Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Balking Phenomenon in the $M^{[x]}/G/1$ Vacation Queue

  • Madan, Kailash C. (Department of Statistics, Yarmouk University)
  • Published : 2002.12.01
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Abstract

We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.

Keywords

References

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