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.