A network equilibrium model with travellers' perception of stochastic travel times

In this paper, we consider a network whose route travel times are considered to be random variables. In this scenario travellers choose their route, uncertain of the travel time they will experience on any of the available alternative routes. The attractiveness of a given route involves evaluation of both the possible travel time outcomes, and their perceived probability of occurring. We consider a modelling framework where the perceived value and perceived probabilities of travel time outcomes are obtained via nonlinear transformations of the actual travel times and their probabilities. In this context, we present the analysis required to formulate an equilibrium condition analogous to that of User Equilibrium, wherein travellers choose the routes that maximises their perceived value in the face of uncertain travel times. Existence and uniqueness conditions for this equilibrium are established. Cumulative prospect theory (CPT) provides a well supported paradigm for choices made under uncertainty, where each choice alternative presents a discrete probability distribution of a finite number of possible outcomes. Our analysis admits the particular transformations associated with CPT as a special case, and holds for a more general class of transformations and for the case of a continuous distribution of outcomes.