Reference:
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.
Abstract:
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.