1. Traffic Flow Jerusalem to Tel Aviv Kiong Teo 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 S A B D C E G J I K N L F H T

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

7. Model Construct AB (d, 0, 60) y ij

8. Model Construct AB Indexed arcs Index C(y) = d/65 if y < 201 d/35 if 20 <= y <= 402 d/10 if 0 <= y <= 603 (d/35, 0, 20) (d/10, 0, 20) (d/65, 0, 20)

9. 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

10. Mathematical Formulation Min Cost Flow: Shortest Path:

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

12. Best Route - No Blocks S A B D C E G J I K N L F H T 3 8 4.5 19.5 16.5 12 8 3 36 18 15.5 7 4 3 3.5 10 4.5 13.5 8 3.5 12 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 Legend 2 lanes road 3 lanes road 4 lanes road Best Route

13. With 1 Block S A B D C E G J I K N L F H T 3 8 4.5 19.5 16.5 12 8 3 36 18 15.5 7 4 3 3.5 10 4.5 13.5 8 3.5 12 Legend 2 lanes road 3 lanes road 4 lanes road Best Route 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

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

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

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

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

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

19. Resilience Curve Scaled by factor of 100 for comparison

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

22. Alternative Comparison

23. Commuter Alternatives

24. e.g. Source node = G

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