Dynamic models of network traffic assignment: A control theoretic approach

Byung-Wook Wie, University of Pennsylvania


The problem of dynamic traffic assignment is to predict the evolution of the flow pattern in a network where travel demands and costs vary over time and space. Using optimal control theory two continuous time formulations of the dynamic traffic assignment problem are considered, one corresponding to system optimization and the other to user optimization. Optimality conditions are derived by the Pontryagin minimum principle and given economic interpretations which correspond to intuitive notions regarding dynamic system optimized and user optimized traffic flow patterns. We further establish that Pontryagin's necessary conditions are also sufficient under commonly encountered regularity conditions. The existence of singular control is also considered. Notably, we offer in the form of an optimal control problem the first dynamic generalization of Beckmann's equivalent optimization problem for a static user equilibrium traffic assignment. This dynamic model is extended to include time-varying elastic demands and penalties for late arrivals. Finally, another type of dynamic generalization of Wardrop's first principle is considered and the existence of the dynamic user equilibrium flow pattern is conjectured in an infinite-dimensional variational inequality formulation.

Subject Area

Transportation|Urban planning|Area planning & development

Recommended Citation

Wie, Byung-Wook, "Dynamic models of network traffic assignment: A control theoretic approach" (1988). Dissertations available from ProQuest. AAI8824807.