Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach

Stability of dynamic user equilibrium in unidirectional networks is analyzed. An approach combining concepts in traffic assignment and game theory is presented. A relation between the dynamic user equilibrium and the weakly acyclic game is established. Rigorous results on the convergence and the stochastic stability of equilibrium are obtained. Strict improvement of utility of better response dynamics is important for ensuring these results.