No 1 (2016)

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Full Issue


Analysis of the Multichannel Exponential System of Service with the Limited Store and Resequence of Requests

Matyushenko S.I., Pyatkina D.A., Kalenichenko V.N.


The multi-channel finite-capacity queuing system with Poisson flow is considered. The customer caught all the places in the queue employed, is lost and will not affect the functioning of the system. The service times are random, independent and have exponential distribution. Intensities of service are different. The customer with the possibility of selecting a device, choosing from available devices one, that has the highest intensity ofservice. On leaving the system there is a buffer in which there is a resequence of customers according to order of their receipt. Functioning of the system is described by uniform Markov process. In the assumption that intensities of the flow and service of customers are finite the final probabilities of statuses of Markov process exist, are strictly positive, don’t depend on initial distribution and match the stationary probabilities. An algorithm to calculate the stationary probabilities of the state of the system we developed in previous work. The main objective of this work is to obtain the stationary performance of the system based on the results of previous work. The distribution function of the resequence time was obtained. The numerical analysis of dependence of the average resequence time from the system load and number of devices was considered.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):5-10
pages 5-10 views

On Some Classes of Optimal Control Problem with State Constraints

Gorbacheva A.V., Karamzin D.Y.


A Borel measure Lagrange multiplier appears in the maximum principle for state constrained problems. The question of continuity or absolute continuity of the measure-multiplier is highly relevant for various applications in particular for some problems of kinematic control. The velocity in such problems is considered as a state variable. As soon as the magnitude of the velocity is bounded, for instance above, (which is quite natural in problems of kinematic control), this leads to the state constraints and to a measure Lagrange multiplier in the necessary optimality conditions. In Control Theory, the methods that are use to solve these conditions often require the continuity of the measure. In this paper, we consider some examples of optimal control problems with state constraints for which one can ensure that this measure is continuous, without a calculation of extremal process.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):11-18
pages 11-18 views

Numerical Modeling and Simulation of RED Active Queue Management Algorithms

Kulyabov D.S., Gevorkyan M.N., Machuca J.R., Diarrassuba K., Dali D.T.


The aim of this paper is to expand the stochastic model of RED (Random Early Detection) for the case of AURED, SARED and GRED queue service disciplines, as well as the verification of numerical simulation results with NS2 software. A stochastic model is based on the a system of three Ito stochastic equations. The numerical solution is carried out using stochastic Runge-Kutta methods with weak convergence of the second order.Software package for the numerical simulation written by authors in Python version 3 using libraries NumPy and SciPy. The article describes in detail the components of software package. For simulation we use open source software package for modeling Computer Networks NS2. In this article, the authors briefly describe those moments that touch queuing disciplines, not dwelling on the general description of NS2. The simulation results are presented as a plot of the average queue length and the current queue length as functions of time. Based on the analysis of the graphs, it is shown thatthe simulation and Numerical simulation gave qualitatively related to each other results.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):19-31
pages 19-31 views

Simulation of Wave Propagation with openEMS

Sharapova A.A., Kulyabov D.S.


Unfortunately, all the existing methods used for modeling computational electrodynamics have their weaknesses. The authors’ goal is to analyze the most popular methods. We use spherical Luneburg lens as an illustration. In this paper authors review the Finite-difference time-domain (FDTD for short), electromagnetic field solver openEMS and its applicability for simulation of wave propagation through medium with the spherical Luneburg lens as an example. Thanks to it’s simplicity and broad capabilities, the FDTD method is widely used in various fields. There are quite a lot of simulation tools that implement FDTD, both open-source and proprietary. OpenEMS is an extension for MATLAB and Octave for solving electromagnetic field using the EC-FDTD method. It supports Cartesian and cylindrical coordinates. OpenEMS is free and open-source. It also supports multi-threading, SIMD (SSE) and MPI. In this paper we simulate wave propagation through spherical Luneburg lens via openEMS thus showing the capabilities of the tool, such as a method to simulate GRIN-optics. We also show how to install and configure it, and how to visualize and analyze the results using ParaView, the application for scientific visualization. Source code of the simulation is presented with appropriate commentaries. In this paper we also briefly reviewthe classic FDTD method and Yee algorithm. We examined the capabilities of openEMS and FDTD method to simulate wave propagation in a medium.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):32-40
pages 32-40 views

Procedure for Constructing Simplectic Numerical Schemes for Solving of Hamiltonian Systems of Equations

Batgerel B., Nikonov E.G., Puzynin I.V.


Numerical schemes which is used for solving of many-particle dynamics systems of equations can have restrictions on a step and an interval of integration because if its increase the numerical schemes became unstable and don’t conserve existing integrals of motion. As a result when we simulate many-particle system behavior on the sufficiently large time interval we should decrease an integration step which leads to considerableincreasing of computation quantity. In this paper a new procedure for constructing simplectic numerical schemes for solving of Hamiltonian systems of equations is proposed. A method for symmetrization of received simplectics numerical schemes is proposed too. Constructed by proposed in the paper procedure numerical schemes conserve energy of a system on the large interval of numerical integration for relatively large integration step incomparison with Verlet method which is usually used for solving of equations of motion in molecular dynamics. Results of numerical experiments are given in the paper. These results show main advantages of received symmetric simplectic numerical schemes of third order of accuracy for the integration step for the Hamiltonian systems of equations in comparison with numerical schemes of Verlet method of second order of accuracy.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):41-58
pages 41-58 views

Session Setup Time Estimation in the Network with a Firewall

Samouylov K.E., Botvinko A.Y., Zaripova E.R.


In modern telecommunication networks is implemented information transmitting security for protection programs and databases. We propose the approach of signaling messages processing estimation in case when the network includes one firewall and two proxy servers. Firewall is based on security rules and define security police. We choose a session setup procedure between two users using the Session Initiation Protocol as anillustration of the method. Signaling messages are moving from the first user to the second through IP/MPLS network, proxy servers and firewall. The chain of signaling messages must successfully service before media traffic starts. We get preliminary estimation of performance measures for modern firewall Cisco ASA 5500-X with Security Service Processor SSP-10. Numerical example shows, that firewall Cisco ASA 5500-X serves signaling messages can be implemented. Mean waiting time and mean service time in this firewall has little effect on the session setup time and the session request delay.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):59-66
pages 59-66 views

Fuzzy Conceptual Graphs for Knowledge Representation in Process-Oriented Organizations

Azofeifa E.J., Novikova G.M.


The use of fuzzy conceptual graphs for representing knowledge in process-oriented organizations is considered. Two types of knowledge, procedural and declarative, are discussed; the difference between them is shown along with representation and usage details in knowledge bases. A formal definition of fuzzy conceptual graphs is given, and their ability to represent declarative and procedural domain knowledge in a simple and understandable way is shown. The structure of the knowledge base includes three levels: an ontological layer, which contains concepts and integrates declarative and procedural knowledge; a middle or interface layer, which describes business processes based on real data; and the ground layer, the layer of real (historical) data, which collects primary information about the current state of objects and the relationships between them. The difference between the types of information on each of the layers of the knowledge base is shown, as well as the application method of fuzzy conceptual graphs on the interface layer. A description of the mechanisms of interaction and rules for reflecting data from the ground layer to the interface layer is provided. Mathematical methods for analysis of primary data and fuzzy knowledge indicators are described, which aid in decision-making, optimization and refinement of procedural knowledge systems.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):67-75
pages 67-75 views

Invariant in the Pattern Recognition

Nguyen Duy Thanh -.


Consider the problem analysis and selection of informative features, which are the luminance and geometric invariants. An analytical overview of the works, which raises the problem of constructing invariants and solve practical problems. Among the invariants to the multiplicative and additive transformations brightness discussed the correlation coefficient, the normalized histogram of some special relationship of line segments and angles. It is considered as the simplest geometric and integral invariants resistant to affine transformations, as well as the transformation strain. Among all geometric invariants allocated invariants Hu, in which interest is not waning and now. Since there is no evidence in the original sources of the invariance of the allegations, the great attention is paid to checking on some points invariance to rotation of frequently used operations. The above features can be used for solving problems of pattern recognition, distance measurement, analysis of complex scenes. It is expected that in the future on the basis of brightness and geometric invariants will be solved the problem of recognizing individual rights. This article is intended for a wide range ofpost-graduate students and engineers involved in pattern recognition tasks in various applications.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):76-85
pages 76-85 views

Lagrangian Density of Lepton and Baryon Phases in Nonlinear 8-Spinor Model

Molotkov V.I.


The Skyrme’s idea (1954) for describing baryons as topological solitons was based on the identification of baryon number B with the topologicalcharge of the degree type B = deg(S3 → S3). It serves as the generator of the third homotopy group π3(S3) = ℤ. The similar idea to describe leptons as topological solitons was announced by Faddeev (1972). He identified the lepton number L with the Hopf invariant QH. The 8-spinor field is suggested to unify Skyrme and Faddeev models describing baryons and leptons as topological solitons. The special 8-spinorBrioschi identity is used to include leptons and baryons as two possible phases of the effective spinor field model, with Higgs potential depending on the jμjμ being added to the Lagrangian. To this end the generalization of the Mie electrodynamics within the scope of the effective 8-spinor field model is suggested. For this field model the quadratic spinor quantities entering the Brioschi identity are constructed. Then the symmetry groups, which generate S2- and S3- submanifolds in general S8 biquadratic spinor manifold, are found. For unifying these phases, common vacuum state should conserve only one component in both lepton and baryon cases. In the present paper we try to construct Lagrange density for homotopy groups π3(S2) and π3(S3), which describe lepton and baryon phases.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):86-90
pages 86-90 views

Comparative Analysis of Spectral-Photometric Characteristics of Domestics Sources of Light

Vasileska I., Korneeva M.A., Stepin V.P.


Correct organization of artificial lighting is very important for creation comfortable living conditions in work places with significant eyestrain, as well as solving the problem of energy efficiency. The purpose of this study is to conduct a comprehensive experimental study of spectral, photometric and electrical characteristics of domestic light sources. Were identified the most and least energy-efficient different light sources in specific circumstances, as well as verification their conformity with the characteristics of the standards SanPiN. In this work were studied incandescent lamps, metal halide, LED, fluorescent and compact fluorescent lamps. According to the results of direct measurements were determined: the directional patterns, the luminous fluxes and energy efficient classes of domestics light sources. All experimental resultants have been summarized in a single table which allows comparing the characteristics of the studied domestic light sources. It was founded that measured values for some of the light sources differ from those stated by the manufacturer, which was noted in compact fluorescent lamps. Analysis of the results allowed us to determine the feasibility of the specific light sources. The results will be useful for the specialists and manufacturers in lighting technology, as well as ordinary users.
Discrete and Continuous Models and Applied Computational Science. 2016;(1):91-98
pages 91-98 views

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Discrete and Continuous Models and Applied Computational Science. 2016;(1):99-100
pages 99-100 views

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Discrete and Continuous Models and Applied Computational Science. 2016;(1):101-102
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