An efficient path-based algorithm for a dynamic user equilibrium problem

The trip distribution and traffic assignment (TDTA) problem characterizes travelers’ choice of route with the lowest travel impedance from trip origin to destination given (fixed and known) trip productions and trip attractions. This problem combines two submodels into a unified framework, namely, trip distribution and traffic assignment, which appear in the traditional four-stage transportation planning process. The combined model accrues no internal inconsistency between two modules. At equilibrium, the combined model must meet the total number of trips generated from origins and the total number of trips attracted to destinations and, in the meantime, comply with the travelers’ behavior of searching for the shortest path from trip origin to destination. To conserve the trips at both ends, a share model that preserves both the trip productions and trip attractions is needed. One of the most commonly used share formulas is based on the entropy maximization principle, which results in a joint entropy distribution/assignment model (JEDA).