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Separation in homogeneous systems with independent identical elements

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  • Levitin, Gregory
  • Hausken, Kjell

Abstract

The paper considers strategic defense and attack of a system which can be separated into independent identical homogeneous parallel elements. The defender distributes its resource between separation of the elements and their protection from outside attacks. The attacker distributes its effort evenly among all attacked elements. The vulnerability of each element is determined by a contest success function between the attacker and the defender. The defender can choose a subset of the elements to defend. The attacker does not know which elements are protected and can choose a number of randomly chosen elements to attack. Separation efficiency conditions are formulated dependent on the defender's and attacker's budgets, separation costs, contest intensity, and system demand. An algorithm for determining the optimal number of protected elements is suggested for the case when both the defender and the attacker can choose the number of protected and attacked elements freely. The article considers both the cases without and with performance redundancy. Illustrative numerical examples are presented.

Suggested Citation

  • Levitin, Gregory & Hausken, Kjell, 2010. "Separation in homogeneous systems with independent identical elements," European Journal of Operational Research, Elsevier, vol. 203(3), pages 625-634, June.
    • Handle: RePEc:eee:ejores:v:203:y:2010:i:3:p:625-634
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    Cited by:

    1. Chen, Shun & Zhao, Xudong & Chen, Zhilong & Hou, Benwei & Wu, Yipeng, 2022. "A game-theoretic method to optimize allocation of defensive resource to protect urban water treatment plants against physical attacks," International Journal of Critical Infrastructure Protection, Elsevier, vol. 36(C).
    2. Levitin, Gregory & Xing, Liudong & Amari, Suprasad V. & Dai, Yuanshun, 2013. "Reliability of non-repairable phased-mission systems with propagated failures," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 218-228.
    3. Hausken, Kjell, 2024. "Fifty Years of Operations Research in Defense," European Journal of Operational Research, Elsevier, vol. 318(2), pages 355-368.
    4. Hiba Baroud & Kash Barker & Jose E. Ramirez‐Marquez & Claudio M. Rocco, 2015. "Inherent Costs and Interdependent Impacts of Infrastructure Network Resilience," Risk Analysis, John Wiley & Sons, vol. 35(4), pages 642-662, April.
    5. Musegaas, Marieke & Schlicher, Loe & Blok, Herman, 2022. "Stackelberg production-protection games: Defending crop production against intentional attacks," European Journal of Operational Research, Elsevier, vol. 297(1), pages 102-119.
    6. Dan Kovenock & Brian Roberson, 2012. "Strategic Defense And Attack For Series And Parallel Reliability Systems: Comment," Defence and Peace Economics, Taylor & Francis Journals, vol. 23(5), pages 507-515, October.
    7. Lins, Isis Didier & Rêgo, Leandro Chaves & Moura, Márcio das Chagas & Droguett, Enrique López, 2013. "Selection of security system design via games of imperfect information and multi-objective genetic algorithm," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 59-66.
    8. Levitin, Gregory & Finkelstein, Maxim, 2017. "Effect of element separation in series-parallel systems exposed to random shocks," European Journal of Operational Research, Elsevier, vol. 260(1), pages 305-315.
    9. Mo, Huadong & Xie, Min & Levitin, Gregory, 2015. "Optimal resource distribution between protection and redundancy considering the time and uncertainties of attacks," European Journal of Operational Research, Elsevier, vol. 243(1), pages 200-210.
    10. Hunt, Kyle & Agarwal, Puneet & Zhuang, Jun, 2021. "Technology adoption for airport security: Modeling public disclosure and secrecy in an attacker-defender game," Reliability Engineering and System Safety, Elsevier, vol. 207(C).

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