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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I I

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JJ

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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

F

F

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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

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Carnegie Mellon University

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Zach McDargh – Team Project Advisor

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PGSS 2014 Teaching Assistants and Residence Life Directors

Thank You.Any Questions?