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Algorithmic approach to Markovian multi-server retrial queues with vacations

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  • Shin, Yang Woo

Abstract

There are many practical situations that have both features of customer retrials and server vacations. The vacation policy is characterized by the vacation startup rules and vacation termination rules. The queueing system with retrials and vacations has been described in variety of ways according to the vacation rules and retrial policies such as constant retrial policy and linear retrial policy and analyzed for each specific model. In this paper, we model the Markovian multi-server queues with customers’ retrials and vacations with level dependent quasi-birth-and-death (LDQBD) process in a unified manner and present an algorithmic approach to compute the performance measures of the system.

Suggested Citation

  • Shin, Yang Woo, 2015. "Algorithmic approach to Markovian multi-server retrial queues with vacations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 287-297.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:287-297
    DOI: 10.1016/j.amc.2014.10.079
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    References listed on IDEAS

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    1. Tuan Phung-Duc & Hiroyuki Masuyama & Shoji Kasahara & Yutaka Takahashi, 2013. "A matrix continued fraction approach to multiserver retrial queues," Annals of Operations Research, Springer, vol. 202(1), pages 161-183, January.
    2. Srinivas R. Chakravarthy, 2009. "Analysis Of A Multi-Server Queue With Markovian Arrivals And Synchronous Phase Type Vacations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(01), pages 85-113.
    3. Yang Woo Shin, 2009. "Fundamental Matrix Of Transient Qbd Generator With Finite States And Level Dependent Transitions," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(05), pages 697-714.
    4. Vladimir Anisimov & Jesus Artalejo, 2002. "Approximation of multiserver retrial queues by means of generalized truncated models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 51-66, June.
    5. Jeffrey Diamond & Attahiru Alfa, 1999. "Matrix analytic methods for a multi-server retrial queue with buffer," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 249-266, December.
    6. Tuan Phung-Duc & Ken'Ichi Kawanishi, 2014. "An Efficient Method For Performance Analysis Of Blended Call Centers With Redial," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-33.
    7. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
    8. J.R. Artalejo & M. Pozo, 2002. "Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue," Annals of Operations Research, Springer, vol. 116(1), pages 41-56, October.
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