The Workload process with a Poisson cluster input can look like a Fractional Brownian motion even in the slow growth regime
| dc.contributor.author | Fasen, Vicky | |
| dc.contributor.author | Samorodnitsky, Gennady | |
| dc.date.accessioned | 2008-06-23T19:17:14Z | |
| dc.date.available | 2008-06-23T19:17:14Z | |
| dc.date.issued | 2008-06-23T19:17:14Z | |
| dc.description.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 Abstract 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: fasen@ma.tum.de. 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: gennady@orie.cornell.edu. Samorodnitsky's research was partially supported by an NSA grant MSPF-05G-049 and an ARO grant W911NF-07-1-0078 at Cornell University. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1813/10915 | |
| dc.language.iso | en_US | en_US |
| dc.title | The Workload process with a Poisson cluster input can look like a Fractional Brownian motion even in the slow growth regime | en_US |
| dc.type | technical report | en_US |
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