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Traffic Flow Jerusalem to Tel Aviv

Traffic Flow Jerusalem to Tel Aviv. Kiong Teo Yuval Nevo Steve Hunt. Agenda. Scenario Basic Traffic Model Analysis: Resilience Stochastic Accidents Commuting alternatives Conclusion / Questions. Scenario. General Assumptions. Model is static Coarse network – only highways

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Traffic Flow Jerusalem to Tel Aviv

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  1. Traffic FlowJerusalem to Tel Aviv KiongTeo Yuval Nevo Steve Hunt

  2. Agenda • Scenario • Basic Traffic Model • Analysis: • Resilience • Stochastic Accidents • Commuting alternatives • Conclusion / Questions

  3. Scenario

  4. 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

  5. Network Overlay N K H E T L I F J G C D B A S

  6. Abstraction 4.5 8 3 8 N K H E 3 12 T 16.5 19.5 4.5 L I 12 10 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Legend 2 lanes road 3 lanes road 4 lanes road 15.5 A S 18

  7. Model Construct yij (d, 0, 60) A B

  8. Model Construct (d/35, 0, 20) (d/65, 0, 20) A B (d/10, 0, 20) • Indexed arcs • Index • C(y) = d/65 if y < 20 1 • d/35 if 20 <= y <= 40 2 • d/10 if 0 <= y <= 60 3

  9. Specific Model Assumptions • Traffic (by lane) • up to 20 cars/minute - avgspeed =65 km/h • 20 to 40 cars/minute - avgspeed =35 km/h • 40 to 60 cars/minute - avgspeed = 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

  10. Mathematical Formulation • Min Cost Flow: • Shortest Path:

  11. Traffic Conditions -60 4.5 8 3 -80 8 N 360 K H E Flow Intensity index 1 index 2 index 3 3 12 T 16.5 19.5 4.5 12 L I 10 -100 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Lane Legend 2 lanes road 3 lanes road 4 lanes road 15.5 A S -120 18

  12. Best Route - No Blocks 4.5 8 3 solve ShortestPath with no roadblocks transit arc S1 -> C transit arc C -> F transit arc F -> I transit arc I -> L transit arc L -> T transit cost= 1.24 8 N K H E 3 12 T 16.5 19.5 4.5 L I 12 10 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Legend 2 lanes road 3 lanes road 4 lanes road Best Route 15.5 A S 18

  13. With 1 Block 4.5 8 3 interdiction plan with 1.00 teams: blocking road: L -> T cost 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 -> T transit cost= 1.92 8 N K H E 3 12 T 16.5 19.5 4.5 L I 12 10 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Legend 2 lanes road 3 lanes road 4 lanes road Best Route 15.5 A S 18

  14. With 2 Blocks 4.5 8 3 interdiction plan with 2.00 teams: blocking road: L -> T blocking road: N -> T cost 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 -> T transit cost= 1.85 8 N K H E 3 12 T 16.5 19.5 4.5 L I 12 10 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Legend 2 lanes road 3 lanes road 4 lanes road Best Route 15.5 A S 18

  15. With 3 Blocks 4.5 8 3 interdiction plan with 3.00 teams: blocking road: S1 -> A blocking road: L -> T blocking road: N -> T cost 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 -> T transit cost= 2.10 8 N K H E 3 12 T 16.5 19.5 4.5 L I 12 10 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Legend 2 lanes road 3 lanes road 4 lanes road Best Route 15.5 A S 18

  16. With 4 Blocks 4.5 8 3 interdiction plan with 4.00 teams: blocking road: S1 -> A blocking road: K -> N blocking road: L -> T blocking road: N -> T cost 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 -> T transit cost= 2.42 8 N K H E 3 12 T 16.5 19.5 4.5 L I 12 10 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Legend 2 lanes road 3 lanes road 4 lanes road Best Route 15.5 A S 18

  17. With 5 Blocks 4.5 8 3 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 -> T cost 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 -> T transit cost= 2.35 8 N K H E 3 12 T 16.5 19.5 4.5 L I 12 10 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Legend 2 lanes road 3 lanes road 4 lanes road Best Route 15.5 A S 18

  18. With 6 Blocks 4.5 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 -> T cost 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 -> T transit cost= 2.35 8 3 8 N K H E 3 12 T 16.5 19.5 4.5 L I 12 10 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Legend 2 lanes road 3 lanes road 4 lanes road Best Route 15.5 A S 18

  19. Resilience Curve Scaled by factor of 100 for comparison

  20. Alternatives 4.5 8 3 8 N K H E 3 12 T 16.5 19.5 4.5 L I 12 10 8 F 3.5 J G C 3.5 4 7 13.5 D B 36 3 Legend Alternative 1 Alternative 2 Alternative 3 15.5 A S 18

  21. Alternative Comparison

  22. Commuter Alternatives

  23. Commuter Alternatives e.g. Source node = G

  24. Conclusion • Simple, yet realistic • Robust capability • Handling uncertainty Questions?

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