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Mathematical Problems in Engineering
Volume 2016, Article ID 7609572, 13 pages
Research Article

Least Expected Time Paths in Stochastic Schedule-Based Transit Networks

Faculty of Computer Science & Engineering, Ho Chi Minh City University of Technology, VNU-HCM, 268 Ly Thuong Kiet Street, Ho Chi Minh City 740500, Vietnam

Received 14 December 2015; Revised 9 February 2016; Accepted 18 February 2016

Academic Editor: Wuhong Wang

Copyright © 2016 Dang Khoa Vo 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.


We consider the problem of determining a least expected time (LET) path that minimizes the number of transfers and the expected total travel time in a stochastic schedule-based transit network. A time-dependent model is proposed to represent the stochastic transit network where vehicle arrival times are fully stochastically correlated. An exact label-correcting algorithm is developed, based on a proposed dominance condition by which Bellman’s principle of optimality is valid. Experimental results, which are conducted on the Ho Chi Minh City bus network, show that the running time of the proposed algorithm is suitable for real-time operation, and the resulting LET paths are robust against uncertainty, such as unknown traffic scenarios.