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A Many-Server Queue with Service Interruptions

Author

Listed:
  • I. L. Mitrany

    (Technion, Israel Institute of Technology, Haifa, Israel)

  • B. Avi-Itzhak

    (Technion, Israel Institute of Technology, Haifa, Israel)

Abstract

A steady-state M / M / N queuing system where each server is subject to random breakdowns of exponentially distributed duration is studied and analyzed. The moment generating function of the queue size is obtained in explicit form for N ≦ 2. For larger values of N a numerical method is suggested.

Suggested Citation

  • I. L. Mitrany & B. Avi-Itzhak, 1968. "A Many-Server Queue with Service Interruptions," Operations Research, INFORMS, vol. 16(3), pages 628-638, June.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:3:p:628-638
    DOI: 10.1287/opre.16.3.628
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    Cited by:

    1. Sheng Zhu & Jinting Wang & Bin Liu, 2020. "Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs," Operational Research, Springer, vol. 20(4), pages 2163-2187, December.
    2. Evsey Morozov & Stepan Rogozin & Hung Q. Nguyen & Tuan Phung-Duc, 2022. "Modified Erlang Loss System for Cognitive Wireless Networks," Mathematics, MDPI, vol. 10(12), pages 1-20, June.
    3. Legros, Benjamin, 2021. "Routing analyses for call centers with human and automated services," International Journal of Production Economics, Elsevier, vol. 240(C).
    4. Baykal-Gürsoy, M. & Xiao, W. & Ozbay, K., 2009. "Modeling traffic flow interrupted by incidents," European Journal of Operational Research, Elsevier, vol. 195(1), pages 127-138, May.
    5. Nadav Lavi & Hanoch Levy, 2020. "Admit or preserve? Addressing server failures in cloud computing task management," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 279-325, April.
    6. Ying-Mei Tu & Hsin-Nan Chen, 2010. "Capacity planning with sequential time constraints under various control policies in the back-end of wafer fabrications," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1258-1264, August.
    7. Benjamin Legros, 2021. "Routing analyses for call centers with human and automated services," Post-Print hal-03605426, HAL.
    8. Andradóttir, Sigrún & Ayhan, Hayriye & Down, Douglas G., 2017. "Resource pooling in the presence of failures: Efficiency versus risk," European Journal of Operational Research, Elsevier, vol. 256(1), pages 230-241.
    9. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    10. Hoseinpour, Pooya & Ahmadi-Javid, Amir, 2016. "A profit-maximization location-capacity model for designing a service system with risk of service interruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 113-134.
    11. Pedram Sahba & Barış Balcıog̃lu & Dragan Banjevic, 2022. "The impact of disruption characteristics on the performance of a server," Annals of Operations Research, Springer, vol. 317(1), pages 239-252, October.
    12. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    13. Chen, Shih-Pin, 2016. "Time value of delays in unreliable production systems with mixed uncertainties of fuzziness and randomness," European Journal of Operational Research, Elsevier, vol. 255(3), pages 834-844.
    14. Tuan Phung-Duc & Kohei Akutsu & Ken’ichi Kawanishi & Osama Salameh & Sabine Wittevrongel, 2022. "Queueing models for cognitive wireless networks with sensing time of secondary users," Annals of Operations Research, Springer, vol. 310(2), pages 641-660, March.
    15. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    16. Pedram Sahba & Bariş Balciog̃lu & Dragan Banjevic, 2013. "Analysis of the finite‐source multiclass priority queue with an unreliable server and setup time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 331-342, June.
    17. Winfried K. Grassmann, 2003. "The Use of Eigenvalues for Finding Equilibrium Probabilities of Certain Markovian Two-Dimensional Queueing Problems," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 412-421, November.
    18. Sauer Cornelia & Daduna Hans, 2003. "Availability Formulas and Performance Measures for Separable Degradable Networks," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 165-194, January.
    19. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.

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