An application of superpositions of two state Markovian source to the modelling of self-similar behaviour

We present a modelling framework and a fitting method for modelling second order self-similar behaviour with the Markovian arrival process (MAP). The fitting method is based on fitting to the autocorrelation function of counts a second order self-similar process. It is shown that with this fitting algorithm it is possible closely to match the autocorrelation function of counts for a second order self-similar process over 3-5 time-scales with 8-16 state MAPs with a very simple structure, i.e. a superposition of 3 and 4 interrupted Poisson processes (IPP) respectively and a Poisson process. The fitting method seems to work well over the entire range of the Hurst (1951) parameter.