Pathwise Rate-Stability for Input-Output Processes

Muhammad El-Taha, Department of Mathematics and Statistics, University of Southern Maine

Abstract

An input-output process Z ~ {Z(t), t > 0} is said to be w-rate stable if Z(t) = o(w(t)) for some non-negative function w(t). We prove that the process Z is w-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 w-rate-stability can be verified from input data. For example, using input information, we establish w-rate stability of the workload for multiserver queues, an ATM multiplexer, and w-rate stability of queue-length processes for infinite server queues.