**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.

Corresponding technical report: pdf file (122 KB)

@inproceedings{VanDeC:97-109,

author={T. {V}an Gestel and K. {D}e Cock and R. Jans and B. {D}e Schutter and Z. Degraeve and B. {D}e Moor},

title={Discrete stochastic modelling of {ATM}-traffic with circulant transition matrices},

booktitle={Mathematical Theory of Networks and Systems \rm(Proceedings of the MTNS-98 Symposium, held in Padova, Italy, July 1998)},

editor={A. Beghi and L. Finesso and G. Picci},

publisher={Padova, Italy: Il Poligrafo},

pages={891--894},

year={1998}

}

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