A queueing system with single arrival bulk service and single departure

In this note, we study a Markovian queueing system with accessible batches for service, but units depart individually. This system generalizes the MIM IC, bulk service, and accessible batch queueing systems. We compute the sys tem size probabilities in transient and steady states, waiting time distrib ution, busy period distribution, expected queue length; etc. Little's formu la is shown to hold for the present set up. We investigate the optimal valu es of the maximum batch size for service and capacity of the system. (C) 20 00 Elsevier Science Ltd. All rights reserved.