Fast algorithms for measurement-based traffic modeling

This paper develops fast algorithms for the construction of a circulant modulated rate process to match with the two primary traffic statistical functions: rate distribution f(x) and autocorrelation R(τ). Using existing modeling techniques, f(x) has to be limited to certain forms such as Gaussian or binomial; R(τ) can only consist of one or two exponential terms which are often real exponentials rather than complex. In reality, these two functions are collected from real traffic traces and generally expressed in a very complicated form. We only consider the traffic whose correlation function can be approximated by the sum of complex exponentials. Our emphasis is placed on the algorithm design for matching complicated R(τ) in traffic modeling. The typical CPU time for traffic modeling with R(τ) consisting of five or six complex exponential terms is found to be in the range of a few minutes by the proposed algorithms. Our study further shows an excellent agreement between the original traffic traces and the sequences generated by the matched analytical model. The selection of the measurement-window in traffic statistics collection for queueing performance analysis is also discussed