Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user-classes

This paper presents a formulation of the multiple user class, variable demand, probit stochastic user equilibrium model (SUE). Sufficient conditions are stated for differentiability of the equilibrium flows of this model. This justifies the derivation of sensitivity expressions for the equilibrium flows. This paper then considers the network design problem (NDP), assuming that users' responses to changes in the design variables follow the probit SUE. With probit SUE stated as a fixed-point condition, the NDP is a mathematical program with equilibrium constraints (MPEC). The probit SUE sensitivity expressions provide the information necessary to adopt a gradient-based approach to solving the probit SUE NDP. Numerical examples verify the sensitivity expressions, and the NDP solution.