Extending a recent work (Pang et al., in press) pertaining to a simple single-bottleneck model, this paper is the first of a two-part research wherein we undertake a mathematically rigorous study of the continuous-time dynamic user equilibrium (DUE) problem using the recently introduced...

In this paper we present a continuous-time network loading procedure based on the Lighthill–Whitham–Richards model proposed by Lighthill and Whitham (1955) and Richards (1956). A system of differential algebraic equations (DAEs) is proposed for describing traffic flow propagation, travel...

Models to describe or predict of time-varying traffic flows and travel times on road networks are usually referred to as dynamic traffic assignment (DTA) models or dynamic user equilibrium (DUE) models. The most common form of algorithms for DUE consists of iterating between two components...

In this paper, we present an approach for determining dynamic user equilibria. The method is suitable for disaggregated microscopic and mesoscopic simulation-based models. It is a modification of the convex-simplex method, which disposes with the line search step, and controls the subset of...