Fast algorithms for measurement-based traffic modeling

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