Three urban neighborhoods are mutually connected by freeways admitting traffic in both directions. Net output bi,k (per hour) at each neighborhood k of vehicles originating at i can be estimated from known patterns 1bi,k = -aki bi,k2. The delay vehicles experience on any arc (i, j) is an increasing nonlinear function di,j of the total flow on that arc reflecting the number of lanes and other characteristics of the road link. Formulate an NLP to compute a “system optimal” traffic flow (i.e., one that minimizes the total delay experienced in carrying the required traffic), using the decision variables 1i, j, k = 1,

c, 32 xi,j,k ! flow on arc 1i, j2 bound for node k

(Observe that this may not be the same as a “user optimal” flow where each driver tries to minimize his or her own delay.)