State-dependent coupling of quasireversible nodes (Q5934399)

Quasireversibility is a powerful property of continuous-time Markov chains leading to product-form results discovered for networks of queues. The authors show how to couple quasireversible nodes into a network in a state-independent manner, allowing simultaneous transitions at an arbitrary number of nodes to be triggered by a departure at a single node. \textit{X. Chao} and \textit{M. Miyazawa} [Adv. Appl. Probab. 32, No. 1, 284-313 (2000; Zbl 0959.60083)] have recently established that this type of coupling is possible in a network of quasireversible nodes. Here the authors present a different proof to this result. They also extend their coupling procedure to encompass transition rates which are dependent on the entire network state. They apply their theory to several examples.