Doubly Dynamic Equilibrium Distribution Approximation Model for Dynamic Traffic Assignment

The paper presents research aimed at unifying the fields of (i) dynamic network equilibrium, (ii) dynamic whole-link models and (iii) stochastic process models of between- and within-day dynamics. An approximation result and computational procedure is derived for determining the equilibrium probability distribution of a within- and between-day dynamic stochastic process traffic assignment model. The method is based on an analytic procedure requiring only knowledge of within-day dynamic stochastic user equilibrium flows, together with the Jacobians of the dynamic network loading map and of the choice probability function. An implementation is reported with a particular form of whole-link, continuous-time, dynamic network loading model, commonly found in the literature on dynamic traffic assignment, where travel times at the time of entry to a link are a function of the number of vehicles on the link at that time. Illustrative numerical examples are presented.