Note on an Unreliable Quorum Queueing System with Random Server Capacity

Abstract

We consider a bulk-service queueing system with random server capacity where the server is subject to random breakdowns. Start and end of idle periods are regulated by an accumulation level r. If the queue is larger than or equal to r when a service ends, the server takes a group of r customers to serve. On the other hand, if the queue is smaller than r when a service ends, the server remains idle and waits for the queue to reach r, then takes a group of at most r customers to serve. We derive the probability generating function of the state probabilities in the steady-state at a service completion instant and at an arbitrary instant of time. We also derive various performance measures. A detailed numerical example is provided.