On extreme values of orbit lengths in M/G/1 queues with constant retrial rate |
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Authors: | Antonio Gómez-Corral |
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Affiliation: | (1) Department of Statistics and Operations Research I, Faculty of Mathematics, University Complutense of Madrid, 28040 Madrid, Spain (e-mail: antonio_gomez@mat.ucm.es) , ES |
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Abstract: | In the design of waiting facilities for the units in a retrial queue, it is of interest to know probability distributions
of extreme values of the orbit length. The purpose of this paper is to investigate the asymptotic behavior of the maximum
orbit length in the queue with constant retrial rate, as the time interval increases. From the classical extreme value theory, we observe that,
under standard linear normalizations, the maximum orbit length up to the nth time the positive recurrent queue becomes empty does not have a limit distribution. However, by allowing the parameters
to vary with n, we prove the convergence of maximum orbit lengths to three possible limit distributions when the traffic intensity approaches 1 from below and n approaches infinity.
Received: October 7, 1999 / Accepted: November 21, 2000 |
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Keywords: | : Extreme values – Queueing theory – Limit theorems – Repeated attempts |
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