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|Title: ||The Workload process with a Poisson cluster input can look like a Fractional Brownian motion even in the slow growth regime|
|Authors: ||Fasen, Vicky|
|Issue Date: ||23-Jun-2008|
|Abstract: ||The workload process with a Poisson cluster input can look like a Fractional Brownian motion even in the slow growth regime
Vicky Fasen_and Gennady Samorodnitsky ?
May 20, 2008
We show that, contrary to the common wisdom, the workload process in a _uid queue with
a cluster Poisson input can converge, in the slow growth regime, to a Fractional Brownian
motion, and not to a L?vy stable motion. This emphasizes lack of robustness of L?vy stable
motions as _bird-eye_ descriptions of the tra_c in communication networks.
AMS 2000 Subject Classi_cations: primary: 90B22 secondary: 60F17
Keywords: cluster Poisson process, _uid queue, Fractional Brownian motion, slow growth regime, scaling limit, workload process
? Center for Mathematical Sciences, TU M?nchen, D-85747 Garching, Germany, email: firstname.lastname@example.org. Parts of the paper were written while the _rst author was visiting the Department of Operations Research and Information Engineering at Cornell University. Financial support from the Deutsche Forschungsgemeinschaft through a research grant is gratefully acknowledged.
?School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, email:
email@example.com. Samorodnitsky's research was partially supported by an NSA grant MSPF-05G-049 and an ARO grant W911NF-07-1-0078 at Cornell University.|
|Appears in Collections:||ORIE Technical Reports|
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