Uniqueness of stochastic user equilibrium with asymmetric volume-delay functions for merging and diversion

Abstract

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, even when their Jacobian is asymmetric and non-positive semi-definite. This apparently unusual setup for an assignment model permits to improve the representation of congestion in urban networks. Indeed, the supply models allowed by the standard uniqueness conditions, such as the monotonicity of separable cost-flow functions, can lack realism and thus may lead to wrong decision in the planning process. Actually, the main source of delay suffered by drivers when links are short is intersections, where vehicle flows conflict, competing to use the capacity of links ahead (merging), or are held back by other vehicles that are queuing (diversion). These traffic phenomena do not either lead to separable functions, or to symmetric Jacobians. A suitable supply model is then proposed to which the extended sufficient conditions are applied, showing that the uniqueness of the stochastic equilibrium can be proved also for more realistic volume-delay functions derived from traffic flow theory.

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