A note on stochastic bounds for queueing networks

Abstract

Recently, Massey [1] proved that the vector of queue lengths of some queueing networks is stochastically dominated at any given time by that of a corresponding system of parallel M/M/l queues. This result is interesting, even though the bounds are generally quite conservative, in that the transient behavior of independent parallel M/M/l queues is considerably easier to analyze than that of a network. This note provides an alternative proof of a generalized form of that result.