On the maximum workload of a queue fed by fractional Brownian motion

Assaf J. Zeevi*, Peter W. Glynn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Consider a queue with a stochastic fluid input process modeled as fractional Brownian motion (fBM). When the queue is stable, we prove that the maximum of the workload process observed over an interval of length t grows like γ(log t)1/(2-2H), where H > 1/2 is the self-similarity index (also known as the Hurst parameter) that characterizes the fBM and can be explicitly computed. Consequently, we also have that the typical time required to reach a level b grows like exp{b2(1-H)}. We also discuss the implication of these results for statistical estimation of the tail probabilities associated with the steady-state workload distribution.

Original languageEnglish
Pages (from-to)1084-1099
Number of pages16
JournalAnnals of Applied Probability
Issue number4
StatePublished - Nov 2000
Externally publishedYes


  • Extreme values
  • Fractional Brownian motion
  • Long-range dependence
  • Queues


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