Steady state analysis and computation of the GI[x]/Mb/1/L queue with multiple working vacations and partial batch rejection

This paper analyzes a finite-buffer bulk-arrival bulk-service queueing system with multiple working vacations and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrarily and exponentially distributed. Using the supplementary variable and the embedded Markov chain techniques, we obtain the waiting queue-length distributions at pre-arrival and arbitrary epochs. We also present Laplace–Stiltjes transform of the actual waiting-time distribution in the queue. Finally, several performance measures and a variety of numerical results in the form of tables and graphs are discussed.