Analyzing discrete-time D-BMAP/G/1/N queue with single and multiple vacations

This paper analyzes a single-server finite-buffer vacation (single and multiple) queue wherein the input process follows a discrete-time batch Markovian arrival process (D-BMAP). The service and vacation times are generally distributed and their durations are integral multiples of a slot duration. We obtain the state probabilities at service completion, vacation termination, arbitrary, and prearrival epochs. The loss probabilities of the first-, an arbitraryand the last-customer in a batch, and other performance measures along with numerical aspects have been discussed. The analysis of actual waiting time of these customers in an accepted batch is also carried out. 2006 Elsevier B.V. All rights reserved.