A new traffic aggregation technique based on Markov modulated Poisson processes

In this paper, we propose a technique to approximate the traffic aggregation processes described by Markov modulated Poisson processes (MMPP) models. It is found that the decaying time constants of the aggregated traffic process are the product of the eigenvalues of the transition matrix of the individual traffic. If the time constants are well clustered around some representative time constants (RTC´s), the corresponding states can be merged in the state space. In the worst case, if the time constants are uniformly distributed over the log-scale, we prove that there exist a minimum number of states that can approximate the traffic aggregation. We develop a clustering algorithm to search for the RTC´s and extend the rate limit algorithm to the case that the limit of the arrival rate is unknown.