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Arriving on Time

Author

Listed:
  • Y. Y. Fan

    (University of California)

  • R. E. Kalaba

    (University of Southern California)

  • J. E. Moore

    (University of Southern California)

Abstract

This research proposes a procedure for identifying dynamic routing policies in stochastic transportation networks. It addresses the problem of maximizing the probability of arriving on time. Given a current location (node), the goal is to identify the next node to visit so that the probability of arriving at the destination by time t or sooner is maximized, given the probability density functions for the link travel times. The Bellman principle of optimality is applied to formulate the mathematical model of this problem. The unknown functions describing the maximum probability of arriving on time are estimated accurately for a few sample networks by using the Picard method of successive approximations. The maximum probabilities can be evaluated without enumerating the network paths. The Laplace transform and its numerical inversion are introduced to reduce the computational cost of evaluating the convolution integrals that result from the successive approximation procedure.

Suggested Citation

  • Y. Y. Fan & R. E. Kalaba & J. E. Moore, 2005. "Arriving on Time," Journal of Optimization Theory and Applications, Springer, vol. 127(3), pages 497-513, December.
    • Handle: RePEc:spr:joptap:v:127:y:2005:i:3:d:10.1007_s10957-005-7498-5
    DOI: 10.1007/s10957-005-7498-5
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    Citations

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    Cited by:

    1. Li, Wenjie & Yang, Lixing & Wang, Li & Zhou, Xuesong & Liu, Ronghui & Gao, Ziyou, 2017. "Eco-reliable path finding in time-variant and stochastic networks," Energy, Elsevier, vol. 121(C), pages 372-387.
    2. Wu, Xing & (Marco) Nie, Yu, 2011. "Modeling heterogeneous risk-taking behavior in route choice: A stochastic dominance approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(9), pages 896-915, November.
    3. Leilei Zhang & Tito Homem-de-Mello, 2017. "An Optimal Path Model for the Risk-Averse Traveler," Transportation Science, INFORMS, vol. 51(2), pages 518-535, May.
    4. 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.
    5. Verbeeck, C. & Vansteenwegen, P. & Aghezzaf, E.-H., 2016. "Solving the stochastic time-dependent orienteering problem with time windows," European Journal of Operational Research, Elsevier, vol. 255(3), pages 699-718.
    6. Zhaoqi Zang & Xiangdong Xu & Kai Qu & Ruiya Chen & Anthony Chen, 2022. "Travel time reliability in transportation networks: A review of methodological developments," Papers 2206.12696, arXiv.org, revised Jul 2022.
    7. Nie, Yu (Marco) & Wu, Xing, 2009. "Shortest path problem considering on-time arrival probability," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 597-613, July.
    8. Matthias Ruß & Gunther Gust & Dirk Neumann, 2021. "The Constrained Reliable Shortest Path Problem in Stochastic Time-Dependent Networks," Operations Research, INFORMS, vol. 69(3), pages 709-726, May.
    9. Shahabi, Mehrdad & Unnikrishnan, Avinash & Boyles, Stephen D., 2013. "An outer approximation algorithm for the robust shortest path problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 58(C), pages 52-66.
    10. Yang, Lixing & Zhou, Xuesong, 2017. "Optimizing on-time arrival probability and percentile travel time for elementary path finding in time-dependent transportation networks: Linear mixed integer programming reformulations," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 68-91.
    11. Liu, Yang & Blandin, Sebastien & Samaranayake, Samitha, 2019. "Stochastic on-time arrival problem in transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 122-138.
    12. Xing, Tao & Zhou, Xuesong, 2011. "Finding the most reliable path with and without link travel time correlation: A Lagrangian substitution based approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1660-1679.
    13. Manseur, Farida & Farhi, Nadir & Nguyen Van Phu, Cyril & Haj-Salem, Habib & Lebacque, Jean-Patrick, 2020. "Robust routing, its price, and the tradeoff between routing robustness and travel time reliability in road networks," European Journal of Operational Research, Elsevier, vol. 285(1), pages 159-171.
    14. Huang, Kuancheng & Wu, Kun-Feng & Ardiansyah, Muhammad Nashir, 2019. "A stochastic dairy transportation problem considering collection and delivery phases," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 129(C), pages 325-338.
    15. Häme, Lauri & Hakula, Harri, 2013. "Dynamic journeying under uncertainty," European Journal of Operational Research, Elsevier, vol. 225(3), pages 455-471.
    16. Correa, José & Hoeksma, Ruben & Schröder, Marc, 2019. "Network congestion games are robust to variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 69-78.
    17. Qi, Jin & Sim, Melvyn & Sun, Defeng & Yuan, Xiaoming, 2016. "Preferences for travel time under risk and ambiguity: Implications in path selection and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 264-284.
    18. 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.
    19. Nie, Yu (Marco) & Wu, Xing & Dillenburg, John F. & Nelson, Peter C., 2012. "Reliable route guidance: A case study from Chicago," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(2), pages 403-419.
    20. Khani, Alireza & Boyles, Stephen D., 2015. "An exact algorithm for the mean–standard deviation shortest path problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 252-266.
    21. Arthur Flajolet & Sébastien Blandin & Patrick Jaillet, 2018. "Robust Adaptive Routing Under Uncertainty," Operations Research, INFORMS, vol. 66(1), pages 210-229, January.

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