Question: Problem 4: Network Optimization (80 pts) A highway corridor consists of a freeway with a capacity c = 4000 veh/hr and a dense network of

Problem 4: Network Optimization (80 pts) A

Problem 4: Network Optimization (80 pts) A highway corridor consists of a freeway with a capacity c = 4000 veh/hr and a dense network of local roads. The performance function, in hours, for the freeway is: t(q) = + = For local roads the travel time is 1 hour, independent of the flow since there are many routes available. A total of 8000 vehicles travel on this corridor during the peak hour. a. Under user equilibrium, how many vehicles will use the freeway during the peak hour? Compute the total (system-wide, including both freeway and local road) travel time. (20 pts) b. Under system optimal, how many vehicles will use the freeway during the peak hour? Compute the total (system-wide, including both freeway and local road) travel time. (20 pts) c. Repeat part (a) and part (b) using a capacity of c = 6000 veh/hr. Compare the difference in the total (system-wide, including both freeway and local road) travel time. (40 pts)

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