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Mathematical Problems in Engineering
Volume 2018, Article ID 1609238, 10 pages
Research Article

Optimization Model for Reserve Fleet Sizes in Traditional Transit Systems considering the Risk of Vehicle Breakdowns

College of Transportation, Jilin University, Changchun 130022, China

Correspondence should be addressed to Huasheng Liu; moc.361@125gnehsauhuil

Received 17 May 2018; Accepted 12 November 2018; Published 22 November 2018

Academic Editor: Florin Stoican

Copyright © 2018 Bowen Hou 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.


Traditional transit systems are susceptible to unexpected costs and delays due to unforeseen events, such as vehicle breakdowns. The randomness of these events gives the appearance of an imbalance in the number of operating vehicles and of unreliable transit services. Therefore, this paper proposes the queueing theory as a means to characterize the state of any given transit system considering the risk of vehicle breakdowns. In addition, the proposed method is used to create an optimized model for reserve fleet sizes in transit systems, in order to ensure the reliability of the transit system and minimize the total cost of any transit system exposed to the risks of vehicle breakdowns. The optimization is conducted based on the two main characteristics of all bus systems, namely, operator costs and user costs, in both normal and disruptive situations. In addition, the situations in our optimization are generated in scenarios that have a certain degree of probability of experiencing delays. This paper formulates such an optimization model, presents the formulation solution method, and proves the validity of the proposed method.