Data Traffic Modeling—A Signal Processing Perspective - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 208

motion prediction frame, and forward or backward prediction frames, re-
spectively. I , B , and P frames exhibit distinct statistical properties, such as
frame-size distribution, correlations, etc. One can thus model the I , B , and
P frames separately and then assemble these components into one complete
video sequence.
In the following, we focus on heterogeneous traffic modeling, which is more
relevant to the general statistical characterization of today's broadband net-
work traffic. Heterogeneous traffic models can be divided into two classes:
behavior models and structural models. Behavior models do not take into
account the actual traffic generation mechanism, but rather model statisti-
cal characteristics of traffic, e.g., correlation, marginal distribution, or even
high-order statistics. 12 , 14 , 16 , 18 , 19 , 21 Although, in general, behavior models are
amenable to mathematical analysis, their parameters are often not linked to
network parameters, and thus cannot provide insight on network behavior.
On the other hand, structural models 7 , 13 , 17 , 20 are rooted on the packet/traffic
generation mechanism. Their parameters can be easily translated to network
parameters, e.g., number of users, user bandwidth, etc., which facilitates un-
derstanding of network behavior. However, the analysis of structural models
is often more difficult compared to behavior models.
In the following, we present three popular classes of models that have been
proposed for broadband heterogeneous network traffic, based on On/Off
processes, wavelets, and multifractal processes. Whereas the class of On/Off
models are structural models, wavelet models and multifractal models are
behavioral models.

6.4.1 On/Off Models

In high-speed networks, the packets are communicated in a packet train
fashion; 31 once a packet train is triggered, the probability that another packet
will follow is very large. Furthermore, the length of the packet train is heavy-
tail distributed. This observation led to the celebrated On/Off model, 7 which
is sometimes referred to as the Alternating Fractal Renewal Process (AFRP)
model. 32 Based on the On/Off model, a single source/destination active pair
alternates between two states: the On, during which there is data flow between
source and destination, along either way, and the Off, which is the quiet du-
ration. Both the On and Off durations follow a heavy-tail distribution. The
self-similar characteristics of the AFRP have been attributed to the heavy-tail
properties of the On/Off states' durations. The justification for the heavy-
tailed distribution of the On duration lies in the different file size transfer
requirements for various applications, empirically observed hyperbolic-tail
behavior of the file sizes residing in network file systems, Pareto-like tail
behavior of CPU time used by UNIX systems, and also the tendency of multi-
media applications to have very large variance (although perhaps not infinite)
file residing/transmission systems. 6