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

Abstract

Customer retrials commonly occur in many service systems, such as healthcare, call centers, mobile networks, computer systems, and inventory systems. However, because of their complex nature, retrial queues are often more difficult to analyze than queues without retrials. In “Reducing Delay in Retrial Queues by Simultaneously Differentiating Service and Retrial Rates”, J. Wang, Z. Wang, and Y. Liu develop a service grade differentiation policy for queueing models with customer retrials. They show that the average waiting time can be reduced through strategically allocating the rates of service and retrial times without needing additional service capacity. Counter to the intuition that higher service variability usually yields a larger delay, the authors show that the benefits of this simultaneous service-and-retrial differentiation (SSRD) policy outweigh the impact of the increased service variability. To validate the effectiveness of the new SSRD policy, the authors provide (i) conditions under which SSRD is more beneficial, (ii) closed-form expressions of the optimal policy, (iii) asymptotic reduction of customer delays when the system is in heavy traffic, and (iv) insightful observations/discussions and numerical results.