TY - JOUR
T1 - THE BIAS OPTIMAL K IN THE M/M/1/K QUEUE
T2 - AN APPLICATION OF THE DEVIATION MATRIX
AU - Hautphenne, Sophie
AU - Haviv, Moshe
N1 - Publisher Copyright:
Copyright © 2015 Cambridge University Press.
PY - 2015/10/16
Y1 - 2015/10/16
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84943787689&partnerID=8YFLogxK
U2 - 10.1017/S0269964815000285
DO - 10.1017/S0269964815000285
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AN - SCOPUS:84943787689
SN - 0269-9648
VL - 30
SP - 61
EP - 78
JO - Probability in the Engineering and Informational Sciences
JF - Probability in the Engineering and Informational Sciences
IS - 1
ER -