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Some Queuing Problems with the Service Station Subject to Breakdown

Author

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  • B. Avi-Itzhak

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

  • P. Naor

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

Abstract

A number of situations is considered where the single service station is incapacitated from time to time to render service to the incoming (stationary) Poisson stream of customers. Five models are presented Model. A deals with the situation in which the service interruption is brought about by a Poisson process homogeneous in time. The preemptive priority queuing model is shown to be a special case. Model B is concerned with the case in which breakdowns occur only while the station is giving service. In Model C it is assumed that the repair process cannot start without customers at the station. Model D describes a situation in which the repair of the station starts at the initiative of a customer who wishes to improve the standard of service. In Model E the assumption is that the station can break down only while no customer is being serviced. In all models it is assumed that service times and repair times possess arbitrary distribution functions each having a density and finite second moment. The expected queue lengths and related operating characteristics of the various systems are derived using relatively simple mathematical methods.

Suggested Citation

  • B. Avi-Itzhak & P. Naor, 1963. "Some Queuing Problems with the Service Station Subject to Breakdown," Operations Research, INFORMS, vol. 11(3), pages 303-320, June.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:3:p:303-320
    DOI: 10.1287/opre.11.3.303
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    Citations

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    Cited by:

    1. 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.
    2. Herwig Bruneel & Dieter Fiems & Joris Walraevens & Sabine Wittevrongel, 2014. "Queueing models for the analysis of communication systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 421-448, July.
    3. Chan, Wenyaw & Peng, Nan Fu, 2006. "Continuous time Markov chains observed on an alternating renewal process with exponentially distributed durations," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 362-368, February.
    4. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    5. L. G. Afanasyeva, 2020. "Asymptotic Analysis of Queueing Models Based on Synchronization Method," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1417-1438, December.
    6. 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.
    7. Özgecan Ulusçu & Tayfur Altiok, 2013. "Waiting time approximation in multi-class queueing systems with multiple types of class-dependent interruptions," Annals of Operations Research, Springer, vol. 202(1), pages 185-195, January.
    8. 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.
    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. 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.
    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. Lam, Yeh & Zhang, Yuan Lin & Liu, Qun, 2006. "A geometric process model for M/M/1 queueing system with a repairable service station," European Journal of Operational Research, Elsevier, vol. 168(1), pages 100-121, January.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. I. Atencia & G. Bouza & P. Moreno, 2008. "An M [X] /G/1 retrial queue with server breakdowns and constant rate of repeated attempts," Annals of Operations Research, Springer, vol. 157(1), pages 225-243, January.

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