsors
PGSS Alumni Association and PGSS Campaign, INC.
Carnegie Mellon University
Pennsylvania Governor’s School for the Sciences
Dr. Barry Luokkala – PGSS Program Director
Melissa Lessure – Assistant to the Director
Zach McDargh – Team Project Advisor
Kaleigh Felisberto – Teaching Assistant
PGSS 2014 Teaching Assistants and Residence Life Directors
Thank You.Any Questions?
