Linear Representation of Network Traffic With Special Application to Wireless Workload Generation

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 t

Mobile Netw Appl DOI 10.1007/s11036-008-0110-0 Linear Representation of Network Traffic With Special Application to Wireless Workload Generation

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 t