A convex control model of dynamic system optimal traffic assignment

In this paper, the dynamic system optimal traffic assignment model is formulated as a convex control problem for general networks with many origins and many destinations. Analytical and computational difficulties caused by the nonconvexity of previous models are eliminated. The modeling of arc traffic dynamics is also improved to prohibit instantaneous how propagation on each are even though the concave exit functions are still employed to represent the physical process of traffic congestion. Lastly, an economic interpretation of the optimality conditions is given as a dynamic assignment principle which requires equilibration of actual marginal costs on all the paths that an used.