Dynamic equilibria in transport systems

Abstract

In the transportation science the attention has been for some time concentrating on the issue of an appropriate way of introducing the dynamics into the models of equilibria of flows in transport systems. They have been one of the main modeling techniques of transportation planning in the recent decades. Most of the equilibrium notions in use are basically static by nature, which leads to severe problems in approaching the dynamics of the equilibrium behaviour of transport systems. Probably the most important equilibrium notion of this type has been the First Wardrop Equilibrium Principle. Our paper discusses one of the possible mathematical approaches of introducing the dynamics into the underlying network equilibrium model of this notion in a way that would make it possible to analyse the impact of the distribution of the information on the equilibrium behaviour of the users of transport systems. Two such dynamic notions of flow equilibria are introduced. We analyse some of their existence and algorithmic properties, and their implications for the equilibrium dynamics of transport systems.