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A Retrial Queueing Model With Map Arrivals, Catastrophic Failures With Repairs, And Customer Impatience

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  • SRINIVAS R. CHAKRAVARTHY

    (Department of Industrial and Manufacturing, Engineering Kettering University, Flint, MI 48504, USA;
    Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus)

  • ALEXANDER N. DUDIN

    (Department of Industrial and Manufacturing, Engineering Kettering University, Flint, MI 48504, USA;
    Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus)

  • VALENTINA I. KLIMENOK

    (Department of Industrial and Manufacturing, Engineering Kettering University, Flint, MI 48504, USA;
    Department of Applied Mathematics and Computer Science, Belarusian State University, Minsk, Belarus)

Abstract

We consider a single server retrial queueing system in which arrivals occur according to a Markovian arrival process. An arriving customer finding an idle server will get service immediately; otherwise the customer enters into a retrial orbit. The system is subject to catastrophic failures at which time all customers in the system (the one in service as well as the customers, if any, in the orbit) are lost. The system undergoes a repair and after completion of a repair the server in the system will be available for service. The customers in the orbit try to reach the server by sending a signal at random times and get service if the server is idle at those times. While customers are waiting in the orbit, they may become impatient and leave the system after a random amount of time. Any arrival finding the server unavailable (due to busy or under repair) and cannot enter the orbit due to the buffer being full (in the case of finite buffer only) is considered lost. Under exponential assumption for all except for the arrivals, the queueing model (for both finite and infinite orbit sizes) is studied using matrix-analytic methods and the qualitative nature of the model is brought out through some illustrative numerical examples.

Suggested Citation

  • Srinivas R. Chakravarthy & Alexander N. Dudin & Valentina I. Klimenok, 2010. "A Retrial Queueing Model With Map Arrivals, Catastrophic Failures With Repairs, And Customer Impatience," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(06), pages 727-752.
    • Handle: RePEc:wsi:apjorx:v:27:y:2010:i:06:n:s0217595910002971
    DOI: 10.1142/S0217595910002971
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    Cited by:

    1. Sofiane Ouazine & Karim Abbas, 2016. "A functional approximation for retrial queues with two way communication," Annals of Operations Research, Springer, vol. 247(1), pages 211-227, December.
    2. Serife Ozkar & Agassi Melikov & Janos Sztrik, 2023. "Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies," Mathematics, MDPI, vol. 11(23), pages 1-24, December.

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