Sensitivity analysis for a continuum traffic equilibrium problem

This paper develops a sensitivity analysis for the continuum traffic equilibrium problem of a city with several competing facilities. In the city, the customers’ origins are continuously dispersed. We assume that the customer demand is dependent on the total cost of patronizing these facilities. Specific travel cost–flow relationships are considered. The choice of facility in the continuum transportation system follows a user equilibrium principle in which from each origin, no customer can reduce their individual cost to patronize any of the facilities by unilaterally changing route or facility. The problem can be formulated as a minimization problem that is subject to a set of constraints and solved with a finite element method. The sensitivity analysis is based on the implicit function theorem at the equilibrium solution. A numerical example is presented to illustrate the applications of these sensitivity analysis results.