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MONOTONICITY AND CONVEXITY OF SOME FUNCTIONS ASSOCIATED WITH DENUMERABLE MARKOV CHAINS AND THEIR APPLICATIONS TO QUEUING SYSTEMS
Published online by Cambridge University Press: 12 December 2005
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.
- Type
- Research Article
- Information
- Probability in the Engineering and Informational Sciences , Volume 20 , Issue 1 , January 2006 , pp. 67 - 86
- Copyright
- © 2006 Cambridge University Press
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