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

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  • Phung-Duc, Tuan

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.

Suggested Citation

  • Phung-Duc, Tuan, 2015. "Asymptotic analysis for Markovian queues with two types of nonpersistent retrial customers," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 768-784.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:768-784
    DOI: 10.1016/j.amc.2015.05.133
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    References listed on IDEAS

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    1. Tuan Phung-Duc, 2014. "Multiserver Retrial Queues With Two Types Of Nonpersistent Customers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-27.
    2. Florin Avram & Donatien Fotso Chedom, 2011. "On symbolic RG factorization of quasi-birth-and-death processes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 317-335, December.
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    Cited by:

    1. Nesrine Zidani & Natalia Djellab, 2024. "Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(3), pages 365-407, June.
    2. Qihui Bu, 2024. "Transient Analysis for a Queuing System with Impatient Customers and Its Applications to the Pricing Strategy of a Video Website," Mathematics, MDPI, vol. 12(13), pages 1-14, June.

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    1. Nesrine Zidani & Natalia Djellab, 2024. "Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(3), pages 365-407, June.
    2. Hiroyuki Sakurai & Tuan Phung-Duc, 2015. "Two-way communication retrial queues with multiple types of outgoing calls," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 466-492, July.

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