Accurate long-tailed network traffic approximation and its queueing analysis by hyper-Erlang distributions

Internet traffic has been proven to be long-tailed and often modeled by lognormal distribution, Weibull or Pareto distributions theoretically. However, these mathematical models hinder us in traffic analysis and evaluation studies due to their complex representations and theoretical properties. This paper proposes a hyper-Erlang model (mixed Erlang distribution) for such a long-tailed network traffic approximation. It fits network traffic with long-tailed characteristic into a mixed Erlang distribution directly to facilitate our further analysis. Compared with the well-known hyperexponential based method, the mixed Erlang model is more accurate in fitting the tail behavior and also computationally efficient. Further investigations on the M/G/1 queueing behavior also prove the efficiency of the mixed Erlang based approximation