Discrete Stochastic Modelling of ATM-Traffic with Circulant Transition
Matrices: A Time Domain Approach
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. report 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.
Downloads
Bibtex entry
@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}
}
This page is maintained by Bart De Schutter.
Last update: February 21, 2026.