Markov network processes with product form stationary distributions
Queueing Systems: Theory and Applications
State-Dependent Coupling in General Networks
Queueing Systems: Theory and Applications
ON THE STRUCTURE OF THE SPACE OF GEOMETRIC PRODUCT-FORM MODELS
Probability in the Engineering and Informational Sciences
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We are concerned with a queueing network, described by a continuous-time Markov chain, in which each node is quasi-reversible. A new class of local balance equations is derived for the Markov chain with respect to a product-form distribution, which simultaneously provides an alternative and short proof for product form results of queueing networks with customers and signals. Furthermore, if each node is internally balanced, i.e., the total arrival rate equals the total departure rate for each node, the Markov chain is locally balanced in the ordinary sense. Our arguments reveal a close relationship between quasi-reversibility and local balance, and provide further insights into how transition rates are balanced in product form queueing networks.