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by J. Zeevi, Peter W. Glynn
http://www-isl.stanford.edu/people/azeevi/PAPERS/fbm.ps.gz
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Abstract:
Consider a queue with a stochastic fluid input process modeled as fractional Brownian motion (fBM). When the queue is stable, we prove that the maximum of the workload process observed over an interval of length t grows like fl(log t)
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