Efficient phase-type fitting with aggregated traffic traces

Approximating the empirical distribution of a measured data trace by a phase-type (PH) distribution has significant applications in the analysis of stochastic models. For phase-type fitting, a large number of different methods and tools exist. One drawback of all these methods is that the fitting effort strongly depends on the size of the data trace to be fitted. Since large data traces are necessary to capture rare events, which have a strong impact on system performance, current fitting procedures are very time consuming. In this paper, we introduce a method to generate an aggregated trace from the original trace, and we show how to effectively use the aggregated trace within a PH fitting approach, called G-FIT. In particular, we show that elements of a large traffic trace can be aggregated to a smaller number of 50-200 weighted elements, while fitting accuracy remains the same compared to the case of fitting the original trace. As a result, CPU time requirements for fitting PH distributions can be decreased by about four orders of magnitude, such that traces with ten million elements can be accurately fitted in a few seconds. The effectiveness of the proposed method is demonstrated on a set of benchmark traces and two real traffic traces as well as quantitative results from queuing analysis.