A unified approach for modeling and analysis of a versatile batch-service queue with correlated arrival

A batch-service queue with Markovian arrival process can be adopted to deal with highly correlated systems which arises in high speed telecommunication networks. Such complex models are usually dealt by evoking simulation method. However, we carry out modeling and analysis of this queue by developing an analytically tractable methodology which is based on bivariate vector generating function. The queue length and server content distribution at service completion epoch are extracted and presented in terms of the roots. The knowledge of both the queue and server content distributions helps the system designer to evaluate the efficiency of the queueing system in a better way. Some significant key performance measures along with illustrative numerical examples are presented in order to show the usefulness of our results. The notable feature of our methodology is that it is easier to follow and implement.