New stochastic orderings for Markov processes on partially ordered spaces

The purpose of this paper is to develop a unified theory of stochastic ordering for Markov processes on partially ordered state spaces. When such a space is not totally ordered, it can induce a wide range of stochastic orderings, none of which are equivalent to sample path comparisons. Such alternative orderings can be quite useful when analyzing multi-dimensional stochastic models such as queueing networks.