Question

transportation engineering

Two highways connect an origin-destination pair, having performance functions t1 = 5 + 4(x1/01) and t2 = 4 +5(x2/2) for routes 1 and 2, respectively. For the performance functions, the t's are in minutes, and the flows (X's) and capacities (C's) are in thousands of vehicles per hour. The total traffic demand for the two highways is 3,036 vehicles during the peak hour. The capacities of routes 1 and 2 are 3600 veh/h and 4500 veh/h, respectively, Determine the user-equilibrium travel times.

Answer 1

user-egn travel time ti=tz NI+U2=3036 5+4 x1 = 4+ 5 U2 (2 u 5 5 + 24 = 4 +5(3036 - 24) 3600 4500 5(3036)-(1) _4X7 3600 4500 t = 5+ 4X1068 leqm) 3600 =(6.186 min 513036- X,)x9_421 459 x4 36 >100= A J 10083 6= 4 (3036-8, 40, 8x, = 85 44 1068 X = 1908