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→∞. Our results can be interpreted as showing that long delays occur in large clumps of size of order b2−1/H. The conditional limit result involves a finer scaling of the queueing process than fluid analysis, thereby departing from previous related literature.
Citation
Hernan Awad. Peter Glynn. "Conditional limit theorems for regulated fractional Brownian motion." Ann. Appl. Probab. 19 (6) 2102 - 2136, December 2009. https://doi.org/10.1214/09-AAP605
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