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A graph patrol problem with random attack times

Lin, Kyle and Atkinson, Michael and Chung, Timothy and Glazebrook, Kevin (2013) A graph patrol problem with random attack times. Operations Research, 61 (3). pp. 694-710. ISSN 0030-364X

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    Abstract

    This paper presents a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. To design a patrol policy, the patroller needs to take into account not only the graph structure, but also the different attack time distributions, as well as different costs incurred due to successful attacks, at different nodes. We consider both random attackers and strategic attackers. A random attacker chooses which node to attack according to a probability distribution known to the patroller. A strategic attacker plays a two-person zero-sum game with the patroller. For each case, we give an exact linear program to compute the optimal solution. Because the linear programs quickly become computationally intractable as the problem size grows, we develop index-based heuristics. In the random-attacker case, our heuristic is optimal when there are two nodes, and in a suitably chosen asymptotic regime. In the strategic-attacker case, our heuristic is optimal when there are two nodes if the attack times are deterministic taking integer values. In our numerical experiments, our heuristic typically achieves within 1% of optimality with computation time orders of magnitude less than what is required to compute the optimal policy.

    Item Type: Article
    Journal or Publication Title: Operations Research
    Uncontrolled Keywords: Military ; dynamic programming/optimal control ; game/group decisions ; search/surveillance
    Subjects: H Social Sciences > HB Economic Theory
    Departments: Lancaster University Management School > Management Science
    ID Code: 59457
    Deposited By: ep_importer_pure
    Deposited On: 24 Oct 2012 11:11
    Refereed?: Yes
    Published?: Published
    Last Modified: 31 Oct 2014 00:04
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/59457

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