The Annals of Applied Probability

Conditional limit theorems for regulated fractional Brownian motion

Hernan Awad and 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→∞. 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.

Article information

Source
Ann. Appl. Probab., Volume 19, Number 6 (2009), 2102-2136.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1259158768

Digital Object Identifier
doi:10.1214/09-AAP605

Mathematical Reviews number (MathSciNet)
MR2588241

Zentralblatt MATH identifier
1204.60084

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 90B22: Queues and service [See also 60K25, 68M20] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 60F99: None of the above, but in this section

Keywords
Queues fractional Brownian motion conditional limit laws large buffer asymptotic

Citation

Awad, Hernan; Glynn, Peter. Conditional limit theorems for regulated fractional Brownian motion. Ann. Appl. Probab. 19 (2009), no. 6, 2102--2136. doi:10.1214/09-AAP605. https://projecteuclid.org/euclid.aoap/1259158768


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