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Queueing Systems with Service Interruptions

Author

Listed:
  • Awi Federgruen

    (Columbia University, New York, New York)

  • Linda Green

    (Columbia University, New York, New York)

Abstract

In many queueing systems, the service process is subject to interruptions resulting from breakdowns, scheduled off-periods or the arrival of customers with preemptive priority. We consider a single server, first-come, first-served queueing system that alternates between periods when service is available (“on-periods”) and periods when the server is unavailable (“off-periods”). We consider the case of Poisson arrivals and general service, on- and off-time distributions and derive bounds and approximations for the mean waiting time, probability of delay and steady-state distribution of the number in system. These results are exact for the case of exponentially distributed on-times. Computational results are reported.

Suggested Citation

  • Awi Federgruen & Linda Green, 1986. "Queueing Systems with Service Interruptions," Operations Research, INFORMS, vol. 34(5), pages 752-768, October.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:5:p:752-768
    DOI: 10.1287/opre.34.5.752
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    Citations

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    Cited by:

    1. A. Krishnamoorthy & S. Jaya & B. Lakshmy, 2015. "Queues with interruption in random environment," Annals of Operations Research, Springer, vol. 233(1), pages 201-219, October.
    2. Carri W. Chan & Jing Dong & Linda V. Green, 2017. "Queues with Time-Varying Arrivals and Inspections with Applications to Hospital Discharge Policies," Operations Research, INFORMS, vol. 65(2), pages 469-495, April.
    3. Awi Federgruen & Linda Green, 1988. "Queueing systems with service interruptions II," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(3), pages 345-358, June.
    4. 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.
    5. 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.
    6. Jianzhe Luo & Vidyadhar G. Kulkarni & Serhan Ziya, 2012. "Appointment Scheduling Under Patient No-Shows and Service Interruptions," Manufacturing & Service Operations Management, INFORMS, vol. 14(4), pages 670-684, October.
    7. 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.
    8. 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.
    9. 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.
    10. Dijk, N.M. van & Trapman, F.J.J., 1989. "Exact solutions for central service systems with breakdowns," Serie Research Memoranda 0028, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    11. Fiems, Dieter & Maertens, Tom & Bruneel, Herwig, 2008. "Queueing systems with different types of server interruptions," European Journal of Operational Research, Elsevier, vol. 188(3), pages 838-845, August.
    12. S. Creemers & M. Lambrecht & N. Vandaele, 2007. "Queueing Models in Healthcare," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(3), pages 471-498.
    13. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.
    14. Wartenhorst, Pieter, 1995. "N parallel queueing systems with server breakdown and repair," European Journal of Operational Research, Elsevier, vol. 82(2), pages 302-322, April.

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