Fitting Markovian Arrival Processes by Incorporating Correlation into Phase Type Renewal Processes

This paper presents a novel MAP fitting method. As many recent fitting methods, it is based on the separate fitting of the distribution of the inter-arrival times and the correlation structure of the arrival process. We assume that a Phase-type(PH) distribution representing the inter-arrival times is available. Our procedure obtains a MAP featuring the prescribed PH distributed inter-arrival times and capturing several correlation measures as accurately as possible. The correlation measures being used during the fitting are the joint moments of two inter-arrival times (including higher order ones). Contrary to other available MAP fitting methods, the proposed method does not only fit the lag-1, but also higher lag joint moments. The special MAP structure used for fitting enables to formulate the fitting problem as a non-negative least-squares problem for which efficient numerical implementations exist. Several numerical examples are presented to demonstrate that our method can be used in various practical applications.