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Optimizing randomized patrols

Alpern, Steven and Morton, Alec and Papadaki, Katerina (2009) Optimizing randomized patrols. Operational Research working papers, LSEOR 09.116. Operational Research Group, London School of Economics and Political Science, London, UK.

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Identification Number: LSEOR 09.116

Abstract

A key operational problem for those charged with the security of vulnerable facilities (such as airports or art galleries) is the scheduling and deployment of patrols. Motivated by the problem of optimizing randomized, and thus unpredictable, patrols, we present a class of patrolling games on graphs. The facility can be thought of as a graph Q of interconnected nodes (e.g. rooms, terminals) and the Attacker can choose to attack any node of Q within a given time T: He requires m consecutive periods there, uninterrupted by the Patroller, to commit his nefarious act (and win). The Patroller can follow any path on the graph. Thus the patrolling game is a win-lose game, where the Value is the probability that the Patroller successfully intercepts an attack, given best play on both sides. We determine analytically optimal (minimax) patrolling strategies for various classes of graphs, and discuss how our results could support decisions about hardening facilities or changing the topology of the terrain to be patrolled.

Item Type: Monograph (Working Paper)
Official URL: http://www.lse.ac.uk/collections/operationalResear...
Additional Information: © 2009 The London School of Economics and Political Science
Subjects: U Military Science > U Military Science (General)
Q Science > QA Mathematics
Sets: Research centres and groups > Management Science Group
Departments > Management
Date Deposited: 07 Dec 2009 16:54
Last Modified: 06 Jun 2012 17:16
URI: http://eprints.lse.ac.uk/id/eprint/26218

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