Data Traffic Modeling—A Signal Processing Perspective - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 219

dependence poses great challenges for network traffic engineering. For ex-
ample, it has been shown 20 that both marginal impulsiveness and long-range
dependence can change the packet loss behavior radically. In particular, for
a single-server queue with a constant service rate and a long-range depen-
dent and impulsive input source, the buffer overflow probability becomes a
power-law function of buffer size; that is, the probability that a packet is lost
during transmission, due to overflow, decays polynomially fast as buffer size
increases, and the speed of decay is dominated either by the Hurst parame-
ter or the tail index of the marginal distribution of the traffic. Note that for
traffic of Markov type, e.g., voice traffic, the buffer overflow probability is an
exponential function of buffer size.
We have introduced the basic concepts of self-similarity, long-range de-
pendence, heavy-tail distributions, and impulsiveness, along with the math-
ematical tools to characterize them. Motivated by the intuitive observation of
the self-similar and impulsive nature of real-data traffic, we discussed vari-
ous traffic models that can capture the relevant statistical characteristics, i.e.,
self-similarity and impulsiveness, of data traffic. In particular, we studied
the On/Off models in detail, because they not only can account for the two
salient features of impulsive self-similar data traffic, but also provide insights
into the physical understanding of these statistical properties. We also re-
viewed wavelet models and multifractal models, as they represent another
perspective on describing the time-scaling variant/invariant specialties of
data traffic. We also provided a review of various techniques for estimating
the Hurst parameter and tail indexes for long-range dependent and/or im-
pulsive processes, as they play an indispensable role in statistical analysis
and modeling.

Acknowledgment

The authors thank Dr. Harish Sethu for his helpful discussions with them.

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