ATM modelling: parameterisation of the 4-phase MMPP model for the superposed traffic sources

A new approach is adopted to parameterise the 4-phase Markov modulated Poisson process (MMPP) to find the arrival and transition rate parameters for each of the phases. The MMPP has been used to model various B-ISDN sources, such as voice and video, as well as characterising the superposed traffic. It is able to capture the time-varying arrival rates and correlations between the interarrival times. The eight parameters are obtained from the eigenvalues and eigenvectors of the transition matrix and the exponential decay time constant of the autocorrelation between time slots. A finite relationship has been discovered between the exponential decay time constant and the sum of the transition and arrival rates of the phases; this is exploited in evaluating the parameters. This parameterisation is a major step in applying the 4-phase MMPP model to asynchronous transfer (ATM) modelling in the connection admission control (CAC) environment and in the bandwidth allocation of traffic.