**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: A time domain approach," Tech. rep. 97-108,
ESAT-SISTA, K.U.Leuven, Leuven, Belgium, 15 pp., Nov. 1997.

**Abstract:**

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.

Technical report: pdf file (183 KB)

@techreport{VanDeC:97-108,

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: A time domain approach},

number={97-108},

institution={ESAT-SISTA, K.U.Leuven},

address={Leuven, Belgium},

month=nov,

year={1997}

}

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