Stability analysis of multiserver discrete-time queueing systems with renewal-type server interruptions

For many queueing systems, the server is not continuously available. Service interruptions may result from repair times after server failures, planned maintenance periods or periods during which customers from other queues are being served. These service interruptions cause an overall performance degradation which is most striking when interruptions can start while a customer is being served and his service has to start all over after the interruption. This is the so-called preemptive repeat service discipline. This paper investigates stability conditions for discrete-time queueing systems with preemptive server interruptions. Under renewal assumptions for arrival, service and interruption processes, sufficient conditions for the positive recurrence of the single-server and multiserver queueing processes are established for the preemptive repeat different and the preemptive resume service disciplines.