IP packet generation: statistical models for TCP start times based on connection-rate superposition

• Authors: William S. Cleveland;Dong Lin;Don X. Sun
• Venue: Proceedings of the 2000 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
• Year: 2000

TCP start times for HTTP are nonstationary. The nonstationarity occurs because the start times on a link, a point process, are a superposition of source traffic point processes, and the statistics of superposition changes as the number of superposed processes changes. The start time rate is a measure of the number of traffic sources. The univariate distribution of the inter-arrival times is approximately Weibull, and as the rate increases, the Weibull shape parameter goes to 1, an exponential distribution. The autocorrelation of the log inter-arrival times is described by a simple, two-parameter process: white noise plus a long-range persistent time series. As the rate increases, the variance of the persistent series tends to zero, so the log times tend to white noise. A parsimonious statistical model for log inter-arrivals accounts for the autocorrelation, the Weibull distribution, and the nonstationarity in the two with the rate. The model, whose purpose is to provide stochastic input to a network simulator, has the desirable property that the superposition point process is generated as a single stream. The parameters of the model are functions of the rate, so to generate start times, only the rate is specified. As the rate increases, the model tends to a Poisson process. These results arise from theoretical and empirical study based on the concept of connection-rate superposition. The theory is the mathematics of superposed point processes, and the empiricism is an analysis of 23 million TCP connections organized into 10704 blocks of approximately 15 minutes each.