Summary: In order to refine the basic model of traffic assignment to capture supplementary flow relationships, the traditional modelling strategy is to modify the travel cost mapping. This strategy is well suited for capturing relationships such as interactions among vehicles on different road links and turning priorities in junctions, and it usually results in nonseparable and asymmetric travel cost functions. It is, however, not the proper approach for incorporating traffic flow restrictions such as those imposed by joint capacities on two-way streets or in junctions, or the presence of a traffic control policy. We consider the introduction of side constraints to describe those flow relationsships that have more natural interpretations as flow restrictions than as additional travel costs. Such a refinement should be easier to construct and calibrate as well as lead to more reliable traffic models than that using the traditional refinement strategy only.
The utilization of the appropriate combination of these two modelling strategies results, in general, in a variational inequality model of the traffic assignment problem augmented with a set of side constraints. We establish characterizations of its solutions as Wardrop and queuing delay equilibria in terms of well-defined and natural generalized travel costs, and derive stability results for the model. The results obtained may, for example, be applied to derive link tolls for achieving traffic management goals without using centralized traffic control.