A note on sample-path stability conditions for input-output processes

Using sample-path (deterministic asymptotic) analysis, the authors show that an input-output process is stable, in the sense that its growth is o(t) as t approaches infinity, if the exogeneous input rate, and the output rate while the process is in sufficient large states, are both well defined and finite and the latter is greater than the former. This generalizes a known result for the workload process in a G/G/1 queue. The authors give other examples in which these conditions can be expressed in terms of primary quantities and thus check a priori.