Data networks as cascades

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Abstract
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 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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