Reducing Delay in Retrial Queues by Simultaneously Differentiating Service and Retrial Rates

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-and-retrial 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.