Equilibrium Flows

1.Two routes connect a suburban area and a city, with route travel times (in minutes) given by the expressions tl = 6 + 8(x1/c1) and t2 = 10 + 3(x2/c2), where the x’s are expressed in thousands of vehicles per hour and the c’s are the route capacities in thousands of vehicles per hour. Initially, the capacities of routes 1 and 2 are 4000 and 2000 veh/h, respectively. A reconstruction project on route 1 reduces the capacity to 3000 veh/h, but total traffic demand is unaffected. Observational studies note a 35.28-second increase in average travel time on route 1 and a 68.5% increase in flow on route 2 after reconstruction begins. User-equilibrium conditions exist before and during reconstruction. If both routes are always used, determine equilibrium flows and travel times before and after reconstruction begins.

2. Three routes connect an origin and destination with performance functions tl = 2 + 0.5×1, t2 = 1 + x2, and t3 = 4 + 0.2×3 (with t’s in minutes and x’s in thousands of vehicles per hour). Determine user- equilibrium flows if the total origin-to-destination demand is (a) 10,000 veh/h and (b) 5000 veh/h.

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