Approaching long-tailed distribution by increasing the process complexity

We propose to model network traffic using a probabilistic context-free grammar, which is based on the multi-type branching process. Since this research is in its very early stages, the purpose of this paper is merely to suggest a justification for this model. This paper demonstrates how the lengths of the strings generated by one simple example of a probabilistic context-free grammar have first-order statistics with the characteristic "long tail" that is observed in real network traffic. The paper also shows that the lengths of the strings generated by corresponding Poisson or Markov models fall short of having this long tailed distribution.