AN EFFICIENT PATH-BASED ALGORITHM FOR A DYNAMIC USER EQUILIBRIUM PROBLEM. IN: URBAN AND REGIONAL TRANSPORTATION MODELING. ESSAYS IN HONOR OF DAVID BOYCE

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. 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. This chapter on an efficient path-based algorithm for the dynamic user equilibrium problem is from a book of essays published in honor of David Boyce for his contributions to the fields of transportation modeling and regional science. The authors note that one of the most commonly used share formulas is based on the entropy maximization principle, which results in a joint entropy distribution/assignment (JEDA) model. In this chapter, the authors propose and compare a path-based algorithm with a type of JEDA algorithm for the dynamic user equilibrium problem. The authors algorithm uses a doubly constrained origin-destination/departure time/route choice (DUE-DC-OD-D-R), which is a dynamic extension of the JEDA problem. An associated path-based solution algorithm is proposed, with the general scheme of the nested diagonalization (ND) and the path-based algorithm herein named the nested diagonalization-augmented Lagrangian-gradient projection (ND-AL-GP). The authors provide three numerical examples in order to compare the computation efficiency of each method for the DUE-DC-OD-D-R problem. Appendices include a summary of notation, equivalence analysis, and a description of link-based algorithms, including the FW method and the Evans algorithm.