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Data networks as
cascades: Explaining the multifractal nature of Internet WAN
traffic
Anja Feldmann, Anna Gilbert, and Walter Willinger (AT&T Labs-Research)
In apparent contrast to the well-documented self-similar (i.e.,
monofractal) scaling behavior of measured LAN traffic, recent studies
have suggested that measured TCP/IP and ATM WAN traffic exhibits more
complex scaling behavior, consistent with multifractals. To bring
multifractals into the realm of networking, this paper provides a
simple construction based on cascades (also known as multiplicative
processes) that is motivated by the protocol hierarchy of IP data
networks. The cascade framework allows for a plausible physical
explanation of the observed multifractal scaling behavior of data
traffic and suggests that the underlying multiplicative structure is a
traffic invariant for WAN traffic that co-exists with
self-similarity. In particular, cascades allow us to refine the
previously observed self-similar nature of data traffic to account for
local irregularities in WAN traffic that are typically associated with
networking mechanisms operating on small time scales, such as TCP flow
control.
To validate our approach, we show that recent measurements of Internet
WAN traffic from both an ISP and a corporate environment are fully
consistent with the proposed cascade paradigm and hence with
multifractality. We rely on wavelet-based time-scale analysis
techniques to visualize and to infer the scaling behavior of the
traces, both globally and locally. We also discuss and illustrate with
some examples how this cascade-based approach to describing data
network traffic suggests novel ways for dealing with networking
problems and helps in building intuition and physical understanding
about the possible implications of multifractality on issues related
to network performance analysis.
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