Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/G^Y/1/M

Abstract

In this article, we consider a single-server, finite-capacity queue with random bulk service rule where customers arrive according to a discrete-time Markovian arrival process (D-MAP). The model is denoted by D-MAP/G Y /1/M where server capacity (bulk size for service) is determined by a random variable Y at the starting point of services. A simple analysis of this model is given using the embedded Markov chain technique and the concept of the mean sojourn time of the phase of underlying Markov chain of D-MAP. A complete solution to the distribution of the number of customers in the D-MAP/G Y /1/M queue, some computational results, and performance measures such as the average number of customers in the queue and the loss probability are presented.