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Confidence Intervals for Performance Measures of M/M/1 Queue with Constant Retrial Policy

Author

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  • Dmitry Efrosinin

    (Institute for Stochastics, Johannes Kepler University, Altenbergerstrasse 69, Linz 4040, Austria)

  • Anastasia Winkler

    (Institute for Stochastics, Johannes Kepler University, Altenbergerstrasse 69, Linz 4040, Austria)

  • Pinzger Martin

    (Institute of Telecooperation, Johannes Kepler University, Altenbergerstrasse 69, Linz 4040, Austria)

Abstract

We consider the problem of estimation and confidence interval construction of a Markovian controllable queueing system with unreliable server and constant retrial policy. For the fully observable system the standard parametric estimation technique is used. The arrived customer finding a free server either gets service immediately or joins a retrial queue. The customer at the head of the retrial queue is allowed to retry for service. When the server is busy, it is subject to breakdowns. In a failed state the server can be repaired with respect to the threshold policy: the repair starts when the number of customers in the system reaches a fixed threshold level. To obtain the estimates for the system parameters, performance measures and optimal threshold level we analyze the system in a stationary regime. The performance measures including average cost function for the given cost structure are presented in a closed matrix form.

Suggested Citation

  • Dmitry Efrosinin & Anastasia Winkler & Pinzger Martin, 2015. "Confidence Intervals for Performance Measures of M/M/1 Queue with Constant Retrial Policy," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-12, December.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:06:n:s0217595915500463
    DOI: 10.1142/S0217595915500463
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    References listed on IDEAS

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    1. Tsung-Yin Wang & Jau-Chuan Ke & Kuo-Hsiung Wang & Siu-Chuen Ho, 2006. "Maximum Likelihood Estimates and Confidence Intervals of an M/M/R Queue with Heterogeneous Servers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 371-384, May.
    2. Artalejo, J. R. & Gomez-Corral, A. & Neuts, M. F., 2001. "Analysis of multiserver queues with constant retrial rate," European Journal of Operational Research, Elsevier, vol. 135(3), pages 569-581, December.
    3. Efrosinin, Dmitry & Winkler, Anastasia, 2011. "Queueing system with a constant retrial rate, non-reliable server and threshold-based recovery," European Journal of Operational Research, Elsevier, vol. 210(3), pages 594-605, May.
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