Supermodular Ordering of Markov Processes and Queueing Networks

In this paper we characterize supermodular dependence ordering of Markov processes on partially ordered state space both in discrete and continuous time. A characterization is given in terms of infinitesimal generators. As a special case it allows us to obtain correlation-in-time inequality for Markov processes. We applied our results for a comparison of a transient behavior of standard Jackson networks and Jackson networks which are subject to breakdowns and repairs. 1