Abstract
An input-output processZ = {Z(t), t ⩾ 0} is said to beω-rate stable ifZ(t) = o(ω(t)) for some non-negative functionω(t). We prove that the processZ 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 forω-rate-stability can be verified from input data. For example, using input information, we establishω-rate stability of the workload for multiserver queues, an ATM multiplexer, andω-rate stability of queue-length processes for infinite server queues.
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El-Taha, M. Pathwise rate- stability for input-output processes. Queueing Syst 22, 47–63 (1996). https://doi.org/10.1007/BF01159392
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DOI: https://doi.org/10.1007/BF01159392