Calculation of the Fractal Dimension of a Numerical Sequence From the Probability Distribution of the Values of Its Elements
Journal Title: Центральноукраїнський науковий вісник. Технічні науки - Year 2018, Vol 31, Issue
Abstract
In today's works to optimize work of telecommunication systems and networks, it is mandatory to take into account the fractal nature of traffic on the Internet. Inclusion of fractality makes it much better to predict the system parameters to the actual values, so the definition of fractal dimension is an actual and important task. Known criteria for determining the fractal dimension have significant errors and variations for individual implementations, so it is advisable to obtain new methods for evaluating the fractal characteristics of the investigated signals, which is followed in a number of publications, in which methods are presented using wavelet analysis. The problem of analytical expression of the fractal dimension of a numerical sequence based on its distribution density of a random variable was solved. Based on the constructed approach, we consider a specific case of a random binary sequence in which the dependence of the fractal dimension on the width of the partition of the sequence on the rectangles is shown. Based on the presence of such dependence, a requirement is made to perform partitioning in the ranges used to solve specific problems. The results can be used to improve the simulation of fractal random sequences; mass service systems; simulation of traffic of telecommunication networks. The result of the practical verification of the mathematical expectation of fractal dimension with different partitions testifies to the dependence of the fractal dimension on the scaling of the partition. This means that from the selected scale of the partition into rectangles, it is possible to get an arbitrary value of the dimension from 1 to 2, which is quite significant when considering the limiting cases. In particular, with a fairly wide division, when a rectangle contains a large number of elements of a numerical sequence, the height of the rectangle covers almost the entire permitted range of the realization of random values; A sequence of almost equal to the height of rectangles is formed, which is an analogue of a two-dimensional strip, which almost does not change its width with increasing partition. According to the logical construction, the strip is a two-dimensional object, and the exit from the band in practice is forbidden by physical real processes in which no unlimited signal growth is allowed.
Authors and Affiliations
Ganna Dreyeva, Olexandr Dreyev, O. Denisenko
Keywords
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- EP ID EP509182
- DOI 10.32515/2409-9392.2018.31.119-128
- Views 75
- Downloads 0
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