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Chapter 2 self-similarity and long-range dependence.
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| Abstract | The traffic behavior in a network has serious implications for the design, control, and analysis of the network. By analyzing data collected, it was demonstrated that the Ethernet Local Area Network traffic is statistically self similar. [LTWW94] Asynchronous Transfer mode, high speed, cell relay, networks, mostly are used as backbones for the interconnection of enterprise networks composed of several LAN's, thus leading to self similar behavior of the traffic in ATM Networks. [PF95] Self-similarity is the property we associate with fractals- the object appears the same regardless of the scale at which it is viewed. It is manifested in the absence of a natural length of a "burst "; at every time scale ranging from a few milliseconds to minutes and hours, bursts consisting of bursty subperiods separated by less bursty subperiods. A phenomenon that is self similar looks the same or behaves the same when viewed at different degrees of "magnification " or different scales on a dimension. This dimension may be space (length, width) or time. The commonly assumed models for network traffic, (e.g., the Poisson distribution, etc.) did not fit the recorded traces, since these models were not able to capture the fractal behavior of the traffic. [TG97] Were traffic to follow a Poisson or Markovian arrival process, it would have a characteristic burst length which would tend to be smoothed by averaging over a long enough time scale whereas measurements of real traffic indicate that significant traffic variance (burstiness) is present on a wide range of time scales. The effect of self-similarity in network traffic is shown in [LTWW95], which compares a self-similar series, with a compound Poisson series with the same distributional characteristics. The paper shows that Poisson models for network traffic become essentially uniform when aggregated by a factor of 1,000; while actual network traffic shows no such decrease in variability over the same range of aggregation. 4.1 Definition: [S98] The degree of self-similarity, defined via the Hurst parameter, typically depends on the utilization level of the network and can be used to measure the "burstiness " of the traffic. As H increases the degree of self similarity is increasing. 0.5 < H < 1.For H=0.5 and H>1, there is almost no self similarity. H is the measure of length of a long-range dependence of a stochastic process. |
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| Subject Keyword | Pf95 Self-similarity Fractal Behavior Long-range Dependence Compound Poisson Series Time Scale Network Traffic Ltww94 Asynchronous Transfer Mode Poisson Model Magnification Quot Serious Implication Atm Network Significant Traffic Variance Assumed Model Ethernet Local Area Network Traffic Hurst Parameter Traffic Behavior Characteristic Burst Length Actual Network Traffic Enterprise Network Similar Behavior Self-similarity Long-range Dependence Natural Length Distributional Characteristic Self Similarity Different Degree Recorded Trace Wide Range Real Traffic Tg97 Traffic High Speed Bursty Subperiods Markovian Arrival Process Stochastic Process Cell Relay Utilization Level Different Scale Poisson Distribution Several Lan Self-similar Series |
| Content Type | Text |
