Imperial College London
Markovian Arrival Processes (MAPs) are a tractable class of point-processes useful to model correlated time series, such as those commonly found in network traces and system logs used in performance analysis and reliability evaluation. Marked MAPs (MMAPs) generalize MAPs by further allowing the modeling of multi-class traces, possibly with cross-correlation between multi-class arrivals. In this paper, the author's present analytical formulas to fit second order acyclic MMAPs with an arbitrary number of classes. They initially define closed-form formulas to fit second-order MMAPs with two classes, where the underlying MAP is in canonical form. Their approach leverages forward and backward moments, which have recently been defined, but never exploited jointly for fitting.