Modeling the Morning Commute Problem With Stochastic Travel Time in a Bottleneck Model

Xiao Guo,Lu Tian,Aomuhan Zhang,Tongfei Li

doi:10.1109/access.2020.3016701

Abstract

This paper studies the traffic behavior of travelers who drive from living areas to workplaces through bottleneck roads during the early rush hours when the travel time on the road is uncertain. Based on the travel time which is assumed stochastic and follows a uniform distribution, the equilibrium properties of the proposed model are derived and individual travel cost is obtained. According to the assumptions, three possible departure-time intervals have been considered when users always arrive early, arrive early or late, always arrive late. Travelers' travel choice behaviors are analyzed in detail and equilibrium is achieved with these three situations. The results show that even if they start at the same time, they may arrive early or late, but not necessarily early or late. Numerical examples verify the theoretical analysis, and it is found that the time interval of arriving at the workplace also changes when the stochastic degree of travel time increases.

Highlights

The well-known bottleneck model was originally developed by Vickrey [1]
Jenelius [20] extended the analysis of the value of mean travel time (VMTT) and travel time variability (VTTV) from bottleneck model to a more general multi-trip setting, incorporating the effects of flexibility in activity scheduling and dependence of travel times across trips
PROPERTIES OF THE STOCHASTIC BOTTLENECK MODEL We present the following propositions to reveal some interesting properties of the equilibrium solution of the proposed bottleneck model

Summary

INTRODUCTION

The well-known bottleneck model was originally developed by Vickrey [1]. This model is a common situation during the morning rush hour, where a fixed and very large number of travelers travel from home to workplace along the same stretch of road. Jenelius [20] extended the analysis of the value of mean travel time (VMTT) and travel time variability (VTTV) from bottleneck model to a more general multi-trip setting, incorporating the effects of flexibility in activity scheduling and dependence of travel times across trips In those stochastic capacity bottleneck models, they transform all the random events into the changes of capacity and construct their bottleneck models. In those stochastic travel time bottleneck models, most of them assumed everyone may arrive early or late, regarded the congestion as endogenous existence, and consider the reliability of travel time. The earliest travelers are bound to arrive early, and the latest travelers are bound to arrive late Based on this phenomenon, this paper studies the travelers’ travel behavior in the stochastic bottleneck model.

OVERVIEW OF THE CLASSICAL BOTTLENECK MODEL

PROPERTIES OF THE STOCHASTIC BOTTLENECK MODEL

NUMERICAL EXAMPLES

CONCLUSION