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Abstract: We consider a stationary fluid queue with fractional Brownian motion input.Conditional on the workload at time zero being greater than a large value $b$,we provide the limiting distribution for the amount of time that the workloadprocess spends above level $b$ over the busy cycle straddling the origin, as$b\to\infty$. Our results can be interpreted as showing that long delays occurin large clumps of size of order $b^{2-1-H}$. The conditional limit resultinvolves a finer scaling of the queueing process than fluid analysis, therebydeparting from previous related literature.



Author: Hernan Awad, Peter Glynn

Source: https://arxiv.org/







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