Side constrained traffic equilibrium models— analysis, computation and applications

We consider the introduction of side constraints for refining a descriptive or prescriptive traffic equilibrium assignment model, and analyze a general such a model. Side constraints can be introduced for several diverse reasons; we consider three basic ones. First, they can be used to describe the effects of a traffic control policy. Second, they can be used to improve an existing traffic equilibrium model for a given application by introducing, through them, further information about the traffic flow situation at hand. As such, these two strategies complement the refinement strategy based on the use of non-separable, and typically asymmetric, travel cost functions. Third, they can be used to describe flow restrictions that a central authority wishes to impose upon the users of the network. We study a general convexly side constrained traffic equilibrium assignment model, and establish several results pertaining to the above described areas of application. First, for the case of prescriptive side constraints that are associated with queueing effects, for example those describing signal controls, we establish a characterization of the solutions to the model through a Wardrop user equilibrium principle in terms of generalized travel costs and an equilibrium queueing delay result; in traffic networks with queueing the solutions may therefore be characterized as Wardrop equilibria in terms of well-defined and natural travel costs. Second, we show that the side constrained problem is equivalent to an equilibrium model with travel cost functions properly adjusted to take into account the information introduced through the side constraints. Third, we show that the introduction of side constraints can be used as a means to derive the link tolls that should be levied in order to achieve a set of traffic management goals. The introduction of side constraints makes the problem computationally more demanding, but this drawback can to some extent be overcome through the use of dualization approaches, which we also briefly discuss.