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Time-dependent Hyperstar algorithm for robust vehicle navigation

Author

Listed:
  • Bell, Michael G.H.
  • Trozzi, Valentina
  • Hosseinloo, Solmaz Haji
  • Gentile, Guido
  • Fonzone, Achille

Abstract

The vehicle navigation problem studied in Bell (2009) is revisited and a time-dependent reverse Hyperstar algorithm is presented. This minimises the expected time of arrival at the destination, and all intermediate nodes, where expectation is based on a pessimistic (or risk-averse) view of unknown link delays. This may also be regarded as a hyperpath version of the Chabini and Lan (2002) algorithm, which itself is a time-dependent A* algorithm. Links are assigned undelayed travel times and maximum delays, both of which are potentially functions of the time of arrival at the respective link. Probabilities for link use are sought that minimise the driver’s maximum exposure to delay on the approach to each node, leading to the determination of a pessimistic expected time of arrival at the destination and all intermediate nodes. Since the context considered is vehicle navigation, the probability of link use measures link attractiveness, so a link with a zero probability of use is unattractive while a link with a probability of use equal to one will have no attractive alternatives. A solution algorithm is presented and proven to solve the problem provided the node potentials are feasible and a FIFO condition applies to undelayed link travel times. The paper concludes with a numerical example.

Suggested Citation

  • Bell, Michael G.H. & Trozzi, Valentina & Hosseinloo, Solmaz Haji & Gentile, Guido & Fonzone, Achille, 2012. "Time-dependent Hyperstar algorithm for robust vehicle navigation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(5), pages 790-800.
  • Handle: RePEc:eee:transa:v:46:y:2012:i:5:p:790-800
    DOI: 10.1016/j.tra.2012.02.002
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    References listed on IDEAS

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    1. Nguyen, S. & Pallottino, S., 1988. "Equilibrium traffic assignment for large scale transit networks," European Journal of Operational Research, Elsevier, vol. 37(2), pages 176-186, November.
    2. Spiess, Heinz & Florian, Michael, 1989. "Optimal strategies: A new assignment model for transit networks," Transportation Research Part B: Methodological, Elsevier, vol. 23(2), pages 83-102, April.
    3. 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.
    4. Bell, Michael G.H., 2009. "Hyperstar: A multi-path Astar algorithm for risk averse vehicle navigation," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 97-107, January.
    5. Sung, Kiseok & Bell, Michael G. H. & Seong, Myeongki & Park, Soondal, 2000. "Shortest paths in a network with time-dependent flow speeds," European Journal of Operational Research, Elsevier, vol. 121(1), pages 32-39, February.
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    Cited by:

    1. repec:eee:transb:v:105:y:2017:i:c:p:235-248 is not listed on IDEAS
    2. Li, Qianfei & (Will) Chen, Peng & (Marco) Nie, Yu, 2015. "Finding optimal hyperpaths in large transit networks with realistic headway distributions," European Journal of Operational Research, Elsevier, vol. 240(1), pages 98-108.

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