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Reliable a Priori Shortest Path Problem with Limited Spatial and Temporal Dependencies

In: Transportation and Traffic Theory 2009: Golden Jubilee

Author

Listed:
  • Yu Marco Nie

    (Northwestern University)

  • Xing Wu

    (Northwestern University)

Abstract

This paper studies the problem of finding most reliable a priori shortest paths (RASP) in a stochastic and time-dependent network. Correlations are modeled by assuming the probability density functions of link traversal times to be conditional on both the time of day and link states. Such correlations are spatially limited by the Markovian property of the link states, which may be such defined to reflect congestion levels or the intensity of random disruptions. We formulate the RASP problem with the above correlation structure as a general dynamic programming problem, and show that the optimal solution is a set of non-dominated paths under the first-order stochastic dominance. Conditions are proposed to regulate the transition probabilities of link states such that Bellman’s principle of optimality can be utilized. We prove that a non-dominated path should contain no cycles if random link travel times are consistent with the stochastic first-in-first-out principle. The RASP problem is solved using a non-deterministic polynomial label correcting algorithm. Approximation algorithms with polynomial complexity may be achieved when further assumptions are made to the correlation structure and to the applicability of dynamic programming. Numerical results are provided.

Suggested Citation

  • Yu Marco Nie & Xing Wu, 2009. "Reliable a Priori Shortest Path Problem with Limited Spatial and Temporal Dependencies," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 169-195, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-0820-9_9
    DOI: 10.1007/978-1-4419-0820-9_9
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    Citations

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    Cited by:

    1. Zhang, Yuli & Max Shen, Zuo-Jun & Song, Shiji, 2017. "Lagrangian relaxation for the reliable shortest path problem with correlated link travel times," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 501-521.
    2. Borzou Rostami & Guy Desaulniers & Fausto Errico & Andrea Lodi, 2021. "Branch-Price-and-Cut Algorithms for the Vehicle Routing Problem with Stochastic and Correlated Travel Times," Operations Research, INFORMS, vol. 69(2), pages 436-455, March.
    3. He Huang & Song Gao, 2018. "Trajectory-Adaptive Routing in Dynamic Networks with Dependent Random Link Travel Times," Transportation Science, INFORMS, vol. 52(1), pages 102-117, January.
    4. Du, Bo & Wang, David Z.W., 2014. "Continuum modeling of park-and-ride services considering travel time reliability and heterogeneous commuters – A linear complementarity system approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 58-81.
    5. Ehsan Jafari & Stephen D. Boyles, 2017. "Multicriteria Stochastic Shortest Path Problem for Electric Vehicles," Networks and Spatial Economics, Springer, vol. 17(3), pages 1043-1070, September.
    6. Hao Hu & Renata Sotirov, 2020. "On Solving the Quadratic Shortest Path Problem," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 219-233, April.

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