Partition-reversible Markov processes

This study introduces a generalization of reversibility called partition-re versibility. A Markov jump process is partition-reversible if the average n umbers of its transitions between sets that partition the state space are e qual. In this case, its stationary distribution is obtainable by solving th e balance equations separately on the sets. We present several characteriza tions of partition-reversibility and identify subclasses of treelike, starl ike, and circular partition-reversible processes. A new circular birth-deat h process is used in the analysis. The results are illustrated by a queuein g model with controlled service rate, a multitype service system with block ing, and a parallel-processing model. A few comments address partition-reve rsibility for non-Markovian processes.