Internet Performance Modeling Using Mixture Dynamical System Models

This paper models Internet traffic input stream and TCP connection durations using dynamical system models. A linear dynamical model with mixture Gaussian output is proposed for the Internet traffic input stream, and a linear dynamical system with mixture lognormal output is developed to model the TCP connection durations. In the proposed models, a sum of independent AR (1) processes is used to approximate the autocorrelation of the real data, and a Gaussian mixture or lognormal mixture is used to fit the marginal distribution. As a result, the output processes can capture the correlation and the marginal distribution simultaneously. Making use of the fact that at each iteration the parameter increment of the EM algorithm has a positive projection on the gradient of the likelihood, a stochastic approximation-based recursive EM algorithm is proposed to fit the traffic marginal distribution. A cross-validation criterion is used for the model selection. To illustrate the usefulness of the proposed models, several experimental results are provided.