TY - GEN
T1 - Statistical modeling and design of discrete-time chaotic processes: Advanced finite-dimensional tools and applications
AU - Rovatti, Riccardo
AU - Mazzini, Gianluca
AU - Setti, Gianluca
AU - Giovanardi, Alessandra
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 2003/1/1
Y1 - 2003/1/1
N2 - With the aim of explaining the formal development behind the chaos-based modeling of network traffic and other similar phenomena, here we generalize the tools presented in the companion paper (Setti et at., 2002) to the case of piecewise-affine Markov maps with a possibly infinite, but countable number of Markov intervals. Since, in doing so, we keep the dimensionality of the space of the observables finite, we still obtain a finite tensor-based framework Nevertheless, the increased complexity of the model forces the use of tensors of functions whose handling is greatly simplified by extensive z transformation. With this, a systematic procedure is devised to write analytical expressions for the tensors that take into account the joint probability assignments needed to compute any-order expectations. As an example of use, this machinery is finally applied to the study of self-similarity of quantized processes both in the analysis of higher order phenomena as well as in the analysis and design of second-order self-similar sources suitable for artificial network traffic generation.
AB - With the aim of explaining the formal development behind the chaos-based modeling of network traffic and other similar phenomena, here we generalize the tools presented in the companion paper (Setti et at., 2002) to the case of piecewise-affine Markov maps with a possibly infinite, but countable number of Markov intervals. Since, in doing so, we keep the dimensionality of the space of the observables finite, we still obtain a finite tensor-based framework Nevertheless, the increased complexity of the model forces the use of tensors of functions whose handling is greatly simplified by extensive z transformation. With this, a systematic procedure is devised to write analytical expressions for the tensors that take into account the joint probability assignments needed to compute any-order expectations. As an example of use, this machinery is finally applied to the study of self-similarity of quantized processes both in the analysis of higher order phenomena as well as in the analysis and design of second-order self-similar sources suitable for artificial network traffic generation.
UR - http://ieeexplore.ieee.org/document/1490918/
UR - http://www.scopus.com/inward/record.url?scp=84945971000&partnerID=8YFLogxK
U2 - 10.1109/TUTCAS.2003.1490918
DO - 10.1109/TUTCAS.2003.1490918
M3 - Conference contribution
SN - 0780379918
SP - 93
EP - 114
BT - Proceedings - IEEE International Symposium on Circuits and Systems
PB - Institute of Electrical and Electronics Engineers Inc.
ER -