Spline-approximation-based restoration for self-similar traffic

Using spline-extrapolation in the research of self-similar traffic characteristics

“…Earlier, problem solving extrapolation of random processes was based on the use of Lagrange interpolation polynomials, Chebyshev polynomials, etc. When predicting self-similar traffic, we use the extrapolation method based on the spline-function, since [14]: 1) splines are more resistant to local perturbations, that is, the behavior of the spline in the neighborhood of the point does not affect the spline behavior as a whole, as, for example, this occurs in polynomial interpolation; and 2) good convergence of spline-interpolation as opposed to polynomial interpolation. In particular, splineinterpolation is an indisputable priority for functions with irregular smoothness properties (an example of which self-similar traffic serves).…”

“…Let us consider the Weibull distribution, given by the differential distribution function [14][15][16][17]…”

“…where α is a parameter of Weibull distribution curve form, 0 < α < 1 , which is determined according to [14][15][16] by expression α = 2 − 2H , with H being the Hurst parameter, 0.5 ≤ H ≤ 1 , and β = [λΓ(1 + 1/α)] α the Weibull distribution parameter with β > 0 , λ is the intensity of requests arrivals for QS servicing, Γ(k) is the Euler gamma function…”

Development of the method of distribution of memory in nonstationary loaded information processing systems

“…Research works to determine the load parameters of sections of the GSM network [4] and network devices of new-generation networks (NGN) [5] prove the existence of "bottlenecks" in these networks, which undergo local overloads during peak hours. Such exceptional cases are most likely to occur on days of mass events or extraordinary events (major accidents, terrorist acts, etc.).…”

“…This behavior of the stream of requests implies Despite all advantages of stream description, the fractal apparatus is quite complex, and its use for constructing a dynamic model requires a large amount of computing resources. To simulate real traffic with similar properties, a number of distributions can also be used: Weibull [5], hyperexponential, log-normal [11], also known as heavy-tailed distributions [12].…”