IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v112y2013icp214-224.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832012002463
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2012.11.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Patterson, S.A. & Apostolakis, G.E., 2007. "Identification of critical locations across multiple infrastructures for terrorist actions," Reliability Engineering and System Safety, Elsevier, vol. 92(9), pages 1183-1203.
    2. Kjell Hausken, 2011. "Protecting complex infrastructures against multiple strategic attackers," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(1), pages 11-29.
    3. 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.
    4. 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.
    5. Scaparra, Maria P. & Church, Richard L., 2008. "An exact solution approach for the interdiction median problem with fortification," European Journal of Operational Research, Elsevier, vol. 189(1), pages 76-92, August.
    6. Azaiez, M.N. & Bier, Vicki M., 2007. "Optimal resource allocation for security in reliability systems," European Journal of Operational Research, Elsevier, vol. 181(2), pages 773-786, September.
    7. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    8. Jun Zhuang & Vicki M. Bier, 2007. "Balancing Terrorism and Natural Disasters---Defensive Strategy with Endogenous Attacker Effort," Operations Research, INFORMS, vol. 55(5), pages 976-991, October.
    9. Hausken, Kjell, 2008. "Strategic defense and attack for reliability systems," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1740-1750.
    10. Zhuang, Jun & Bier, Vicki M. & Alagoz, Oguzhan, 2010. "Modeling secrecy and deception in a multiple-period attacker-defender signaling game," European Journal of Operational Research, Elsevier, vol. 203(2), pages 409-418, June.
    11. Jun Zhuang & Vicki Bier, 2011. "Secrecy And Deception At Equilibrium, With Applications To Anti-Terrorism Resource Allocation," Defence and Peace Economics, Taylor & Francis Journals, vol. 22(1), pages 43-61.
    12. Ramirez-Marquez, Jose E. & Rocco, Claudio M. & Levitin, Gregory, 2011. "Optimal network protection against diverse interdictor strategies," Reliability Engineering and System Safety, Elsevier, vol. 96(3), pages 374-382.
    13. Ramirez-Marquez, Jose E. & Rocco S, Claudio M. & Levitin, Gregory, 2009. "Optimal protection of general source–sink networks via evolutionary techniques," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1676-1684.
    14. Gerald Brown & Matthew Carlyle & Douglas Diehl & Jeffrey Kline & Kevin Wood, 2005. "A Two-Sided Optimization for Theater Ballistic Missile Defense," Operations Research, INFORMS, vol. 53(5), pages 745-763, October.
    15. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    16. Bier, Vicki M. & Gratz, Eli R. & Haphuriwat, Naraphorn J. & Magua, Wairimu & Wierzbicki, Kevin R., 2007. "Methodology for identifying near-optimal interdiction strategies for a power transmission system," Reliability Engineering and System Safety, Elsevier, vol. 92(9), pages 1155-1161.
    17. Boardman, Anthony E. & Lave, Lester B., 1977. "Highway congestion and congestion tolls," Journal of Urban Economics, Elsevier, vol. 4(3), pages 340-359, July.
    18. Hausken, Kjell & Levitin, Gregory, 2009. "Minmax defense strategy for complex multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 577-587.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bricha, Naji & Nourelfath, Mustapha, 2014. "Extra-capacity versus protection for supply networks under attack," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 185-196.
    2. Cen Song & Jun Zhuang, 2018. "Modeling Precheck Parallel Screening Process in the Face of Strategic Applicants with Incomplete Information and Screening Errors," Risk Analysis, John Wiley & Sons, vol. 38(1), pages 118-133, January.
    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. 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.
    7. 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.
    8. 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).
    9. Yan, Xihong & Ren, Xiaorong & Nie, Xiaofeng, 2022. "A budget allocation model for domestic airport network protection," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    10. 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.
    11. 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.
    12. 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.
    13. Kosanoglu, Fuat & Bier, Vicki M., 2020. "Target-oriented utility for interdiction of transportation networks," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    14. 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.
    15. 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).
    16. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Chi & Ramirez-Marquez, José Emmanuel & Wang, Jianhui, 2015. "Critical infrastructure protection using secrecy – A discrete simultaneous game," European Journal of Operational Research, Elsevier, vol. 242(1), pages 212-221.
    2. Kjell Hausken & Jun Zhuang, 2011. "Governments' and Terrorists' Defense and Attack in a T -Period Game," Decision Analysis, INFORMS, vol. 8(1), pages 46-70, March.
    3. Qingqing Zhai & Rui Peng & Jun Zhuang, 2020. "Defender–Attacker Games with Asymmetric Player Utilities," Risk Analysis, John Wiley & Sons, vol. 40(2), pages 408-420, February.
    4. Kjell Hausken, 2019. "Special versus general protection and attack of two assets," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(4), pages 53-93.
    5. Hausken, Kjell, 2017. "Special versus general protection and attack of parallel and series components," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 239-256.
    6. Talarico, Luca & Reniers, Genserik & Sörensen, Kenneth & Springael, Johan, 2015. "MISTRAL: A game-theoretical model to allocate security measures in a multi-modal chemical transportation network with adaptive adversaries," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 105-114.
    7. Chi Zhang & Jose Ramirez-Marquez, 2013. "Protecting critical infrastructures against intentional attacks: a two-stage game with incomplete information," IISE Transactions, Taylor & Francis Journals, vol. 45(3), pages 244-258.
    8. 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.
    9. R Peng & G Levitin & M Xie & S H Ng, 2011. "Optimal defence of single object with imperfect false targets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 134-141, January.
    10. Hausken, Kjell, 2017. "Defense and attack for interdependent systems," European Journal of Operational Research, Elsevier, vol. 256(2), pages 582-591.
    11. 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.
    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. Kjell Hausken, 2012. "Game Theoretic Analysis of Standby Systems," Chapters, in: Yair Holtzman (ed.), Advanced Topics in Applied Operations Management, IntechOpen.
    14. Levitin, Gregory & Hausken, Kjell, 2009. "Intelligence and impact contests in systems with redundancy, false targets, and partial protection," Reliability Engineering and System Safety, Elsevier, vol. 94(12), pages 1927-1941.
    15. Shan, Xiaojun & Zhuang, Jun, 2013. "Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender–attacker game," European Journal of Operational Research, Elsevier, vol. 228(1), pages 262-272.
    16. Bricha, Naji & Nourelfath, Mustapha, 2014. "Extra-capacity versus protection for supply networks under attack," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 185-196.
    17. Ben Yaghlane, Asma & Azaiez, M. Naceur, 2017. "Systems under attack-survivability rather than reliability: Concept, results, and applications," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1156-1164.
    18. Peiqiu Guan & Jun Zhuang, 2016. "Modeling Resources Allocation in Attacker‐Defender Games with “Warm Up” CSF," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 776-791, April.
    19. Hausken, Kjell, 2010. "Defense and attack of complex and dependent systems," Reliability Engineering and System Safety, Elsevier, vol. 95(1), pages 29-42.
    20. Ye, Zhi-Sheng & Peng, Rui & Wang, Wenbin, 2017. "Defense and attack of performance-sharing common bus systemsAuthor-Name: Zhai, Qingqing," European Journal of Operational Research, Elsevier, vol. 256(3), pages 962-975.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:112:y:2013:i:c:p:214-224. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.