Multi-class Markovian arrival processes and their parameter fitting

Markovian arrival processes are a powerful class of stochastic processes to represent stochastic workloads that include autocorrelation in performance or dependability modeling. However, fitting the parameters of a Markovian arrival process to given measurement data is non-trivial and most known methods focus on a single class case, where all events are of the same type and only the sequence of interarrival times is of interest. In this paper, we propose a method to fit data to a multi-class Markovian arrival process, where arrivals can be partitioned into a finite set of classes. This allows us to use a Markovian arrival process to represent workloads where interarrival times are correlated across customer classes and to achieve models of greater accuracy. The fitting approach performs in several consecutive steps and applies a single non-linear optimization step and several non-negative least squares computations.