State-Dependent Coupling in General Networks

Authors:
Xiuli Chao;W. Henderson;P. G. Taylor
Affiliations:
Department of Industrial Engineering and Interdisciplinary Operations Research Program, North Carolina State University, Raleigh, NC 27695-7906, USA xchao@eos.ncsu.edu;Department of Applied Mathematics, University of Adelaide, South Australia 5005, Australia whenders@maths.adelaide.edu.au;Department of Applied Mathematics, University of Adelaide, South Australia 5005, Australia ptaylor@maths.adelaide.edu.au
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Abstract

In this paper we extend a result which holds for the class of networks of quasireversible nodes to a class of networks constructed by coupling Markov chains. We begin with a network in which the transition rates governing the stochastic behaviour of the individual nodes depend only on the state of the node. Assuming that the network has an invariant measure, we construct another network with transition rates at each node depending on the state of the entire network, and obtain its invariant measure.