An empirical real-time approximation of waiting time distribution in MMPP(2)/D/1

We propose a simple, empirical real-time approximation method for calculating the waiting time distribution for the MMPP(2)/D/1 system. Our approach is based on approximation using a two-term exponential function. We match the poles, the residue for the asymptotic constant, and the mean waiting time between the Laplace transforms of the exact distribution and the approximate distribution. Numerical examples show that our method yields quite accurate results over a wide range. The result can be adopted in evaluating asynchronous transfer mode (ATM) multiplexers for real-time ATM traffic control.