Fitting with matrix exponential mixtures generated by discrete probabilistic scaling

Matrix exponential (ME) distributions generalize phase-type distributions; however, their use in queueing theory is hampered by the difficulty of checking their feasibility. We propose a novel ME fitting algorithm that produces a valid distribution by construction. The ME distribution used during the fitting is a product of independent random variables that are easy to control in isolation. Consequently, the calculation of the CDF and the Mellin transform factorizes, making it possible to use these measures for the fitting without significant restriction on the distribution order. Trace-driven queueing simulations indicate that the resulting distributions yield highly accurate results.