Analyzing retrial queues by censoring

Abstract

In this paper we analyze the M/M/c retrial queue using the censoring technique. This technique allows us to carry out an asymptotic analysis, which leads to interesting and useful asymptotic results. Based on the asymptotic analysis, we develop two methods for obtaining approximations to the stationary probabilities, from which other performance metrics can be obtained. We demonstrate that the two proposed approximations are good alternatives to existing approximation methods. We expect that the technique used here can be applied to other retrial queueing models.

Multiserver Queue with Guard Channel for Priority and Retrial Customers

“…Liu et al [18] further extend their analysis to the model with nonpersistent customers. B. Kim and J. Kim [19] and Kim et al [20] refine the tail asymptotic results in Liu and Zhao [17] and Liu et al [18], respectively. Phung-Duc [21] presents a perturbation analysis for a multiserver retrial queue with two types of nonpersistent customers.…”

“…Our formula is general in the sense that we can obtain the expansion with arbitrary number of terms. This was not reported in Liu and Zhao [17]. Second, using this result we obtain an asymptotic upper bound for the stationary distribution which is more challenging compared to [17,21] due to the denseness of the rate matrices.…”

“…In [21], the author derives the Taylor series expansion formulae for the nonzero elements of the rate matrices. The difference of our model in comparison with the above work is that the last two rows of the rate matrices are nonzero in our model while for those in [17,21] only the last row is nonzero. This makes the analysis of our model more complex and challenging.…”

“…The QBD process of our model possesses some special structure; that is, only the last two rows are nonzero allowing us to get some insights into the structure of the stationary distribution. Liu and Zhao [17] use this property to obtain upper and lower asymptotic bounds for the stationary distribution of the fundamental retrial model without guard channels. Liu et al [18] further extend their analysis to the model with nonpersistent customers.…”

Error Bounds for Last-Column-Block-Augmented Truncations of Block-Structured Markov Chains

“…Let L(t), t ≥ 0, denote the number of customers in the orbit, called the queue length, at time t. Let B(t), t ≥ 0, denote the number of busy servers at time t. It is known (see, e.g., Liu and Zhao [41]) that {(L(t), B(t)); t ≥ 0} is an LD-QBD whose infinitesimal generator is given by Q in (4.1), where S 0 = S 1 = {0, 1, . .…”