Optimal control theory is applied to the problem of dynamic traffic assignment, corresponding to user optimization, in a congested network with one origin-destination pair connected by n parallel arcs. Two continuous time formulations are considered, one with fixed demand and the other with elastic demand. Optimality conditions are derived by pontryagin's maximum principle and interpreted as a dynamicgeneralization of wardrop's first principle. The existence of singular controls is examined, and the optimality of singular controls isassured by the generalized convexity conditions. Under the steady-state assumptions, a dynamic model with elastic demand is shown to bea proper extension of beckmann's equivalent optimization problem with elastic demand. Finally, the derivation of the dynamic user optimization objective functional is demonstrated, which is analogous to the derivation of the objective function of beckmann's mathematical programming formulation for user equilibrium. This paper appears in transportation research record no. 1251, Transport supply analysis.
Samenvatting