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THE BIAS OPTIMAL K IN THE M/M/1/K QUEUE: AN APPLICATION OF THE DEVIATION MATRIX

Published online by Cambridge University Press:  14 October 2015

Sophie Hautphenne  and
Moshe Haviv
Sophie Hautphenne
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Vic 3010, Australia E-mail: [email protected]
Moshe Haviv
Affiliation:
Department of Statistics and The Center for the Study of Rationality, The Hebrew University of Jerusalem, Mount Scopus Campus, Har Hatsofim, Jerusalem, 91905Israel E-mail: [email protected]
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Abstract

We study the optimal buffer capacity K for the M/M/1/K queue under some standard cost and reward structures by comparing various Markov reward processes. Using explicit expressions for the deviation matrix of the underlying Markov chains, we find the bias optimal value for K in the case of a tie between two consecutive optimal gain policies. We show that the bias optimal value depends both on whether the reward is granted upon arrival or departure of the customers, and on the initial queue size. Moreover, we demonstrate that in some specific cases the optimal policy is threshold-based with respect to the initial queue size.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 1 , January 2016 , pp. 61 - 78
Copyright
Copyright © Cambridge University Press 2015 

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