T. Van Gestel, K. De Cock, R. Jans, B. De Schutter, Z. Degraeve, and B. De Moor, "Discrete stochastic modelling of ATM-traffic with circulant transition matrices: A time domain approach," Tech. rep. 97-108, ESAT-SISTA, K.U.Leuven, Leuven, Belgium, 15 pp., Nov. 1997.
In this report a new fast time domain approach for the identification of ATM-traffic is proposed. The traffic is measured and characterised by its first and second order statistic moments. A Markov Modulated Poisson Process (MMPP) is used to capture the information in these two statistic moments. Since the identification of a general MMPP is time consuming because of the large computational requirements, a circulant MMPP is used to reduce the computational cost. A circulant MMPP is an MMPP with a circulant transition matrix. The main advantages of this approach are the avoidance of inverse eigenvalue problem and the decoupling of the two statistic moments. Since ATM-traffic is highly correlated one can expect slowly decaying autocorrelations, which slows down the time domain identification. Therefore the autocorrelation is rewritten as a sum of exponentials using subspace-identification for stochastic linear time invariant systems. The identification of the second order statistics is decoupled from the first order statistics and uses 0/1 knapsack solvers and unconstrained optimisation.