Dynamic journeying under uncertainty
We introduce a journey planning problem in multi-modal transportation networks under uncertainty. The goal is to find a journey, possibly involving transfers between different transport services, from a given origin to a given destination within a specified time horizon. Due to uncertainty in travel times, the arrival times of transport services at public transport stops are modeled as random variables. If a transfer between two services is rendered unsuccessful, the commuter has to reconsider the remaining path to the destination. The problem is modeled as a Markov decision process in which states are defined as paths in the transport network. The main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time. By assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem. Analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination, the proposed approximations may be useful for practical purposes due to their computational simplicity. In addition to on-time arrival probability, we show how travel and overdue costs can be taken into account, making the model applicable to freight transportation problems.
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- Androutsopoulos, Konstantinos N. & Zografos, Konstantinos G., 2009. "Solving the multi-criteria time-dependent routing and scheduling problem in a multimodal fixed scheduled network," European Journal of Operational Research, Elsevier, vol. 192(1), pages 18-28, January.
- Wong, S. C. & Tong, C. O., 1998. "Estimation of time-dependent origin-destination matrices for transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(1), pages 35-48, January.
- Modesti, Paola & Sciomachen, Anna, 1998. "A utility measure for finding multiobjective shortest paths in urban multimodal transportation networks," European Journal of Operational Research, Elsevier, vol. 111(3), pages 495-508, December.
- Davies, Cedric & Lingras, Pawan, 2003. "Genetic algorithms for rerouting shortest paths in dynamic and stochastic networks," European Journal of Operational Research, Elsevier, vol. 144(1), pages 27-38, January.
- Fosgerau, Mogens & Karlström, Anders, 2007.
"The value of reliability,"
5733, University Library of Munich, Germany.
- 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.
- Kenneth A. Small & Clifford Winston & Jia Yan, 2005. "Uncovering the Distribution of Motorists' Preferences for Travel Time and Reliability," Econometrica, Econometric Society, vol. 73(4), pages 1367-1382, 07.
- Murthy, Ishwar & Sarkar, Sumit, 1997. "Exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function," European Journal of Operational Research, Elsevier, vol. 103(1), pages 209-229, November.
- Thomas, Barrett W. & White III, Chelsea C., 2007. "The dynamic shortest path problem with anticipation," European Journal of Operational Research, Elsevier, vol. 176(2), pages 836-854, January.
- Jonathan F. Bard & James E. Bennett, 1991. "Arc Reduction and Path Preference in Stochastic Acyclic Networks," Management Science, INFORMS, vol. 37(2), pages 198-215, February.
- Brownstone, David & Small, Kenneth A., 2005.
"Valuing time and reliability: assessing the evidence from road pricing demonstrations,"
Transportation Research Part A: Policy and Practice,
Elsevier, vol. 39(4), pages 279-293, May.
- Brownstone, David & Small, Kenneth A., 2003. "Valuing Time and Reliability: Assessing the Evidence from Road Pricing Demonstrations," University of California Transportation Center, Working Papers qt95z0p35k, University of California Transportation Center.
- Chiang, Yu-Sheng & O. Roberts, Paul, 1980. "A note on transit time and reliability for regular-route trucking," Transportation Research Part B: Methodological, Elsevier, vol. 14(1-2), pages 59-65.
- Ziliaskopoulos, Athanasios & Wardell, Whitney, 2000. "An intermodal optimum path algorithm for multimodal networks with dynamic arc travel times and switching delays," European Journal of Operational Research, Elsevier, vol. 125(3), pages 486-502, September.
- Azaron, Amir & Kianfar, Farhad, 2003. "Dynamic shortest path in stochastic dynamic networks: Ship routing problem," European Journal of Operational Research, Elsevier, vol. 144(1), pages 138-156, January.
- 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.
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