Preemptive Repeat Priority Queues as a Special Case of the Multipurpose Server Problem—I

A single station provides service to customers who arrive in a Poisson stream with constant intensity. All the customers require an equal and fixed amount of service but the servicing rate of the station varies randomly, and thus the resulting service time is randomly distributed. The service station itself is subject to random breakdowns rendering it inoperative for random periods of time during which repairs take place. The service of a customer, displaced by a breakdown, is repeated from the beginning as boon as the repair process is completed. The service given to the customer prior to his displacement is wasted. It is shown that this model describes a situation where displacement is not necessarily a result of breakdowns, but may well be caused by other, more urgent, tasks which have to be performed by the station. Some characteristics of the model, such as the expected queue length and queuing time are derived. A solution is given for the preemptive repeat queuing problem as a special case of this model.