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Defense Resource Distribution Between Protection and Redundancy for Constant Resource Stockpiling Pace

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  • Gregory Levitin
  • Kjell Hausken

Abstract

The article considers the optimal resource distribution in a parallel system between increasing protection and providing redundancy in a situation when the attacker's and defender's resources are stockpiling and the resource increment rate is constant. It is assumed that the system must perform within an exogenously given time horizon and the attack time probability is uniformly distributed along this horizon. The defender optimizes the resource distribution in order to minimize the system destruction probability during the time horizon. First, we find the optimal pace of construction of the new redundant elements assuming that the construction must start in the initial stage of the stockpiling process. We show that starting construction of new elements in the beginning of the system's existence results in its high initial vulnerability. Introducing the time delay before starting the construction can reduce the initial system vulnerability and the entire system destruction probability. The problem of optimization of time delay and new element construction pace is considered with and without constraint on the initial system vulnerability. Examples illustrating the methodology of the optimal defense strategy analysis are presented.

Suggested Citation

  • Gregory Levitin & Kjell Hausken, 2011. "Defense Resource Distribution Between Protection and Redundancy for Constant Resource Stockpiling Pace," Risk Analysis, John Wiley & Sons, vol. 31(10), pages 1632-1645, October.
  • Handle: RePEc:wly:riskan:v:31:y:2011:i:10:p:1632-1645
    DOI: 10.1111/j.1539-6924.2011.01593.x
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    References listed on IDEAS

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    1. Levitin, Gregory & Hausken, Kjell, 2008. "Protection vs. redundancy in homogeneous parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1444-1451.
    2. Hausken, Kjell, 2008. "Strategic defense and attack for series and parallel reliability systems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 856-881, April.
    3. Vicki Bier & Santiago Oliveros & Larry Samuelson, 2007. "Choosing What to Protect: Strategic Defensive Allocation against an Unknown Attacker," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(4), pages 563-587, August.
    4. Kjell Hausken, 2005. "Production and Conflict Models Versus Rent-Seeking Models," Public Choice, Springer, vol. 123(1), pages 59-93, April.
    5. Hirshleifer, Jack, 1995. "Anarchy and Its Breakdown," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 26-52, February.
    6. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
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    Cited by:

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    2. Kaiye Gao & Hui Xiao & Li Qu & Shouyang Wang, 2022. "Optimal interception strategy of air defence missile system considering multiple targets and phases," Journal of Risk and Reliability, , vol. 236(1), pages 138-147, February.
    3. Liang, Liang & Chen, Jingxian & Siqueira, Kevin, 2020. "Revenge or continued attack and defense in defender–attacker conflicts," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1180-1190.
    4. Di Wu & Xiangbin Yan & Rui Peng & Shaomin Wu, 2020. "Optimal defence-attack strategies between one defender and two attackers," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(11), pages 1830-1846, November.
    5. Chen, Die & Xu, Maochao & Shi, Weidong, 2018. "Defending a cyber system with early warning mechanism," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 224-234.
    6. Wu, Di & Yan, Xiangbin & Peng, Rui & Wu, Shaomin, 2020. "Risk-attitude-based defense strategy considering proactive strike, preventive strike and imperfect false targets," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    7. 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.

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