Uniqueness of Stochastic User Equilibrium with asymmetric volume-delay functions for merging and diversion

The main aim of this paper is to show how a new type of sufficient conditions can be used to prove uniqueness of a SUE model with non-separable arc cost-flow functions when their Jacobian is asymmetric and non-positive semi-definite. The need to address this apparently unusual set-up for an assignment model stems from the fact that the representation of congestion in urban networks allowed by the standard uniqueness conditions, such as the monotonicity of separable cost-flow functions, is not realistic and thus may lead to wrong decision in the planning process. Indeed, the main delays suffered by drivers when links are short derive from intersections, where vehicle flows conflict, competing to use the capacity of links ahead (merging), or are hold back by other vehicles that are queuing (diversion). These traffic phenomena do not lead to separable functions, nor to symmetric Jacobians. A suitable supply model is then introduced and the extended sufficient conditions are applied, showing that to ensure uniqueness of the equilibrium there is a trade-off between congestion level and utility variance in the route choice.