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Analysis of M X / G / 1 queueing model with balking and vacation

Author

Listed:
  • Charan Jeet Singh
  • Madhu Jain
  • Binay Kumar

Abstract

In this paper, a single server queueing model, wherein the units arrive in bulk with varying arrival rates in Poisson process, is considered. It is assumed that the service time of units is arbitrarily distributed. Also, we incorporate the optional deterministic vacations for the server. The server may take a vacation of a fixed duration at the completion of each service or may continue to be available in the system for the next service. At busy and vacation states, the customers may balk from the system with different balking probabilities. By using the basic assumptions of probability reasoning and supplementary variable technique, the steady state behaviour of the system is studied and various performance measures are obtained. In order to obtain the approximate values of the system state probabilities, the principle of maximum entropy is also employed. To verify the tractability of the performance measures obtained, the numerical illustrations are provided. Further, the sensitivity analysis is carried out to examine the system performance with respect to different parameters.

Suggested Citation

  • Charan Jeet Singh & Madhu Jain & Binay Kumar, 2014. "Analysis of M X / G / 1 queueing model with balking and vacation," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 19(2), pages 154-173.
    • Handle: RePEc:ids:ijores:v:19:y:2014:i:2:p:154-173
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    Citations

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    Cited by:

    1. Meena, Rakesh Kumar & Jain, Madhu & Assad, Assif & Sethi, Rachita & Garg, Deepika, 2022. "Performance and cost comparative analysis for M/G/1 repairable machining system with N-policy vacation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 315-328.
    2. R. Sudhesh & R. Sebasthi Priya & R. B. Lenin, 2016. "Analysis of N-policy queues with disastrous breakdown," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 612-634, October.
    3. 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.
    4. Vijay Rajan Lumb & Indra Rani, 2022. "Analytically simple solution to discrete-time queue with catastrophes, balking and state-dependent service," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 783-817, April.

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