IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v17y2017i3d10.1007_s11067-017-9345-2.html
   My bibliography  Save this article

Finding the Most Reliable Strategy on Stochastic and Time-Dependent Transportation Networks: A Hypergraph Based Formulation

Author

Listed:
  • A. Arun Prakash

    (Singapore-MIT Alliance for Research and Technology)

  • Karthik K. Srinivasan

    (IIT Madras)

Abstract

This study addresses the problem of determining the most reliable time-adaptive strategy on a stochastic and time-dependent transportation network. The reliability is measured as a conic combination of the mean and standard-deviation of travel time and is termed robust-cost. The stochastic time-dependent network is represented as a directed acyclic hypergraph, where the time-adaptive strategies correspond to the hyperpaths. This representation transforms the problem to that of determining the hyperpath with the least robust-cost on the constructed hypergraph. The minimum robust-cost strategy problem is difficult to solve because of the non-linear objective function. Consequently, the solution procedures commonly adopted in the literature —that are based on substrategy optimality and substrategy non-dominance —are not applicable to this problem. In this light, we propose a novel bounds-based iterative algorithm that determines the minimum robust-cost strategy on the stochastic and time-dependent networks. This algorithm needs to determine the least and K-best strategies in the second moment of travel time, for which an efficient procedure is also proposed. The algorithm is shown to be exact and exhibit parameterically polynomial behavior; computational tests were performed to demonstrate its efficiency. Further, tests showed that the minimum robust-cost strategy compromises little in terms of the mean travel time (0.2%–2.9%) —compared to least expected travel time strategy— with significant reduction in travel time variability (6.2%–29.8%).

Suggested Citation

  • A. Arun Prakash & Karthik K. Srinivasan, 2017. "Finding the Most Reliable Strategy on Stochastic and Time-Dependent Transportation Networks: A Hypergraph Based Formulation," Networks and Spatial Economics, Springer, vol. 17(3), pages 809-840, September.
  • Handle: RePEc:kap:netspa:v:17:y:2017:i:3:d:10.1007_s11067-017-9345-2
    DOI: 10.1007/s11067-017-9345-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-017-9345-2
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11067-017-9345-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Carrion, Carlos & Levinson, David, 2012. "Value of travel time reliability: A review of current evidence," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(4), pages 720-741.
    2. Srinivasan, Karthik K. & Prakash, A.A. & Seshadri, Ravi, 2014. "Finding most reliable paths on networks with correlated and shifted log–normal travel times," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 110-128.
    3. Huang, He & Gao, Song, 2012. "Optimal paths in dynamic networks with dependent random link travel times," Transportation Research Part B: Methodological, Elsevier, vol. 46(5), pages 579-598.
    4. 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.
    5. Nielsen, Lars Relund & Andersen, Kim Allan & Pretolani, Daniele, 2014. "Ranking paths in stochastic time-dependent networks," European Journal of Operational Research, Elsevier, vol. 236(3), pages 903-914.
    6. Bi Chen & William Lam & Agachai Sumalee & Qingquan Li & Hu Shao & Zhixiang Fang, 2013. "Finding Reliable Shortest Paths in Road Networks Under Uncertainty," Networks and Spatial Economics, Springer, vol. 13(2), pages 123-148, June.
    7. Fu, Liping & Rilett, L. R., 1998. "Expected shortest paths in dynamic and stochastic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(7), pages 499-516, September.
    8. Jin Y. Yen, 1971. "Finding the K Shortest Loopless Paths in a Network," Management Science, INFORMS, vol. 17(11), pages 712-716, July.
    9. Pretolani, Daniele, 2000. "A directed hypergraph model for random time dependent shortest paths," European Journal of Operational Research, Elsevier, vol. 123(2), pages 315-324, June.
    10. 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.
    11. Yu Nie & Xing Wu & Tito Homem-de-Mello, 2012. "Optimal Path Problems with Second-Order Stochastic Dominance Constraints," Networks and Spatial Economics, Springer, vol. 12(4), pages 561-587, December.
    12. Suvrajeet Sen & Rekha Pillai & Shirish Joshi & Ajay K. Rathi, 2001. "A Mean-Variance Model for Route Guidance in Advanced Traveler Information Systems," Transportation Science, INFORMS, vol. 35(1), pages 37-49, February.
    13. Elise D. Miller-Hooks & Hani S. Mahmassani, 2000. "Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks," Transportation Science, INFORMS, vol. 34(2), pages 198-215, May.
    14. Gao, Song & Chabini, Ismail, 2006. "Optimal routing policy problems in stochastic time-dependent networks," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 93-122, February.
    15. Valentina Trozzi & Guido Gentile & Ioannis Kaparias & Michael Bell, 2015. "Effects of Countdown Displays in Public Transport Route Choice Under Severe Overcrowding," Networks and Spatial Economics, Springer, vol. 15(3), pages 823-842, September.
    16. Yang, Lixing & Zhou, Xuesong, 2014. "Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 22-44.
    17. Randolph W. Hall, 1986. "The Fastest Path through a Network with Random Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 20(3), pages 182-188, August.
    18. Yueyue Fan & Yu Nie, 2006. "Optimal Routing for Maximizing the Travel Time Reliability," Networks and Spatial Economics, Springer, vol. 6(3), pages 333-344, September.
    19. 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.
    20. Bates, John & Polak, John & Jones, Peter & Cook, Andrew, 0. "The valuation of reliability for personal travel," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 37(2-3), pages 191-229, April.
    21. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Prakash, A. Arun, 2018. "Pruning algorithm for the least expected travel time path on stochastic and time-dependent networks," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 127-147.
    2. Arun Prakash, A., 2020. "Algorithms for most reliable routes on stochastic and time-dependent networks," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 202-220.
    3. Watling, David P. & Hazelton, Martin L., 2018. "Asymptotic approximations of transient behaviour for day-to-day traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 90-105.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Prakash, A. Arun, 2018. "Pruning algorithm for the least expected travel time path on stochastic and time-dependent networks," Transportation Research Part B: Methodological, Elsevier, vol. 108(C), pages 127-147.
    3. 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.
    4. 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.
    5. A. Arun Prakash & Karthik K. Srinivasan, 2018. "Pruning Algorithms to Determine Reliable Paths on Networks with Random and Correlated Link Travel Times," Transportation Science, INFORMS, vol. 52(1), pages 80-101, January.
    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. Arun Prakash, A., 2020. "Algorithms for most reliable routes on stochastic and time-dependent networks," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 202-220.
    8. 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.
    9. 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.
    10. Yang, Lixing & Zhou, Xuesong, 2014. "Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 22-44.
    11. 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.
    12. Srinivasan, Karthik K. & Prakash, A.A. & Seshadri, Ravi, 2014. "Finding most reliable paths on networks with correlated and shifted log–normal travel times," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 110-128.
    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. 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.
    15. 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.
    16. 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.
    17. 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.
    18. David Corredor-Montenegro & Nicolás Cabrera & Raha Akhavan-Tabatabaei & Andrés L. Medaglia, 2021. "On the shortest $$\alpha$$ α -reliable path problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 287-318, April.
    19. 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).
    20. Levering, Nikki & Boon, Marko & Mandjes, Michel & Núñez-Queija, Rudesindo, 2022. "A framework for efficient dynamic routing under stochastically varying conditions," Transportation Research Part B: Methodological, Elsevier, vol. 160(C), pages 97-124.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:netspa:v:17:y:2017:i:3:d:10.1007_s11067-017-9345-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.