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March 2016 Correlation formulas for Markovian network processes in a random environment
Hans Daduna, Ryszard Szekli
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Adv. in Appl. Probab. 48(1): 176-198 (March 2016).


We consider Markov processes, which describe, e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit steady-state distribution of product form available in the literature, we note that this steady-state distribution does not provide information about the correlation structure in time and space (over nodes). We study this correlation structure via one-step correlations for the queueing-environment process. Although formulas for absolute values of these correlations are complicated, the differences of correlations of related networks are simple and have a nice structure. We therefore compare two networks in a random environment having the same invariant distribution, and focus on the time behaviour of the processes when in such a network the environment changes or the rules for travelling are perturbed. Evaluating the comparison formulas we compare spectral gaps and asymptotic variances of related processes.


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Hans Daduna. Ryszard Szekli. "Correlation formulas for Markovian network processes in a random environment." Adv. in Appl. Probab. 48 (1) 176 - 198, March 2016.


Published: March 2016
First available in Project Euclid: 8 March 2016

zbMATH: 1337.60250
MathSciNet: MR3473573

Primary: 60K25
Secondary: 60J25 , 60K37

Keywords: asymptotic variance , Peskun ordering , Product-form network , space-time correlation , spectral gap

Rights: Copyright © 2016 Applied Probability Trust


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Vol.48 • No. 1 • March 2016
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