Retrial Queuing System with Randomized Push-Out Mechanism and Non-Preemptive Priority

Abstract

A single-server retrial queueing system with finite buffer size, Poisson arrivals, an exponentially distributed service time is considered. If an arriving customer finds the queue completely occupied, it joins a special retrial waiting group (named orbit) in order to seek service over again after some period of time which have exponential distribution. The primary customers take non-preemptive priority over secondary customers. We also introduce so-called randomized push-out buffer management mechanism. It allows you push secondary customers out of the system to free up space that could be taken by primary customers. It is shown that such a queueing system can be reduced to analogous model without retrials. Using generating function technique, the loss probabilities for both types of customers are obtained. Theoretical results allow to investigate the dependency of loss probabilities on the main model parameters (like push-out and retrial probabilities). Special areas of loads are found, where the model locks itself up for secondary customers or follows linear loss law as well. A detailed comparison is made with the case of preemptive priority, which was studied by the authors earlier.