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Time-dependent Hyperstar algorithm for robust vehicle navigation.

Bell, Michael G H; Trozzi, Valentina; Hosseinloo, Solmaz Haji; Gentile, Guido; Fonzone, Achille


Michael G H Bell

Valentina Trozzi

Solmaz Haji Hosseinloo

Guido Gentile


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.


Bell, M. G. H., Trozzi, V., Hosseinloo, S. H., Gentile, G., & Fonzone, A. (2012). Time-dependent Hyperstar algorithm for robust vehicle navigation. Transportation Research Part A: Policy and Practice, 46, 790-800.

Journal Article Type Article
Publication Date 2012
Deposit Date Apr 10, 2014
Print ISSN 0965-8564
Electronic ISSN 1879-2375
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 46
Pages 790-800
Keywords Robust route guidance; Vehicle navigation;
Uncertain networks;
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