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 p k . 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.

Retrial Queueing Models: A Survey on Theory and Applications

“…Assuming that the behaviors of nodes are independent, Bianchi [28] demonstrates a simple analysis of this complex system. Recently, Fiems and Phung-Duc [60] propose a light traffic analysis by a series expansion method for a retrial model which represents all the states of nodes concurrently. The accuracy of the model is validated by simulations.…”

“…The accuracy of the model is validated by simulations. The series expansion method [60] might be useful for other retrial models for local area networks with random access protocols.…”

“…Recently, Fiems and Phung-Duc [60] present a light-traffic analysis for finite-source retrial systems arising from CSMA protocols without collision. These systems could be formulated by multidimensional Markov chains which are also used to represent retrial queueing networks.…”

“…These systems could be formulated by multidimensional Markov chains which are also used to represent retrial queueing networks. The analysis by Fiems and Phung-Duc [60] is based on series expansion subject to the arrival rate around the origin and is validated by simulation. Thus, power series expansion may be useful for analyzing queueing networks with retrials.…”