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," Mathematical Theory of Networks and Systems (Proceedings of the MTNS-98 Symposium, held in Padova, Italy, July 1998) (A. Beghi, L. Finesso, and G. Picci, eds.), Padova, Italy: Il Poligrafo, pp. 891-894, 1998.
In this paper a new approach to the modelling 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 stochastic moments. Instead of a general MMPP, a circulant MMPP is used to reduce the computational cost. A circulant MMPP (CMMPP) is an MMPP with a circulant transition matrix. The main advantages of this approach are that the eigenvalue decomposition is a Fast Fourier Transform and that the optimisation towards the two stochastic moments is decoupled. Based on these properties, a fast time domain identification algorithm is developed.