traffic flow jerusalem to tel aviv kiong teo yuval nevo steve hunt
TRANSCRIPT
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
J
I
KN
L
F
H
T
Abstraction
SA
BD
C
E
G
J
I
K
N
L
F
H
T
384.5
19.516.512
8
3
36
18
15.5
74
3
3.5
10
4.5
13.5
8
3.5
12
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
SA
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N
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H
T
384.5
19.516.512
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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
SA
BD
C
E
G
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K
N
L
F
H
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384.5
19.516.512
8
3
36
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3.5
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4.5
13.5
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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
SA
BD
C
E
G
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I
K
N
L
F
H
T
384.5
19.516.512
8
3
36
18
15.5
74
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 -> 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
J
I
K
N
L
F
H
T
384.5
19.516.512
8
3
36
18
15.5
74
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 -> 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
BD
C
E
G
J
I
K
N
L
F
H
T
384.5
19.516.512
8
3
36
18
15.5
74
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 -> 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
C
E
G
J
I
K
N
L
F
H
T
384.5
19.516.512
8
3
36
18
15.5
74
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 -> 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
E
G
J
I
K
N
L
F
H
T
384.5
19.516.512
8
3
36
18
15.5
74
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 -> 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
E
G
J
I
K
N
L
F
H
T
384.5
19.516.512
8
3
36
18
15.5
74
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 -> 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
SA
BD
C
E
G
J
I
K
N
L
F
H
T
384.5
19.516.512
8
3
36
18
15.5
74
3
3.5
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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?