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**An application of deterministic chaotic maps to model packet traffic.**
*(English)*
Zbl 0836.60103

Summary: We investigate the application of deterministic chaotic maps to model traffic sources in packet based networks, motivated in part by recent measurement studies which indicate the presence of significant statistical features in packet traffic more characteristic of fractal processes than conventional stochastic processes. We describe one approach whereby traffic sources can be modeled by chaotic maps, and illustrate the traffic characteristics that can be generated by analyzing several classes of maps. We outline a potential performance analysis approach based on chaotic maps that can be used to assess the traffic significance of fractal properties. We show that low order nonlinear maps can capture several of the fractal properties observed in actual data, and show that the source characteristics observed in actual traffic can lead to heavy-tailed queue length distributions. It is our conclusion that while there are considerable analytical difficulties, chaotic maps may allow accurate, yet concise, models of packet traffic, with some potential for transient and steady state analysis.

### MSC:

60K25 | Queueing theory (aspects of probability theory) |

90B18 | Communication networks in operations research |

### Keywords:

packet traffic modelling; deterministic chaotic maps; self-similar traffic; fractals; chaos; performance analysis
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\textit{A. Erramilli} et al., Queueing Syst. 20, No. 1--2, 171--206 (1995; Zbl 0836.60103)

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