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Queues with interruption in random environment

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  • A. Krishnamoorthy
  • S. Jaya
  • B. Lakshmy

Abstract

In this paper we discuss a queueing system with service interruption. The service gets interrupted due to different environmental factors. Here it is assumed that interruption due to only one factor is allowed at a time. Further we assume that while in interruption no other interruption befalls the system. Even though any number of interruptions can occur during the service of a customer, the maximum number of interruptions is restricted to a finite number K and if the number of interruptions exceeds the maximum, the customer leaves the system without completing service. The difference between the model under discussion and those considered earlier in literature is that the customer/server is unaware of the interruption until a random amount of time elapses from the moment interruption strikes. At the moment the interruption occurs, a random clock and a superclock start ticking. The interruption is identified only when the random clock is realized. The superclock measures the total interruption time during the service of a customer. On realization of superclock the customer goes out of the system without completing service. The kind of service to be started after the interruption depends on the environmental factor that caused the interruption. Here we first analyze the service process to find the response time and to compute the stability condition. The optimal values of K for a suitable cost function is investigated. Numerical investigations indicates the cost function as convex/increasing/decreasing in K. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:233:y:2015:i:1:p:201-219:10.1007/s10479-015-1931-4
    DOI: 10.1007/s10479-015-1931-4
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    References listed on IDEAS

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    1. Harrison White & Lee S. Christie, 1958. "Queuing with Preemptive Priorities or with Breakdown," Operations Research, INFORMS, vol. 6(1), pages 79-95, February.
    2. Bhaskar Sengupta, 1990. "A Queue with Service Interruptions in an Alternating Random Environment," Operations Research, INFORMS, vol. 38(2), pages 308-318, April.
    3. Awi Federgruen & Linda Green, 1986. "Queueing Systems with Service Interruptions," Operations Research, INFORMS, vol. 34(5), pages 752-768, October.
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    Cited by:

    1. Tao Jiang & Liwei Liu & Yuanyuan Zhu, 2018. "Analysis of a Batch Service Polling System in a Multi-phase Random Environment," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 699-718, June.
    2. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2019. "Service system design for managing interruption risks: A backup-service risk-mitigation strategy," European Journal of Operational Research, Elsevier, vol. 274(2), pages 417-431.
    3. Alexander Moiseev & Maria Shklennik & Evgeny Polin, 2023. "Infinite-server queueing tandem with Markovian arrival process and service depending on its state," Annals of Operations Research, Springer, vol. 326(1), pages 261-279, July.
    4. Won Seok Yang & Nam K. Kim & Sungjune Park & Chandrasekar Subramaniam, 2020. "Improving service in the presence of surge traffic: a K-policy voluntary flushing queueing system," Annals of Operations Research, Springer, vol. 295(1), pages 411-423, December.

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