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Balking Phenomenon in the $M^{[x]}/G/1$ Vacation Queue
Madan, Kailash C. The Korean Statistical Society 2002 Journal of the Korean Statistical Society Vol.31 No.4
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.
A Batch Arrival Queue with Bernoulli Vacation Schedule under Multiple Vacation Policy
Gautam Choudhury,Kailash C. Madan 한국경영과학회 2006 Management Science and Financial Engineering Vol.12 No.2
We consider an MX/G /1 queueing system with Bernoulli vacation schedule under multiple vacation policy, where after each vacation completion or service completion the server takes sequence of vacations until a batch of new customer arrive. This generalizes both MX/G /1 queueing system with multiple vacation as well as M /G /1 Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further attempts have been made to unify the results of related batch arrival vacation models.