In this article, we introduce a service grade differentiation policy for queueing models with customer retrials. We show that the average waiting time can be reduced through strategically allocating the rates of service and retrial times without needing additional service capacity. Countering to the intuition that higher service variability usually yields a larger delay, we show that the benefits of our simultaneous service-andretrial differentiation policy outweigh the impact of the increased service variability. We present a necessary and sufficient condition under which the proposed policy reduces the waiting time and a closed-form expression for the optimal allocation policy. In heavy traffic, our policy can asymptotically reduce both the delay and the number of customer retrials before entering service by a significant factor, which is a function of the ratio of the service rate to the retrial rate.

Retrial queues have been widely used to model many problems arising in telephone switching systems, telecommunication networks, computer networks and computer systems, etc. It is of basic importance to study reliability of retrial queues with server breakdowns and repairs because of limited ability of repairs and heavy influence of the breakdowns on the performance measure of the system. However, so far the repairable retrial queues are analyzed only by queueing theory. In this paper we give a detailed analysis for reliability of retrial queues. By using the supplementary variables method, we obtain the explicit expressions of some main reliability indexes such as the availability, failure frequency and reliability function of the server. In addition, some special queues, for instance, the repairable M/G/1 queue and repairable retrial queue can be derived from our results. These results may be generalized to the repairable multi-server retrial models.