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An M/M/1 Queue In Random Environment With Disasters

Author

Listed:
  • NOAM PAZ

    (Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel)

  • URI YECHIALI

    (Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel;
    Afeka Academic College of Engineering, Afeka, Tel Aviv 69107, Israel)

Abstract

We study a M/M/1 queue in a multi-phase random environment, where the system occasionally suffers a disastrous failure, causing all present jobs to be lost. The system then moves to a repair phase. As soon as the system is repaired, it moves to phase i with probability qi ≥ 0. We use two methods of analysis to study the probabilistic behavior of the system in steady state: (i) via probability generating functions, and (ii) via matrix geometric approach. Due to the special structure of the Markov process describing the disaster model, both methods lead to explicit results, which are related to each other. We derive various performance measures such as mean queue sizes, mean waiting times, and fraction of lost customers. Two special cases are further discussed.

Suggested Citation

  • Noam Paz & Uri Yechiali, 2014. "An M/M/1 Queue In Random Environment With Disasters," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-12.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:03:n:s021759591450016x
    DOI: 10.1142/S021759591450016X
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    Citations

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    Cited by:

    1. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    2. Mor Armony & Efrat Perel & Nir Perel & Uri Yechiali, 2019. "Exact analysis for multiserver queueing systems with cross selling," Annals of Operations Research, Springer, vol. 274(1), pages 75-100, March.

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