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

Dmitry Efrosinin, Anastasia Winkler () and Pinzger Martin ()
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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

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 06, 1-12

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.

Keywords: Quasi-birth-and-death process; retrial queues; confidence intervals (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0217595915500463

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