Correlated phase-type distributed random numbers as input models for simulations

The adequate modeling of correlated input processes is an important step in building simulation models. Modeling independent identically distributed data is well established in simulation whereas the integration of correlation is still a challenge. In this paper, ARTA processes which have been used several times for describing correlated input processes in simulation are extended by using ARMA instead of AR processes to realize the correlation and Acyclic Phase Type distributions to model the marginal distribution. For this new process type a fitting algorithm is presented. By means of some real network traces it is shown that the extended model allows a better fitting of the marginal distribution as well as the correlation structure and results in a compact process description that can be used in simulation models.