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An M [ X ] / G (1, K ) /1 queue with unreliable server and Bernoulli vacation

Author

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  • P. Nagarajan
  • R. Kalyanaraman

Abstract

A Poisson arrival queue with batch arrival, service in a batch of variable size with a minimum of '1' and a maximum of 'K' customers is considered. After completion of service to the customers the server takes on Bernoulli vacation, also during the service of customers the server may breakdown. The supplementary variable technique is applied. The probability generating function of number of customers in the queue at different server states, mean queue size, and probability of server being idle are obtained. Some particular models are deduced. The amenability of the numerical treatment of this study is carried out. The numerical results are given in the form of tables and figures.

Suggested Citation

  • P. Nagarajan & R. Kalyanaraman, 2023. "An M [ X ] / G (1, K ) /1 queue with unreliable server and Bernoulli vacation," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 25(4), pages 492-510.
    • Handle: RePEc:ids:ijmore:v:25:y:2023:i:4:p:492-510
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