Pathwise comparison results for stochastic fluid networks (Q600899)

The paper deals with single class stochastic fluid networks, i.e., 4-tuples \(\{J,r,P,W(0)\}\) where \(\{J(t): t \geq 0\}\) is a cumulative input process, \(r\) is the service rate, \(P\) is a routing matrix, and \(W(0)\geq 0\) represents the initial workload. It is assumed that the queues are work conserving, and the networks are open with \(N\) queues, each having a single server with infinite capacity. Some results for pathwise comparisons are proven. Under certain conditions monotonicity with respect to the routing matrices is shown and under more restrictive conditions also with respect to the service rates.