On M/G(a,b)/1/N queue with batch size- and queue length-dependent service

Abstract

In this paper, we analyze finite buffer M/G/1 queue where service is offered in groups/batches according to ‘general bulk service’ rule by a single server. The service time distribution is considered to be generally distributed and allowed to change dynamically depending on the batch size under service and queue length just before the service initiation of the batch under consideration. Using the embedded Markov chain technique and supplementary variable technique, we obtain the joint distribution of the queue length and batch size at various epoch. At the end, we present several numerical results in the form of self-explanatory table and graphs to bring out some interesting features of the model. © Springer Nature Singapore Pte Ltd. 2018.