Linear Representation of Network Traffic

Abstract

We propose a representation of wireless workload patterns as large, sparse matrices and provide a method for stochastically generating experimental workloads from a given matrix. The essential property of the algebraic representation is that the summation of vectors naturally yields a faithful description of the aggregate behavior of the corresponding flows. This deceptively simple property allows us to express many common concepts from traffic modeling succinctly in terms of a few linear transformations. The algebraic representation has many benefits: (1) it makes the meaning of generally understood but vague concepts, such as "uniform behavior," mathematically precise and unambiguous; (2) it allows us to see clearly, through the lens of linear algebra, the implications of common modeling assumptions; (3) the implementation of traffic models becomes unprecedentedly simple and orthogonal, requiring only a handful of high-level matrix operations, which can be freely composed; (4) the vast body of algebraic theory and highly optimized numerical software may immediately be applied to traffic modeling. We use the paired differential simulation methodology introduced by the authors in previous work to experimentally demonstrate that the general matrix model accurately reproduces realistic network performance (Karpinski et al. 2007a, b). We use the same experimental methodology to explore the implications of various assumptions and simplifications that are commonly made in traffic modeling.