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Impact of Routeing on Correlation Strength in Stationary Queueing Network Processes

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Hans Daduna  and
Ryszard Szekli
Hans Daduna*
Affiliation:
Hamburg University
Ryszard Szekli*
Affiliation:
Wrocław University
*
∗Postal address: Department of Mathematics, Hamburg University, Bundesstrasse 55, 20146 Hamburg, Germany. Email address: daduna@math.uni-hamburg.de
∗∗Postal address: Mathematical Institute, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland.
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Abstract

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For exponential open and closed queueing networks, we investigate the internal dependence structure, compare the internal dependence for different networks, and discuss the relation of correlation formulae to the existence of spectral gaps and comparison of asymptotic variances. A central prerequisite for the derived theorems is stochastic monotonicity of the networks. The dependence structure of network processes is described by concordance order with respect to various classes of functions. Different networks with the same first-order characteristics are compared with respect to their second-order properties. If a network is perturbed by changing the routeing in a way which holds the routeing equilibrium fixed, the resulting perturbations of the network processes are evaluated.

Keywords

Product form networkconcordance orderingspace-time correlationspectral gapasymptotic variancestochastic monotonicityMCMCPeskun ordering

MSC classification

Secondary: 60K25: Queueing theory 60J25: Continuous-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 846 - 878
Copyright
Copyright © Applied Probability Trust 2008 

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