Stochastic Upper and Lower Bounds for General Markov Fluids

Promising perspectives of a hypothetical 'Tactile Internet', or 'Internet at the speed of light', whereby network latencies become imperceptible to users, have (again) triggered a broad interest to understand and mitigate Internet latencies. In this paper we revisit the queueing analysis of the versatile Markov Fluid traffic model, which was mainly investigated in the 1980-90s, yet with low accuracy. We derive upper bounds on the tail distribution of the queue size, which improve state-of-the-art results by an exponential factor O (κn) in a special case, where 0

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