Abstract
This paper analyzes a finite buffer single server queueing system with multiple working vacations in which customers balk (i.e., refuse to join the queue). The inter-arrival times and service times during regular busy period are, respectively, arbitrarily and exponentially distributed. Vacation times and service times during vacation are exponentially distributed. Using embedded Markov chain and supplementary variable techniques, we obtain the system length distributions at pre-arrival and arbitrary epochs. Various performance measures of the model, waiting time analysis and some special cases are also presented. Finally, a variety of numerical results in the form of tables and graphs are discussed.
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