Network traffic estimation using Markov chain and Incremental Gaussian Mixture

Abstract

This paper presents a traffic flow estimation method for communication networks using higher order Markov chain and Incremental Gaussian Mixture Model (IGMM). Given the previous and current values of network traffic flow, the optimal prediction under the minimum mean square error criteria is given as the conditional expectation according to the transition probability of Markov chain. Since the transition probability is not known beforehand, IGMM, whose mixtures are updated on-line as traffic flow values become known, is used to instantaneously change the probability density function of mixtures. IGMM with an on-line learning mechanism has lower computational complexity and requires lower memory compared to Gaussian Mixture Model (GMM) which uses batch processing. Numerical experiments using publicly available “Abilene” data-set show that IGMM outperforms GMM, and it is more robust.