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A self-similar behavior characterizes the traffic in many real-world communication networks. This traffic is traditionally modeled as an ON/OFF discrete-time second-order self-similar random process. The self-similar processes are identified by means of a polynomially decaying trend of the autocovariance function. In this work we concentrate on two criteria to build a chaotic system able to generate self-similar trajectories. The first criterion relates self-similarity with the polynomially decaying trend of the autocovariance function. The second one relates self-similarity with the *heavy*-tailedness of the distributions of the sojourn times in the ON and/or OFF states. A family of discrete-time chaotic systems is then devised among the countable piecewise affine Pseudo-Markov maps. These maps can be constructed so that the quantization of their trajectories emulates traffic processes with different Hurst parameters and average load. Some simulations are reported showing how, according to the theory, the map design is able to fit those specifications.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.9 pp.2155-2164

- Publication Date
- 2001/09/01

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and its Applications)

- Category
- Chaos & Dynamics

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Alessandra GIOVANARDI, Gianluca MAZZINI, Riccardo ROVATTI, "Criteria to Design Chaotic Self-Similar Traffic Generators" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 9, pp. 2155-2164, September 2001, doi: .

Abstract: A self-similar behavior characterizes the traffic in many real-world communication networks. This traffic is traditionally modeled as an ON/OFF discrete-time second-order self-similar random process. The self-similar processes are identified by means of a polynomially decaying trend of the autocovariance function. In this work we concentrate on two criteria to build a chaotic system able to generate self-similar trajectories. The first criterion relates self-similarity with the polynomially decaying trend of the autocovariance function. The second one relates self-similarity with the *heavy*-tailedness of the distributions of the sojourn times in the ON and/or OFF states. A family of discrete-time chaotic systems is then devised among the countable piecewise affine Pseudo-Markov maps. These maps can be constructed so that the quantization of their trajectories emulates traffic processes with different Hurst parameters and average load. Some simulations are reported showing how, according to the theory, the map design is able to fit those specifications.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_9_2155/_p

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@ARTICLE{e84-a_9_2155,

author={Alessandra GIOVANARDI, Gianluca MAZZINI, Riccardo ROVATTI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Criteria to Design Chaotic Self-Similar Traffic Generators},

year={2001},

volume={E84-A},

number={9},

pages={2155-2164},

abstract={A self-similar behavior characterizes the traffic in many real-world communication networks. This traffic is traditionally modeled as an ON/OFF discrete-time second-order self-similar random process. The self-similar processes are identified by means of a polynomially decaying trend of the autocovariance function. In this work we concentrate on two criteria to build a chaotic system able to generate self-similar trajectories. The first criterion relates self-similarity with the polynomially decaying trend of the autocovariance function. The second one relates self-similarity with the *heavy*-tailedness of the distributions of the sojourn times in the ON and/or OFF states. A family of discrete-time chaotic systems is then devised among the countable piecewise affine Pseudo-Markov maps. These maps can be constructed so that the quantization of their trajectories emulates traffic processes with different Hurst parameters and average load. Some simulations are reported showing how, according to the theory, the map design is able to fit those specifications.},

keywords={},

doi={},

ISSN={},

month={September},}

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TY - JOUR

TI - Criteria to Design Chaotic Self-Similar Traffic Generators

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2155

EP - 2164

AU - Alessandra GIOVANARDI

AU - Gianluca MAZZINI

AU - Riccardo ROVATTI

PY - 2001

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E84-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 2001

AB - A self-similar behavior characterizes the traffic in many real-world communication networks. This traffic is traditionally modeled as an ON/OFF discrete-time second-order self-similar random process. The self-similar processes are identified by means of a polynomially decaying trend of the autocovariance function. In this work we concentrate on two criteria to build a chaotic system able to generate self-similar trajectories. The first criterion relates self-similarity with the polynomially decaying trend of the autocovariance function. The second one relates self-similarity with the *heavy*-tailedness of the distributions of the sojourn times in the ON and/or OFF states. A family of discrete-time chaotic systems is then devised among the countable piecewise affine Pseudo-Markov maps. These maps can be constructed so that the quantization of their trajectories emulates traffic processes with different Hurst parameters and average load. Some simulations are reported showing how, according to the theory, the map design is able to fit those specifications.

ER -