On a queue with interruptions and repeat or resumption of service Original Research Article

This paper presents an infinite-capacity queueing system with a single server where service rule is FIFO. A customer, on arrival to an idle server, is immediately taken for service; or else he joins the tail of the queue. The arrival of customers constitutes a MAP. During the service of a customer, one or more interruptions may occur. It takes a random amount of time to clear the interruption. Interruption processes occur according to a Poisson process of rate γγ and the duration of interruption is PH-distributed. When the duration of an interruption exceeds a threshold random variable (also PH-distributed), the customer whose service was interrupted has to undergo the service process right from the beginning on completion of the interruption; or else his service is resumed. We investigate this queueing system. Long-run system distribution is obtained under a stable regime. Several performance measures are evaluated. Numerical illustrations of the system behavior is also provided.