Traffic Flow Jerusalem to Tel Aviv Kiong Teo Yuval Nevo Steve Hunt.

Traffic FlowJerusalem to Tel Aviv

Kiong TeoYuval NevoSteve Hunt

Agenda

• Scenario• Basic Traffic Model• Analysis:– Resilience– Stochastic Accidents– Commuting alternatives

• Conclusion / Questions

Scenario

General Assumptions

• Model is static • Coarse network – only highways• All traffic goes to Tel Aviv• All traffic coming from four locations • Discrete traffic conditions• Accidents add a fixed delay

Network Overlay

SA

BD

C

E

G

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I

KN

L

F

H

T

Abstraction

SA

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C

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Legend 2 lanes road 3 lanes road 4 lanes road

Model Construct

A B(d, 0, 60)yij

Model Construct

A B

• Indexed arcs Index

• C(y) = d/65 if y < 20 1d/35 if 20 <= y <= 40 2d/10 if 0 <= y <= 60 3

(d/35, 0, 20)

(d/10, 0, 20)

(d/65, 0, 20)

Specific Model Assumptions• Traffic (by lane)

– up to 20 cars/minute - avg speed = 65 km/h– 20 to 40 cars/minute - avg speed = 35 km/h– 40 to 60 cars/minute - avg speed = 10 km/h– 60 is the max capacity– Network arc upper bound is (# lanes)*20

• Cost = distance / speed ( with some adjustments)• Delay

– Delay1 = light traffic = 10 minutes– Delay2 = medium traffic = 30 minutes– Delay3 = heavy traffic = 60 minutes

• Accident probability– arc length / total road length– 50% between Jerusalem and Tel Aviv

Mathematical Formulation• Min Cost Flow:

• Shortest Path:

Traffic Conditions

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-120

Lane Legend 2 lanes road 3 lanes road 4 lanes road

Flow Intensityindex 1index 2index 3

-80

-60

360

-100

Best Route - No Blocks

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solve ShortestPath with no roadblocks transit arc S1 -> C transit arc C -> F transit arc F -> I transit arc I -> L transit arc L -> Ttransit cost= 1.24

Legend 2 lanes road 3 lanes road 4 lanes road Best Route

With 1 Block

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interdiction plan with 1.00 teams: blocking road: L -> Tcost with interdiction =3.04806E+2****solve ShortestPath with 1.00 roadblocks: transit arc S1 -> C transit arc C -> F transit arc F -> I transit arc I -> K transit arc K -> N transit arc N -> Ttransit cost= 1.92

With 2 Blocks

SA

BD

C

E

G

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K

N

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interdiction plan with 2.00 teams: blocking road: L -> T blocking road: N -> Tcost with interdiction =3.64447E+2****solve ShortestPath with 2.00 roadblocks: transit arc S1 -> C transit arc C -> F transit arc F -> I transit arc I -> K transit arc K -> N transit arc N -> Ttransit cost= 1.85

With 3 Blocks

SA

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interdiction plan with 3.00 teams: blocking road: S1 -> A blocking road: L -> T blocking road: N -> Tcost with interdiction =3.76059E+2****solve ShortestPath with 3.00 roadblocks: transit arc S1 -> A transit arc A -> B transit arc B -> D transit arc D -> G transit arc G -> I transit arc I -> K transit arc K -> N transit arc N -> Ttransit cost= 2.10

With 4 Blocks

SA

BD

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interdiction plan with 4.00 teams: blocking road: S1 -> A blocking road: K -> N blocking road: L -> T blocking road: N -> Tcost with interdiction =4.04510E+2****solve ShortestPath with 4.00 roadblocks: transit arc S1 -> A transit arc A -> B transit arc B -> D transit arc C -> F transit arc D -> C transit arc F -> I transit arc I -> L transit arc L -> Ttransit cost= 2.42

With 5 Blocks

SA

BD

C

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G

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N

L

F

H

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384.5

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interdiction plan with 5.00 teams: blocking road: I -> L blocking road: J -> L blocking road: K -> N blocking road: L -> T blocking road: N -> Tcost with interdiction =4.47780E+2****solve ShortestPath with 5.00 roadblocks: transit arc S1 -> C transit arc C -> F transit arc F -> I transit arc I -> K transit arc K -> N transit arc N -> Ttransit cost= 2.35

With 6 Blocks

SA

BD

C

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G

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N

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F

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interdiction plan with 6.00 teams: blocking road: E -> H blocking road: I -> L blocking road: J -> L blocking road: K -> N blocking road: L -> T blocking road: N -> Tcost with interdiction =4.67780E+2****solve ShortestPath with 6.00 roadblocks: transit arc S1 -> C transit arc C -> F transit arc F -> I transit arc I -> K transit arc K -> N transit arc N -> Ttransit cost= 2.35

Resilience Curve

Scaled by factor of 100 for comparison

Alternatives

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Legend Alternative 1 Alternative 2 Alternative 3

Alternative Comparison

Worst Case Scenario

Expected Time

Worst Case Regret

Expected Regret

0

0.5

1

1.5

2

2.5

3

Alternative 1Alternative 2Alternative 3

Commuter Alternatives

Commuter Alternatives

Worst Case Scenario

Expected Time

Worst Case Regret

Expected Regret

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Alternative 1Alternative 2Alternative 3

e.g. Source node = G

Conclusion

• Simple, yet realistic• Robust capability• Handling uncertainty

Questions?

Traffic Flow Jerusalem to Tel Aviv Kiong Teo Yuval Nevo Steve Hunt.

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Transcript of Traffic Flow Jerusalem to Tel Aviv Kiong Teo Yuval Nevo Steve Hunt.