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COMPARISONS OF DEPENDENCE FOR STATIONARY MARKOV PROCESSES

Published online by Cambridge University Press:  01 July 2000

Taizhong Hu  and
Xiaoming Pan
Taizhong Hu
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
Xiaoming Pan
Affiliation:
Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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Abstract

Results and conditions which quantify the decrease in dependence with lag for a stationary Markov process and enable one to compare the dependence for two stationary Markov processes are obtained. The notions of dependence used in this article are the supermodular ordering and the concordance ordering. Both discrete-time and continuous-time Markov processes are considered. Some applications of the main results are given. In queueing theory, the monotonicity results of the waiting time of the nth customer as well as the stationary waiting time in an MR/GI/1 queue and the stationary workload in a Markov-modulated queue are established, thus strengthening previous results while simplifying their derivation. This article is a continuation of those by Fang et al. [7] and Hu and Joe [10].

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 14 , Issue 3 , July 2000 , pp. 299 - 315
Copyright
© 2000 Cambridge University Press

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Footnotes

Supported by NSF grant 19701030, the Doctoral Program Foundation of Insititute of High Education and a grant of Chinese Academy of Sciences.