INTRODUCTION

It has been suggested that Internet traffic is far too complicated to be modeled using the techniques developed for telephone networks or computer systems. More speci?cally, there is increasing evidence of the so-called self-similar (or fractal) and heavytailed nature of data traffic. Self-similarity manifests itself usually through the display of persistence or long range dependence (LRD)

As a consequence, a large number of traffic models have been proposed in order to successfully characterize the nature of the traffic in networks today. The reason is that fractality and heavy-tailness have serious implications for analysis, design, and control of computer networks. In contrast, traditional schemes, typically Markovian in nature, which have been (and currently are) extensively used, may lead to substantial underestimation of Quality of Service (QoS) metrics such as delay and blocking.

Unfortunately, the proposed self-similar models, such as the ones based on Fractional Brownian Motion (FBM) and Linear Fractional Stable Motion (LFSM), cannot be used to describe the Short Range Dependences (SRD). For example, it is known that the Variable Bit Rate (VBR) video frame sizes exhibit both short and long range dependences and their distribution is non-Gaussian. Therefore, models are required to describe both short and long memories, as well as heavy-tailed marginal distribution simultaneously.

1. A THEME URGENCY

Until recently, the theoretical basis for the design of the distribution of the information provided teletraffic theory, which is one of the branches of the queuing theory.

This theory describes the processes occurring in telephone networks, built on the principle of circuit switching. The most common model of the flow of calls in teletraffic theory is a simple flow (stationary stream without aftereffect ordinary). It also called stationary Poisson flow.

Now we construct a network with packet switching. Therefore, there is a problem, "self-similarity. That's why the problem of self-similarity is very relevant today.

2. THE PURPOSE AND PROBLEM STATEMENT

The aim is to determine the characteristics of fractal processes of different data streams on wireless networks and subsequent decision on how to manage them.

3. RESEARCHES ON THE THEME

3.1. Researches on the theme in DonNTU

Among workers DonNTU note assistant of the department AT Evgenia Ignatenko, Senior Lecturer of the Department AT Vladimir Bessarab, which in [9] conducted a study of the properties of real traffic in networks with packet switching. Using the method R/S analysis showed self-similar nature of network traffic in information networks. The authors developed a model of the generator of traffic reflecting multifraktalnore behavior of data streams in real-world information systems, allowing to simulate traffic from the specified indicators of self-similarity.

3.2. Researches on the theme in Ukraine

Among domestic ukrainian should note the work of Neumann V.I., Tsybakov B.S., Likhanov N.B., Shelukhin I., Zaborovsky B.C., Gorodetsky A.J., etc. For example, in [3], the authors showed that the network standard 802.16b Self-similar of traffic appear on a link layer and on transport-level security. The values of the main indicators of the degree of fractality network traffic, and proposed methods of aggregation of the original statistics [5].

3.3. Researches on the theme in the world

Among the foreign scientists to identify the authors K. Park, W. Ryu, V. Paxson, R. Mondragon and others. In [6] described an experiment on the removal of the traffic network of one of the largest Intrenet providers, as well as the results of the analysis of structural features of the traffic.

In [7] American scientists studied the processes of heavy-tailed distribution. To generate such processes the authors proposed to use fractal model of an integrated moving average FARIMA (p, d, q).

4. SELF-SIMILAR

Self-Similarity and fractal are notions pioneered by Benoit B. Mandelbrot, who describe the phenomenon where a certain property of an object, such as a natural image, is preserved with respect to scaling in space or in time. The empirical studies in the early 1990s at Bell core that resulted in the finding that Ethernet LAN traffic is self-similar or fractal in nature serves as a reminder that new discoveries do not necessarily require new mathematical concepts, or novel statistical methodologies, or for that case, new networking technologies. Instead, the aspect of discovery often lies in applying a well-known mathematical concept (e.g., self-similar processes) in a new context (e.g., networking). Network traffic that is bursty on many or all timescales can be described statistically using the notion of self-similarity, that is, the traffic relational structure remains unchanged at varying timescales. There are a number of different, not equivalent, definitions of self-similarity. The standard one states that a continuous-time process Y=Y(t) is self-similar (with self-similarity parameter H) if it satisfies the condition:

A second definition of self-similarity, more appropriate in the context of standard time series theory, involves a stationary sequence X=X(i). Let be the corresponding aggregatd sequence with level of aggregation m, obtained by dividing the orignial series X into non-overlapping blocks of size m and averaging over each block. The index k labels the block. If X is the increment process of a self-similar process Y defined in 1, that is, X(i)=Y(i+1)-Y(i), then for all integers m,

A stationary sequence X=X(i) is called exactly self-similar if it satisfies 3 for all aggregation levels m. This second definition of self-similarity is closely related to the first, with mX(m) corresponding to Y(a)

A stationary sequence X(i) is said to be asymptotically self-similar if 3 holds as m-->~. Similarly, we call a covariance-stationary sequence X(i) exactly second-order self-similar or asymptotically second-order self-similar if m(1-H)X(m) has the same variance and autocorrelation as X, for all m, or as m-->~.

5. RESULTS

As initial data we take the time between arrivals of packages of different types of traffic. These data were obtained using Wireshark through its settings accordingly:
- to monitor the flow of data to browse Web-pages on the Internet;
- to monitor video traffic watch videos in the online mode;
- to monitor the audio traffic to listen to music on-line.

CONCLUSION

1. The characteristics of fractal processes of various types of traffic converged networks. Hurst coefficient for the data flow is equal to 0.7595 for audiotrafika the rate is 0.7158 and for video traffic H = 0.7152.
2. The study suggests that combining different types of traffic, the Hurst exponent is set higher than that of individual flows, as it is 0.7625.
3. The increasing level of self-similarity by combining various data flows in multiservice networks should be considered when develop control algorithms for them.

BIBLIOGRAPHY

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NOTE

When writing this abstract the master’s qualification work is not completed. Date of final completion of work: December, 1, 2011. Full text of the work and materials on a work theme can be received from the author or his scientific supervisor after that date.





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