scholarly journals Crossover from Self-Similar to Self-Affine Structures in Percolation

1994 ◽  
Vol 26 (6) ◽  
pp. 413-418 ◽  
Author(s):  
E Frey ◽  
U. C Täuber ◽  
F Schwabl
Fractals ◽  
2005 ◽  
Vol 13 (04) ◽  
pp. 265-282 ◽  
Author(s):  
BRENT M. TROUTMAN

Natural river channel networks have been shown in empirical studies to exhibit power-law scaling behavior characteristic of self-similar and self-affine structures. Of particular interest is to describe how the distribution of distance to the outlet changes as a function of network size. In this paper, networks are modeled as random self-similar rooted tree graphs and scaling of distance to the root is studied using methods in stochastic branching theory. In particular, the asymptotic expectation of the width function (number of nodes as a function of distance to the outlet) is derived under conditions on the replacement generators. It is demonstrated further that the branching number describing rate of growth of node distance to the outlet is identical to the length ratio under a Horton-Strahler ordering scheme as order gets large, again under certain restrictions on the generators. These results are discussed in relation to drainage basin allometry and an application to an actual drainage network is presented.


2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  

Author(s):  
Irina Strelkovskay ◽  
Irina Solovskaya ◽  
Anastasija Makoganjuk ◽  
Nikolaj Severin

The problem of forecasting self-similar traffic, which is characterized by a considerable number of ripples and the property of long-term dependence, is considered. It is proposed to use the method of spline extrapolation using linear and cubic splines. The results of self-similar traffic prediction were obtained, which will allow to predict the necessary size of the buffer devices of the network nodes in order to avoid congestion in the network and exceed the normative values ​​of QoS quality characteristics. The solution of the problem of self-similar traffic forecasting obtained with the Simulink software package in Matlab environment is considered. A method of extrapolation based on spline functions is developed. The proposed method has several advantages over the known methods, first of all, it is sufficient ease of implementation, low resource intensity and accuracy of prediction, which can be enhanced by the use of quadratic or cubic interpolation spline functions. Using the method of spline extrapolation, the results of self-similar traffic prediction were obtained, which will allow to predict the required volume of buffer devices, thereby avoiding network congestion and exceeding the normative values ​​of QoS quality characteristics. Given that self-similar traffic is characterized by the presence of "bursts" and a long-term dependence between the moments of receipt of applications in this study, given predetermined data to improve the prediction accuracy, it is possible to use extrapolation based on wavelet functions, the so-called wavelet-extrapolation method. Based on the results of traffic forecasting, taking into account the maximum values ​​of network node traffic, you can give practical guidance on how traffic is redistributed across the network. This will balance the load of network objects and increase the efficiency of network equipment.


Sign in / Sign up

Export Citation Format

Share Document