Finite buffer renewal input multiple exponential vacations queue with accessible and non-accessible batches

Abstract

In this paper, we study a finite buffer single server accessible and non-accessible batch service queue with multiple exponential vacations. The inter-arrival and service times are, respectively, arbitrarily and exponentially distributed. Using the supplementary variable technique (SVT) and the embedded Markov chain technique (EMCT), we obtain the steady state system (queue) length distributions at pre-arrival and arbitrary epochs. Some numerical results are presented in the form of table and graphs.

Keywords:

• queueing
• Markov chain
• probability—random processes
• traffic control
• mathematical models