Light-traffic analysis of queues with limited heterogenous retrials

Abstract

We consider a Markovian single-server retrial queueing system. Customers in orbit retry after an exponentially distributed amount of time, the retrial rate depending on the number of times the customer has retried before. Moreover, the number of retrials by a single customer is bounded by K, customers abandoning after the kth retrial with probability pk. As this queueing system is not amenable for exact analysis, we focus on its performance in light traffic. In particular, we describe a fast algorithm for calculating the terms in the Maclaurin series expansion of various performance measures, the arrival rate being the independent parameter of the expansion. We illustrate our approach by various numerical examples and verify the accuracy of the light traffic approximation by means of simulation.