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

Abstract

We propose a new class of path-based solution algorithms to solve the Restricted Stochastic User Equilibrium (RSUE), as introduced in Watling et al (2014). The class allows a flexible specification of how the choice sets are 'systematically' grown by considering congestion effects and how the flows are allocated among routes. The specification allows adapting traditional pathbased stochastic user equilibrium flow allocation methods (designed for pre-specified choice sets) to the generic solution algorithm. We also propose a cost transformation function and show that by using this we can, for certain Logit-type choice models, modify existing path-based Deterministic User Equilibrium solution methods to fit the RSUE solution algorithm. The transformation function also leads to a two-part relative gap measure for consistently monitoring convergence to a RSUE solution. Numerical tests are reported on two real-life cases, in which we explore convergence patterns and choice set composition and size, for alternative specifications of the RSUE solution algorithm.

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

“…The RSUE seems more straightforward to apply in short term, as an extension of existing, calibrated SUE models, especially if supplemented with some information on routes actually chosen to aid in the determination of the operator. In a companion paper (Rasmussen et al, 2014), we develop solution methods for generating RSUE solutions for large-scale networks, and explore the characteristics of the solutions produced. Beyond these two papers, what is required next, we believe, is a further development and study of the capabilities and potential of RSUE and SUEGE.…”

“…In the present paper, and a companion paper (Rasmussen et al, 2014), we are particularly interested in developing a theoretical foundation for SUE-style approaches which does not suffer from such scaleability problems. Of course we are aware that practical solution algorithms, after a finite number of iterations, will typically produce an estimated SUE solution which includes only a subset of the available routes.…”

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).…”

Investigating the Empirical Existence of Static User Equilibrium

“…a description by Han (2003)). An intermediate between static and stochastic frameworks is the Restricted Stochastic User Equilibrium, for which route choice sets are constrained to be realistic (Rasmussen et al (2015)). Extensions that incorporate user behavior with choice models have more recently been proposed, such as Zhang et al (2013) taking into account both the influence of road pricing and congestion on user choice with a Probit model.…”