Analysis of a finite-buffer bulk-service queue under Markovian arrival process with batch-size-dependent service

We consider a finite capacity single server queue in which the customers arrive according to a Markovian arrival process. The customers are served in batches following a ‘general bulk service rule’. The service times, which depend on the size of the batch, are generally distributed. We obtain, in steady-state, the joint distribution of the random variables of interest at various epochs. Efficient computational procedures in the case of phase type services are presented. An illustrative numerical example to bring out the qualitative nature of the model is presented.