Traffic modeling with a combination of phase-type distributions and ARMA processes

The adequate modeling of correlated input processes is necessary to obtain realistic models in areas like computer or communication networks but is still a challenge in simulation modeling. In this paper we present a new class of stochastic processes which has been developed for describing correlated input processes and combines acyclic Phase-type distributions to model the marginal distribution with an ARMA process to capture the autocorrelation. The processes are an extension of ARTA processes, a well established input model in stochastic simulations. For the new process type we propose a fitting algorithm that allows one to approximate arbitrary sets of joint moments and autocorrelation coefficients and investigate the effect of different sets of approximated quantities on the quality of the fitted process empirically. We furthermore present an efficient way to generate random numbers and show how the processes can be easily integrated into simulation models.