Asymptotic analysis for Markovian queues with two types of nonpersistent retrial customers

Tuan Phung-Duc

Applied Mathematics and Computation, 2015, vol. 265, issue C, 768-784

Abstract: We consider Markovian multiserver retrial queues where a blocked customer has two opportunities for abandonment: at the moment of blocking or at the departure epoch from the orbit. In this queueing system, the number of customers in the system (servers and buffer) and that in the orbit form a level-dependent quasi-birth-and-death (QBD) process whose stationary distribution is expressed in terms of a sequence of rate matrices. Using a simple perturbation technique and a matrix analytic method, we derive Taylor series expansion for nonzero elements of the rate matrices with respect to the number of customers in the orbit. We also obtain explicit expressions for all the coefficients of the expansion. Furthermore, we derive tail asymptotic formulas for the joint stationary distribution of the number of customers in the system and that in the orbit. Numerical examples reveal that the tail probability of the model with two types of nonpersistent customers is greater than that of the corresponding model with one type of nonpersistent customers. They also reveal that the series expansion with a few terms can be used to obtain an accurate approximation to the stationary distribution.

Keywords: Taylor series expansion; Asymptotic analysis; Multiserver retrial queue; Level-dependent QBD; Matrix analytic method; Censoring (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:768-784

DOI: 10.1016/j.amc.2015.05.133

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