Three routes connect an origin-destination pair with performance functions: t₁ = 20 +0.5x1 t2 = 4+ 2x2 t3=3+0.2x3 with t in minutes and x in thousand vehicles per hour. (a) Determine the User Equilibrium flow on each route if q = 4000veh/h. (b) What is the minimum q (origin-destination demand) to ensure that all the three routes are used under user equilibrium? (c) Suppose that Route 1 is closed for repair. Find the system optimal flow on routes 2 and 3 and compute the total travel times.

Three routes connect an origin-destination pair with performance functions: t₁ = 20 +0.5x1 t2 = 4+ 2x2 t3=3+0.2x3 with t in minutes and x in thousand vehicles per hour. (a) Determine the User Equilibrium flow on each route if q = 4000veh/h. (b) What is the minimum q (origin-destination demand) to ensure that all the three routes are used under user equilibrium? (c) Suppose that Route 1 is closed for repair. Find the system optimal flow on routes 2 and 3 and compute the total travel times.

Traffic and Highway Engineering

5th Edition

ISBN:9781305156241

Author:Garber, Nicholas J.

Publisher:Garber, Nicholas J.

Chapter13: Evaluating Transportation Alternatives

Section: Chapter Questions

Problem 4P

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Question

Three routes connect an origin-destination pair with performance functions:
t₁ = 20 +0.5x1
t2 = 4+ 2x2
t3=3+0.2x3
with t in minutes and x in thousand vehicles per hour.
(a) Determine the User Equilibrium flow on each route if q = 4000veh/h.
(b) What is the minimum q (origin-destination demand) to ensure that all the three routes are used under user equilibrium?
(c) Suppose that Route 1 is closed for repair. Find the system optimal flow on routes 2 and 3 and compute the total travel times.

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