Analysis of BMAP∕R∕1 Queues Under Gated-Limited Service with the Server’s Single Vacation Policy

Abstract

This paper deals with the finite-buffer single server vacation queues with batch Markovian arrival process (BMAP ). The server follows gated-limited service discipline, i.e., the server can serve a maximum of L customers out of those that are waiting at the start of the busy period or all the waiting customers, whichever is minimum. It has been assumed that the server can take only one vacation, i.e., if no customers are found at the end of a vacation, the server remains idle until a batch of customers arrives. The service time and vacation time distributions are considered to possess rational Laplace-Stieltjes transform. The queue-length distribution at postdeparture, arbitrary, and pre-arrival epochs has been obtained. Various performance measures like mean queue-length, mean waiting time of an arbitrary customer, and mean length of busy and idle periods have been derived for this model. Numerical results have been presented based on the analysis done.