Partition-reversible Markov processes

This study introduces a generalization of reversibility called partition-reversibility. A Markov jump process is partition-reversible if the average numbers of its transitions between sets that partition the state space are equal. In this case, its stationary distribution is obtainable by solving the balance equations separately on the sets. We present several characterizations of partition-reversibility and identify subclasses of treelike, starlike, and circular partition-reversible processes. A new circular birth–death process is used in the analysis. The results are illustrated by a queueing model with controlled service rate, a multitype service system with blocking, and a parallel-processing model. A few comments address partition-reversibility for non-Markovian processes.