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Study on mean-standard deviation shortest path problem in stochastic and time-dependent networks: A stochastic dominance based approach

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  • Wu, Xing

Abstract

This paper studies a mean-standard deviation shortest path model, also called travel time budget (TTB) model. A route’s TTB is defined as this route’s mean travel time plus a travel time margin, which is the route travel time’s standard deviation multiplied with a factor. The TTB model violates the Bellman’s Principle of Optimality (BPO), making it difficult to solve it in any large stochastic and time-dependent network. Moreover, it is found that if path travel time distributions are skewed, the conventional TTB model cannot reflect travelers’ heterogeneous risk-taking behavior in route choice. This paper proposes to use the upper or lower semi-standard deviation to replace the standard deviation in the conventional TTB model (the new models are called derived TTB models), because these derived TTB models can well capture such heterogeneous risk-taking behavior when the path travel time distributions are skewed. More importantly, this paper shows that the optimal solutions of these two derived TTB models must be non-dominated paths under some specific stochastic dominance (SD) rules. These finding opens the door to solve these derived TTB models efficiently in large stochastic and time-dependent networks. Numerical examples are presented to illustrate these findings.

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  • Wu, Xing, 2015. "Study on mean-standard deviation shortest path problem in stochastic and time-dependent networks: A stochastic dominance based approach," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 275-290.
    • Handle: RePEc:eee:transb:v:80:y:2015:i:c:p:275-290
    DOI: 10.1016/j.trb.2015.07.009
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    Cited by:

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    2. Chai, Huajun, 2019. "Dynamic Traffic Routing and Adaptive Signal Control in a Connected Vehicles Environment," Institute of Transportation Studies, Working Paper Series qt9ng3z8vn, Institute of Transportation Studies, UC Davis.
    3. Anny B. Wang & W. Y. Szeto, 2020. "Bounding the Inefficiency of the Reliability-Based Continuous Network Design Problem Under Cost Recovery," Networks and Spatial Economics, Springer, vol. 20(2), pages 395-422, June.
    4. Chen, Bi Yu & Li, Qingquan & Lam, William H.K., 2016. "Finding the k reliable shortest paths under travel time uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 189-203.
    5. Shen, Liang & Shao, Hu & Wu, Ting & Fainman, Emily Zhu & Lam, William H.K., 2020. "Finding the reliable shortest path with correlated link travel times in signalized traffic networks under uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    6. Yang, Lixing & Zhang, Yan & Li, Shukai & Gao, Yuan, 2016. "A two-stage stochastic optimization model for the transfer activity choice in metro networks," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 271-297.
    7. Zhang, Yufeng & Khani, Alireza, 2019. "An algorithm for reliable shortest path problem with travel time correlations," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 92-113.
    8. Xiangfeng Ji & Xuegang (Jeff) Ban & Mengtian Li & Jian Zhang & Bin Ran, 2017. "Non-expected Route Choice Model under Risk on Stochastic Traffic Networks," Networks and Spatial Economics, Springer, vol. 17(3), pages 777-807, September.
    9. Liu, Siyuan & Qu, Qiang, 2016. "Dynamic collective routing using crowdsourcing data," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 450-469.

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