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Maximum entropy analysis of bulk arrival retrial queue with second optional service and Bernoulli vacation

Author

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  • Madhu Jain
  • Richa Sharma
  • G.C. Sharma

Abstract

This paper deals with the maximum entropy principle (MEP) to explore the steady state behaviour of the bulk arrival retrial queuing system. The concepts of Bernoulli vacation schedule and second optional service are taken into consideration. After the completion of first essential service (second optional service), the server has an option to go for vacation with probability p(q) or may continue to serve the next customer, if any with complementary probability. During vacation, the server is allowed to do some secondary work and is called on working vacation. By introducing supplementary variables and using generating function technique, we obtain the expected number of the customers and expected waiting time of the customers in the retrial group. By employing the maximum entropy approach, we derive various system performance measures. By taking the numerical illustrations we perform a comparative study between the exact waiting time and the approximate waiting time based on MEP analysis. The sensitivity analysis is also carried out to validate the analytical results.

Suggested Citation

  • Madhu Jain & Richa Sharma & G.C. Sharma, 2015. "Maximum entropy analysis of bulk arrival retrial queue with second optional service and Bernoulli vacation," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 20(3), pages 369-396.
    • Handle: RePEc:ids:ijisen:v:20:y:2015:i:3:p:369-396
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    Cited by:

    1. 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.
    2. Sunita Kumari & Pooja Khurana & Shakuntla Singla, 2022. "Behavior and profit analysis of a thresher plant under steady state," 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(1), pages 166-171, February.

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