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 M/M/C, bulk service, and accessible batch queueing systems. We compute the system size probabilities in transient and steady states, waiting time distribution, busy period distribution, expected queue length, etc. Littleʹs formula is shown to hold for the present set up. We investigate the optimal values of the maximum batch size for service and capacity of the system.