Monotonicity And Convexity Of Some Functions Associated With Denumerable Markov Chains And Their Applications To Queuing Systems

Authors:
Hai-Bo Yu;Qi-Ming He;Hanqin Zhang
Affiliations:
The College of Economics and Management, Beijing University of Technology, Beijing 100022, People's Republic of China, E-mail: haibo@bjut.edu.cn;Department of Industrial Engineering, Dalhousie University, Halifax, Nova Scotia, Canada B3J 2X4, E-mail: Qi-Ming.He@dal.ca;Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People's Republic of China, E-mail: hanqin@mail.amt.ac.cn
Venue:
Probability in the Engineering and Informational Sciences
Year:
2006

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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.