Multiscale analysis and data networks

The empirical nding of self-similarity over many time scales in data network traac motivates the need for analysis tools that are particularly well-adapted for identifying structures in network traac. These structures span a range of time scales or are scale dependent. Wavelet-based scaling analysis methods are especially successful, both collecting summary statistics from scale to scale and probing the local structure of packet traces. They include both spectral density estimation to identify large time scale features and multifractal estimation for small time scale bursts. While these methods are primarily statistical in nature, we may also adapt them to visualize the \burstiness" or the instantaneous scaling features of network traac. This expository paper discusses the theoretical and implementation issues of wavelet-based scaling analysis for network traac. Because data network traac research does not consist solely of analysis, we show how these wavelet-based methods may be used to monitor and infer network properties (in conjunction with on-line algorithms and careful network experimentation). More importantly, we address what types of networking questions we can and cannot investigate with such tools.