Perturbations of a Multimodal Network Model for Urban Transportation Planning

A theoretical planning model that consists of a composite set of modal networks for serving the population in an urban area or region is presented. By varying and controling various parameters in the model, an equilibrium of modal choices can be obtained by seeking the condition that no user can alter his path without experiencing an increase in cost. The equivalence between equilibrium conditions and a nonlinear programming problem will be established, following a fundamental theorem. Thus, under small perturbations in the composite network, either through changes in the frequency of certain trips or changes in the structure of the network, it is possible to linearize about the observed equilibrium to determine the effects of perturbations.