CONDITIONAL LIMIT THEOREMS FOR REGULATEDFRACTIONAL BROWNIAN MOTION

摘要

We consider a stationary fluid queue with fractional Brownian motioninput. Conditional on the workload at time zero being greater than a largevalue b, we provide the limiting distribution for the amount of time that theworkload process spends above level b over the busy cycle straddling theorigin, as b→∞. Our results can be interpreted as showing that long delaysoccur in large clumps of size of order b2-1/H. The conditional limit resultinvolves a finer scaling of the queueing process than fluid analysis, therebydeparting from previous related literature.