A Unified Approach to Analyze the Discrete-time Finite-buffer Queue with Batch-Markovian Arrival Process Under Partial- and Whole-batch Acceptance Strategies

摘要

This paper presents the analysis of a single-server finite-buffer queue wherein the input follows adiscrete-time batch-Markovian arrival process (D-BMAP), the service times are arbitrarily distributed and their durations are integral multiples of a slot duration. We obtain the state probabilities at departure, arbitrary and prearrival epochs for both partial-batch acceptance strategy and whole-batch acceptance strategy. The loss probability of the first-, an arbitrary- and the last-customer in a batch, and the other performance measures along with numerical results have been discussed. The analysis of actual waiting-time of the first-, an arbitrary- and the last-customer in an accepted batch is also carried out.