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arXiv · 0912.1928

Conditional limit theorems for regulated fractional Brownian motion

Hernan Awad·Peter Glynn
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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 workload process 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 occur in large clumps of size of order $b^{2-1/H}$. The conditional limit result involves a finer scaling of the queueing process than fluid analysis, thereby departing from previous related literature.

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BibTeXRIS

Hernan Awad, Peter Glynn. 2009-12-10. Conditional limit theorems for regulated fractional Brownian motion. https://doi.org/10.1214/09-aap605

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