Internet Traffic and Multiresolution Analysis

Traditional Internet traffic studies have primarily focused on the temporal characteristics of packet traces as observed on a single link within an ISP's network. They have contributed to advances in the areas of self-similar stochastic processes, long-range dependence, and heavy-tailed distributions and have demonstrated the benefits of applying a wavelet-based multireso- lution analysis (MRA) approach when analyzing these traces. However, an ISP's physical infrastructure typically consists of 100s or 1000s of such links which are connected by routers or switches, and the Internet as a whole is made up of about 20,000 such ISPs. When viewed within this bigger context, the importance of the traffic's spatial characteristics becomes evident, and traffic matrices—compact and succinct descriptions of the traffic exchanges between nodes in a given network structure—are used in practice to capture and explore critical aspects of this spatial component of Internet traffic. In this paper, we first review some of the known results about the observed multi- faceted scaling behavior of Internet traffic as seen on a single link. Next, we give a detailed account of how the architectural design of the Internet gives rise to natural representation of traffic matrices at different scales or levels of resolution. Moreover, we discuss the development of a MRA-like framework of traffic matrices that respects the different physically or logically meaningful Internet connectivity structures and provides new insights into Internet traffic as a spatio-temporal object.