Boundedly Rational User Equilibrium with Restricted Unused Routes

Chao Sun,Zhaoming Chu,Menghui Li,Senlai Zhu,Lin Cheng

doi:10.1155/2016/9848916

Abstract

A boundedly rational user equilibrium model with restricted unused routes (R-BRUE) considering the restrictions of both used route cost and unused route cost is proposed. The proposed model hypothesizes that for each OD pair no traveler can reduce his/her travel time by an indifference band by unilaterally changing route. Meanwhile, no route is unutilized if its travel time is lower than sum of indifference band and the shortest route cost. The largest and smallest used route sets are defined using mathematical expression. We also show that, with the increase of the indifference band, the largest and smallest used route sets will be augmented, and the critical values of indifference band to augment these two path sets are identified by solving the mathematical programs with equilibrium constraints. Based on the largest and smallest used route sets, the R-BRUE route set without paradoxical route is generated. The R-BRUE solution set can then be obtained by assigning all traffic demands to the corresponding generated route set. Various numerical examples are also provided to illustrate the essential ideas of the proposed model and structure of R-BRUE route flow solution set.

Highlights

Perfect rationality is widely used in studying traditional transportation network models in which traveler always chooses the shortest route, such as user equilibrium (UE [1]) and stochastic user equilibrium (SUE [2]) traffic assignment models
This paper makes contributions in three major areas: (1) considering both the restrictions of used route cost and unused route cost in the route decision process, we present a boundedly rational user equilibrium model with restricted unused routes (R-Boundedly rational user equilibrium (BRUE))
(2) We propose the largest and smallest used route sets which can be used to generate the used route set of R-BRUE model

Summary

Introduction

Perfect rationality is widely used in studying traditional transportation network models in which traveler always chooses the shortest (i.e., least utility) route, such as user equilibrium (UE [1]) and stochastic user equilibrium (SUE [2]) traffic assignment models. Rational user equilibrium (BRUE) is a network state such that travelers can take any route whose travel time is within a threshold of the shortest route time [22, 23, 25,26,27,28] Such a threshold is phrased by Mahmassani and Chang [7] as “indifference band.”. This paper makes contributions in three major areas: (1) considering both the restrictions of used route cost and unused route cost in the route decision process, we present a boundedly rational user equilibrium model with restricted unused routes (R-BRUE) This new model hypothesizes that for each OD pair no traveler can reduce his/her travel time by an indifference band by unilaterally changing route.

Definition of ε-R-BRUE and Mathematical Formulation

Generation of ε-R-BRUE Route Set without Paradoxical Route

Construction of ε-R-BRUE Route Flow Set without Paradoxical Route

Conclusions