Stochastic user equilibrium with equilibrated choice sets: Part I – Model formulations under alternative distributions and restrictions

• Two theoretical approaches for Stochastic User Equilibrium (SUE) with equilibrated choice sets.
• An SUE formulation with general error distributions.
• An SUE formulation with restrictions on used/unused routes.
• Mathematical formulations, model specifications, and examples.

The aim of this paper is to remove the known limitations of Deterministic and Stochastic User Equilibrium (DUE and SUE), namely that only routes with the minimum cost are used in DUE, and that all permitted routes are used in SUE regardless of their costs. We achieve this by combining the advantages of the two principles, namely the definition of unused routes in DUE and of mis-perception in SUE, such that the resulting choice sets of used routes are equilibrated. Two model families are formulated to address this issue: the first is a general version of SUE permitting bounded and discrete error distributions; the second is a Restricted SUE model with an additional constraint that must be satisfied for unused paths. The overall advantage of these model families consists in their ability to combine the unused routes with the use of random utility models for used routes, without the need to pre-specify the choice set. We present model specifications within these families, show illustrative examples, evaluate their relative merits, and identify key directions for further research.