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

Abstract

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 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 generalised 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.

Using crowd sensed data as input to congestion model

“…The model for congestion used in this paper is presented in detail in two papers [17] [14] by the inventors. This work presents two different implementations, one in MATLAB and one in ArcGIS (with extra extensions for route choice modelling).…”

Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

“…Bringing together these elements, the equilibrium conditions are defined as (for details, see Watling et al, 2014):…”

“…The RSUE conditions, unlike the DUE and SUE, do not provide uniqueness in link flows under the usual sufficient conditions, nor in path flows, as in general the set of used paths may not be uniquely defined by the RSUE conditions (see Watling et al, 2014). Consequently, a given linkflow allocation cannot be mapped to an RSUE path-flow solution via a one-to-one relation, and in any case, the RSUE conditions may be satisfied by multiple link-flow solutions.…”

“…In Deterministic User Equilibrium (DUE) models, on the other hand, routes that are only slightly more costly expensive than the equilibrium cost are unused. In a companion paper (Watling et al, 2014) we argued why neither of these extremes seems particularly realistic, and went on to consider two alternative model families for equilibrating choice sets within an SUE framework.…”

“…In Watling et al (2014) we computed RSUE(min) and RSUE(max) solutions in small networks by enumerating all possible choice sets (i.e. all non-empty subsets of the available routes), but clearly such a strategy will be computationally infeasible for realistic-scale networks.…”