Pathwise comparison results for stochastic fluid networks

We prove some new pathwise comparison results for single class stochastic fluid networks. Under fairly general conditions, monotonicity with respect to the (state- and time-dependent) routing matrices is shown. Under more restrictive assumptions, monotonicity with respect to the service rates is shown as well. We conclude by using the comparison results to establish a moment bound, a stability result for stochastic fluid networks with Lévy inputs, and a comparison result for multi-class GPS networks.