submitted to Transportation Research Part B Dynamic Network Equilibrium Model of Simultaneous Route / Departure Time Choice for a Many-to-One OD Pattern

Dynamic equilibrium traffic assignment with elastic demand is analyzed on an over saturated network for a many-to-one origin-destination pattern. The model aims to obtain time-dependent cumulative arrival curves or equivalently arrival flow rates at each of the nodes explicitly taking into account the effects of queues. We assume that the OD demand is elastic; that is, the departure times of users should be determined through the assignment given time constraints at the single destination such as work starting times. We first show that the problem can be decomposed with respect to the arrival time at the destination. Alternative formulations for the problem are then shown as the Variational Inequality, Nonlinear Complementarity and Fixed Point problems using two kinds of unknowns: link flows and arrival times at nodes. Unlike the path-based formulation in the previous studies, the mapping used in the formulation is simple and, therefore, easy to analyze the mathematical properties of the assignment. Thus, the existence of the solution is established and the uniqueness conditions are examined based upon the formulations. Finally, solution algorithms using merit functions that enforce the global convergence are suggested