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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 767851, 9 pages
Research Article

Congestion Behavior under Uncertainty on Morning Commute with Preferred Arrival Time Interval

1School of Economics and Management, Beihang University, Beijing 100191, China
2Institute for Transport Studies, University of Leeds, Leeds LS2 9JT, UK

Received 5 November 2013; Accepted 18 December 2013; Published 17 February 2014

Academic Editor: Huimin Niu

Copyright © 2014 LingLing Xiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper extends the bottleneck model to study congestion behavior of morning commute with flexible work schedule. The proposed model assumes a stochastic bottleneck capacity which follows a uniform distribution and homogeneous commuters who have the same preferred arrival time interval. The commuters are fully aware of the stochastic properties of travel time and schedule delay distributions at all departure times that emerge from day-to-day capacity variations. The commuters’ departure time choice follows user equilibrium (UE) principle in terms of the expected trip cost. Analytical and numerical solutions of this model are provided. The equilibrium departure time patterns are examined which show that the stochastic capacity increases the mean trip cost and lengthens the rush hour. The adoption of flexitime results in less congestion and more efficient use of bottleneck capacity than fixed-time work schedule. The longer the flexi-time interval is, the more uniformly distributed the departure times are.