MONOTONICITY AND CONVEXITY OF SOME FUNCTIONS ASSOCIATED WITH DENUMERABLE MARKOV CHAINS AND THEIR APPLICATIONS TO QUEUING SYSTEMS-Reference-Cited by-同舟云学术

MONOTONICITY AND CONVEXITY OF SOME FUNCTIONS ASSOCIATED WITH DENUMERABLE MARKOV CHAINS AND THEIR APPLICATIONS TO QUEUING SYSTEMS

Published:2005-12-12 Issue:1 Volume:20 Page:67-86
ISSN:0269-9648
Container-title:Probability in the Engineering and Informational Sciences
language:en
Short-container-title:Prob. Eng. Inf. Sci.

Author:

Yu Hai-Bo,He Qi-Ming,Zhang Hanqin

Abstract

Motivated by various applications in queuing theory, this article is devoted to the monotonicity and convexity of some functions associated with discrete-time or continuous-time denumerable Markov chains. For the discrete-time case, conditions for the monotonicity and convexity of the functions are obtained by using the properties of stochastic dominance and monotone matrix. For the continuous-time case, by using the uniformization technique, similar results are obtained. As an application, the results are applied to analyze the monotonicity and convexity of functions associated with the queue length of some queuing systems.

Publisher

Cambridge University Press (CUP)

Subject

Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability

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