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Defending and attacking a network of two arcs subject to traffic congestion

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  • Bier, Vicki M.
  • Hausken, Kjell

Abstract

To study the effects of intentional attacks on transportation systems, we consider drivers who choose the more time-efficient of two arcs (possibly of different lengths). Both arcs are subjected to traffic congestion, and also to interdiction or blockage (e.g., by a terrorist attack). The model has three types of strategic actors: the government; the terrorist; and potential drivers. The government protects travel, while the terrorist interdicts travel, along the two arcs. Drivers choose the arc that gives the shortest travel time, and cannot choose an interdicted arc. The drivers have reservation travel times, such that if the actual travel time will exceed an individual driver's reservation travel time, that driver would prefer not to travel; the reservation travel times are allowed to vary among drivers. The objective function of the master problem, which the government minimizes and the terrorist maximizes, is the sum of the total travel time plus the reservation travel times of the non-travelers. Each potential driver decides endogenously whether to travel, according to whether the actual travel time is greater or lesser than that driver's reservation travel time.

Suggested Citation

  • Bier, Vicki M. & Hausken, Kjell, 2013. "Defending and attacking a network of two arcs subject to traffic congestion," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 214-224.
    • Handle: RePEc:eee:reensy:v:112:y:2013:i:c:p:214-224
    DOI: 10.1016/j.ress.2012.11.016
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    References listed on IDEAS

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    Citations

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    Cited by:

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    3. Wu, Baichao & Tang, Aiping & Wu, Jie, 2016. "Modeling cascading failures in interdependent infrastructures under terrorist attacks," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 1-8.
    4. Shan, Xiaojun & Zhuang, Jun, 2018. "Modeling cumulative defensive resource allocation against a strategic attacker in a multi-period multi-target sequential game," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 12-26.
    5. Ramirez-Marquez, José Emmanuel & Li, Qing, 2018. "Locating and protecting facilities from intentional attacks using secrecyAuthor-Name: Zhang, Chi," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 51-62.
    6. Hausken, Kjell, 2024. "Fifty Years of Operations Research in Defense," European Journal of Operational Research, Elsevier, vol. 318(2), pages 355-368.
    7. Nogal, Maria & O'Connor, Alan & Caulfield, Brian & Martinez-Pastor, Beatriz, 2016. "Resilience of traffic networks: From perturbation to recovery via a dynamic restricted equilibrium model," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 84-96.
    8. Rui Peng & Di Wu & Mengyao Sun & Shaomin Wu, 2021. "An attack-defense game on interdependent networks," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(10), pages 2331-2341, October.
    9. Peng, Rui & Xiao, Hui & Guo, Jianjun & Lin, Chen, 2020. "Defending a parallel system against a strategic attacker with redundancy, protection and disinformation," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    10. Yan, Xihong & Ren, Xiaorong & Nie, Xiaofeng, 2022. "A budget allocation model for domestic airport network protection," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    11. Bhatt, Sneha Dhyani & Sinha, Ankur & Jayaswal, Sachin, 2024. "The capacitated r-hub interdiction problem with congestion: Models and solution approaches," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 185(C).
    12. 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.
    13. Manxi Wu & Saurabh Amin, 2019. "Securing Infrastructure Facilities: When Does Proactive Defense Help?," Dynamic Games and Applications, Springer, vol. 9(4), pages 984-1025, December.
    14. Yaghlane, Asma Ben & Azaiez, M. Naceur & Mrad, Mehdi, 2019. "System survivability in the context of interdiction networks," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 362-371.
    15. Kosanoglu, Fuat & Bier, Vicki M., 2020. "Target-oriented utility for interdiction of transportation networks," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    16. Gao, Xing & Zhong, Weijun & Mei, Shue, 2013. "A game-theory approach to configuration of detection software with decision errors," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 35-43.
    17. Darvishan, Ayda & Lim, Gino J., 2021. "Dynamic network flow optimization for real-time evacuation reroute planning under multiple road disruptions," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    18. Jiang, J. & Liu, X., 2018. "Multi-objective Stackelberg game model for water supply networks against interdictions with incomplete information," European Journal of Operational Research, Elsevier, vol. 266(3), pages 920-933.

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