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

Sophie Hautphenne, Moshe Haviv

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish
Pages (from-to)61-78
Number of pages18
JournalProbability in the Engineering and Informational Sciences
Volume30
Issue number1
DOIs
StatePublished - 16 Oct 2015

Bibliographical note

Publisher Copyright:
Copyright © 2015 Cambridge University Press.

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