Recursive EM algorithm for finite mixture models with application to Internet traffic modeling

In the past decade, a lot of quantities characterizing high-speed telecommunication network performance have been reported to have heavy-tailed distributions, namely, with tails decreasing hyperbolically rather than exponentially. Since mixture distributions can approximate many heavy-tailed distributions with high precision, this paper uses mixture distributions to model the Internet traffic and applies the EM algorithm to fit the models. Making use of the fact that at each iteration of the EM algorithm the parameter increment has a positive projection on the gradient of the likelihood function, this paper proposes a recursive EM algorithm to fit the models, and the Bayesian Information Criterion is applied to select the best model. To illustrate the efficiency of the proposed algorithm, numerical results and experimental results on real traffic are provided.