Transport Planning: Traffic Assignment

2. Consider a single O-D pair with total volume flow V. Two paths, 1 and 2, exist, each consisting of a single link. The volume delay functions for the two links are:

t1 = 8/[1-(V1/C1)] and t2 = 3/[1-(V2/C2)]

where C1 and C2 are the capacities of the paths in veh/hr, respectively.

Using the user equilibrium criterion, analytically solve for the equilibrium flow on link 2, as a function of total flow, V, C1 and C2.