An input–output process Z ≡ {Z(t), t ≥ 0} is said to be ω-rate stable if Z(t) = o(ω(t)) for some non-negative function ω(t). We prove that the process Z is ω-rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions for ω-rate-stability can be verified from input data. For example, using input information, we establish ω-rate stability of the workload for multiserver queues, an ATM multiplexer, and ω-rate stability of queue-length processes for infinite server queues.
