1. An origin–destination pair is connected by a route with a performance function tl = 8 + x1, and another with a function t2 = 1 + 2×2 (with x’s in thousands of vehicles per hour and t’s in minutes). If the total origin–destination flow is 4000 veh/h, determine user-equilibrium and system-optimal route travel times, total travel time (in vehicle minutes), and route flows.
2. Because of the great increase in vehicle-hours caused by the reconstruction project in Example 8.12, the state transportation department decides to regulate the flow of traffic on the two routes (until reconstruction is complete) to achieve a system- optimal solution. How many vehicle-hours will be saved during each peak-hour period if this strategy is implemented and travelers are not permitted to achieve a user-equilibrium solution?
3. What reduction in peak-hour traffic demand is needed to ensure an equality of total vehicle travel time (in vehicle minutes) assuming a system-optimal solution before and during reconstruction?
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