Network, web, and disk I/O traffic are usually bursty, self-similar and therefore can not be modeled adequately with Poisson arrivals. However, we do want to model these types of traffic and to generate realistic traces, because of obvious applications for disk scheduling, network management, web server design. Previous models (like fractional Brownian motion, ARFIMA etc) tried to capture the 'burstiness'. However the proposed models either require too many parameters to fit and/or require prohibitively large (quadratic) time to generate large traces. We propose a simple, parsimonious method, the b-model, which solves both problems: It requires just one parameter (b), and it can easily generate large traces. In addition, it has many more attractive properties: (a) With our proposed estimation algorithm, it requires just a single pass over the actual trace to estimate b. For example, a one-day-long disk trace in milliseconds contains about 86Mb data points and requires about 3 minutes for model fitting and 5 minutes for generation. (b) The resulting synthetic traces are very realistic: our experiments on real disk and web traces show that our synthetic traces match the real ones very well in terms of queuing behavior.

18 pages

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