V. N. Zadorozhnyi

Fractal Queues Simulation Peculiarities

Relevant to the modern theory of computer networks design questions of developing adequate service models of fractal traffic are considered in the article. The fidelity criteria of heavy-tailed distributions (HTD), which take into account the HTD distortion effect on the results of fractal queues simulation, are offered. The problem of HTD significant distortions in their realization during simulation is revealed and examined. To solve this problem we also developed the method, which does not require the use of “long arithmetic”.

Growing Network: Nonlinear Extension of the Barabasi-Albert Model

We introduce a model of random graphs that follows a nonlinear preferential attachment rule and give a recursive formula to determine the vertex degree distribution for the graphs of this model. We demonstrate how the nonlinear preferential attachment model can be calibrated so that the generated graphs will require vertex degree distributions.

Methods of Simulation Queueing Systems with Heavy Tails

Important problems of correct organization of simulation experiments for calculating fractal queueing systems are considered. Fractal systems are described asymptotically by power laws of arrival interval distribution and service time of requests and are adequate mathematical models of network devices of telecommunication systems with fractal (self-similar) traffic. We propose an effective solution to the problem for the correct realization of heavy-tailed distributions. Accuracy control techniques for calculating fractal queues by means of consecutive or repeated “parallel” runs of simulation models are developed. The application examples of the developed methods are given.

Statistical approach to calculation of number of network motifs

The development of efficient algorithms for the analysis of network motifs is a direction in Network Science, which is of great importance in the study of communication networks, social, biological and other networks. Detection and calculation of number of network motifs are closely related to the counting of typical isomorphic subgraphs in large graphs. The article proposes to accelerate this process by using the Monte Carlo method. Examples of counting of typical subgraphs with 3 and 4 vertices in the undirected graph are given. The proposed approach can also be extended to analysis of directed graphs.

Analytical and numerical methods of calibration for preferential attachment randon graphs

Methods of random graphs growing with nonlinear preferential attachment rule, which have the required distributions of vertices and edges attachment degrees are developed. Application of these methods allows us to generate random graphs, which adequately simulate growing stochastic networks — social, information, transport and many others. Examples of application for the developed methods are given.

Minimization of Packet Loss Probability in Network with Fractal Traffic

Methods for radical reduction of packet loss probability in telecommunication networks with fractal traffic are developed. We investigate ways of preventing the losses within the framework of queueing theory; relevant simulation experiments are carried out. It is determined that strategy for the channel number increase in the network nodes has principally higher efficiency than that for the buffer increasing and/or channel performance increasing. Approximation methods for loss probability in the nodes of multiserver queueing system without buffers are investigated. The paper offers to approximate the loss probability in the node with n channels by steady-state probability in the state n of relating infinite-server queueing systems. We develop an analytical-statistical technique of optimal channel distribution over the nodes in networks with fractal traffic which is based on such approximation. The example of the method application is provided. The developed method could be used by engineers designing the telecommunication networks.

Calculation methods of transient processes in growing networks with non-linear preferential attachment rule

The problem of calculating transient processes in growing stochastic networks with non-linear preferential attachment rule is solved. Network growth dynamics equations are derived. Numerical methods for prompt calculation of transient processes in networks and specified network nodes are developed. The examples of the transient processes calculation are given. The proposed methods are confirmed by the results of simulation modeling. The use of developed methods allow to solve the problems of dynamic identification of the growing networks and regulation of the development processes.

Optimization of transport queuing networks on the basis of the method of directing hyperbole

Multi-level analytic-imitational method is proposed to find the optimal allocation of the financial resource dedicated to road surface quality improvement for traffic network sectors (roads). Using the proposed method aims to reduce the average time of travel through the network. The test results of the method of optimization allow us to conclude the feasibility of further development.

Optimization of Uniform Non-Markov Queueing Networks Using Resources and Transition Probabilities Redistribution

An efficient analytic-imitational method for optimization of uniform non-Markov queueing networks is proposed. The optimization is performed through resources and transition probabilities redistribution by the minimal mean time of the request staying in the network. The convergence rate and precision of the method are evaluated experimentally. The method allows the optimization of the networks with hundreds of single- and multi-channel nodes with precision comparable to the one of the numerical methods for deterministic problems solution. Examples of the method’s application in transport modeling are given. Practical application recommendations are provided.

Preferential attachment random graphs with vertices losses

Analytic and numerical methods are developed to calculate the random graphs characteristics for modeling growing networks with nodes losses. The methods application allows developing effective strategies to affect the growing networks in order to support their growth or hinder it. The application examples of the developed methods are given.