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Analysis of a Multiple Dual-Stage Vacation Queueing System with Disaster and Repairable Server

Author

Listed:
  • Sudhesh R.

    (Anna University)

  • Mohammed Shapique A.

    (IFET College of Engineering)

  • Dharmaraja S.

    (Indian Institute of Technology Delhi)

Abstract

An M/M/1 dual-stage vacation queueing system with a system disaster is analysed in this paper. This work is motivated by the dual-stage sleep mode mechanism in the MAC (Media Access Control) and the physical layer of a WiMAX system with Denial of Service. In this model, the server switches to two types of vacation called stage-I and stage-II vacation. Disaster can occur at any stage of the system and subsequent repair is considered. For this system, explicit expressions for transient and steady-state probabilities are computed. Further, performance indices like the mean, variance of the system size, the probability that the server is on vacation mode and busy mode, and system throughput have been computed. Finally, numerical illustrations are presented to understand the effect of the parameters on the system performance.

Suggested Citation

  • Sudhesh R. & Mohammed Shapique A. & Dharmaraja S., 2022. "Analysis of a Multiple Dual-Stage Vacation Queueing System with Disaster and Repairable Server," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2485-2508, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09926-5
    DOI: 10.1007/s11009-022-09926-5
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    References listed on IDEAS

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    1. Ammar, Sherif I., 2015. "Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 97-105.
    2. R. Sudhesh & P. Savitha & S. Dharmaraja, 2017. "Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 179-205, April.
    Full references (including those not matched with items on IDEAS)

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