A quorum queueing system with unreliable server and restricted admission

We consider in this paper a bulk service, or quorum, queueing system. The server is unreliable and may break down while providing service. The admission to the system is controlled and some arrivals may be denied admission. The queueing process is studied and relevant performance measures, such as the mean number of customers in the system, the mean duration of the idle period, busy period, and busy cycle, are obtained. These measures are then used to design an optimal management policy for the system where the optimal quorum size is sought. The effect of relevant system parameters on the optimal quorum size and optimal expected total cost per unit of time are shown in a numerical example.