On the Existence of Solutions to the Dynamic User Equilibrium Problem

Abstract

This paper is concerned with the existence of solutions to a dynamic network equilibrium problem modeled as an infinite dimensional variational inequality. Our results are based on properties of operators that map path flow departure rates to consistent time-dependent path flows and other link performance functions. The existence result requires the introduction of a novel concept that strengthens the familiar concept of First-In-First-Out (FIFO).