Local conditions for he stochastic comparison of particle systems

We study the stochastic comparison of interacting particle systems where the state space of each particle is a finite set endowed with a partial order, and several particles may change their value at a time. For these processes we give local conditions, on the rates of change, that assure their comparability. We also analyze the case where one of the processes does not have any changes that involve several particles, and obtain necessary and sufficient conditions for their comparability. The proofs are based on the explicit construction of an order-preserving Markovian coupling. We show the applicability of our results by studying the stochastic comparison of infinite-station Jackson networks and batch-arrival, batch-service, and assemble-transfer queueing networks.