Bounding the Inefficiency of the Multiclass, Multicriteria C-Logit Stochastic User Equilibrium in a Transportation Network

Lekai Yuan,Xi Zhang,Chaofeng Shi,Inés P Mariño

doi:10.1155/2021/2601184

Abstract

We derive the exact inefficiency upper bounds of the multiclass C-Logit stochastic user equilibrium (CL-SUE) in a transportation network. All travelers are classified on the basis of different values of time (VOT) into M classes. The multiclass CL-SUE model gives a more realistic path choice probability in comparison with the logit-based stochastic user equilibrium model by considering the overlapping effects between paths. To find efficiency loss upper bounds of the multiclass CL-SUE, two equivalent variational inequalities for the multiclass CL-SUE model, i.e., time-based variational inequality (VI) and monetary-based VI, are formulated. We give four different methods to define the inefficiency of the multiclass CL-SUE, i.e., to compare multiclass CL-SUE with multiclass system optimum, or to compare multiclass CL-SUE with multiclass C-Logit stochastic system optimum (CL-SSO), under the time-based criterion and the monetary-based criterion, respectively. We further investigate the effects of various parameters which include the degree of path overlapping (the commonality factor), the network complexity, degree of traffic congestion, the VOT of user classes, the network familiarity, and the total demand on the inefficiency bounds.

Highlights

Concerning the path choice behavior in networks, Wardrop proposed two basic principles: one is the user equilibrium (UE) and the other is the system optimum (SO) [1]. e UE principle shows that all used paths have minimum and equal travel cost, and all unused paths have higher or equal travel cost
Considering a transportation network with multiple classes of users, Yu et al [38] studied the inefficiency of the multiclass stochastic user equilibrium (SUE), which is the extension of research achievements in [37]
Different from the existing studies, this study extends the logit-based SUE to the multiclass C-Logit stochastic user equilibrium (CL-SUE). e purpose of our study was to derive four efficiency loss upper bounds of the multiclass CL-SUE. e two corresponding models, i.e., multiclass SO model and multiclass C-Logit stochastic system optimum (CL-SSO) model, should be mentioned before exploring the efficiency loss of the multiclass CL-SUE. e multiclass SO model that minimizes the total system travel time (TSTT) has been widely used in the literature

Summary

Introduction

Concerning the path choice behavior in networks, Wardrop proposed two basic principles: one is the user equilibrium (UE) and the other is the system optimum (SO) [1]. e UE principle shows that all used paths have minimum and equal travel cost (or time), and all unused paths have higher or equal travel cost (or time). Considering a transportation network with multiple classes of users, Yu et al [38] studied the inefficiency of the multiclass SUE, which is the extension of research achievements in [37]. Yong et al provided several efficiency loss upper bounds of the CL-SUE by considering the overlapping effects between paths [39], which is the extension of research achievements in [37]. The effects of various parameters (e.g., degree of traffic congestion and total traffic demand of the network) on the inefficiency upper bound has been widely studied, while paying less attention to commonality factor reflecting path overlapping. Is paper studies the effects of commonality factor reflecting path overlapping on the efficiency loss of the multiclass CL-SUE.

Review of Multiclass SUE and CL-SUE Models

Summary of the Main Research Findings

Conclusions