Tail asymptotics for M/M/c retrial queues with non-persistent customers
Censoring technique, Decay function, Decay rate, Exact tail asymptotics, Matrix-analytic method, Non-persistent customers, Retrial queues, Stationary distribution
In this paper, we consider a variant of the classical M/M/c retrial queue, in which we allow non-persistent customers. When c > 1, this system does not have an explicit closed form solution for the joint stationary distribution of the number of retrial customers in the orbit and the number of busy servers. Our main focus is on the tail asymptotics for the joint probabilities. We first present a matrix-product solution for the joint stationary probability vectors, which is further simplified to a scalar-product form, according to matrix-analytic theory. We then apply the censoring technique, which has been proven an efficient approach for analyzing queueing systems including retrial queues, to obtain the censored equations and the Key Lemma. In terms of these results, we finally prove an exact tail asymptotic result for the stationary probabilities. © 2011 Springer-Verlag.
Original Publication Date
DOI of published version
Liu, Bin; Wang, Xi; and Zhao, Yiqiang Q., "Tail asymptotics for M/M/c retrial queues with non-persistent customers" (2012). Faculty Publications. 1767.