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• ## Analysis of the effectiveness of methods for solving systems of linear algebraic equations in calculating the integral characteristics of the functioning of distributed information processing systems

The paper presents the results of numerical experiments on solving systems of linear algebraic equations (SLAE) with discharged matrices by the LU decomposition method, the Jacobi method, the Gauss-Seidel method, the modified Gauss-Seidel method and the modified Jacobi method with a relaxation parameter ω. In the course of numerical experiments on the solution of (SLAE) with test discharged matrices of various dimensions using the MATLAB package, it was found that the best results in the time of solving the problem were obtained by the modified Gauss-Seidel method with a relaxation parameter ω = 0.5 or a given accuracy of solutions ε= 10^-6. In the future, this method was used to calculate the integral characteristics of the functioning of distributed information processing systems for various practical applications.average system response time to user requests).

Keywords: distributed information processing system, a system of linear algebraic, equations, sparse matrix, LU decomposition, Jacobi method, Gauss-Seidel method, relaxation parameter

• ## Simulation models of functioning of distributed information processing systems and their software implementation

The paper describes the main agents, with their components and process diagrams, of the developed simulation model of the functioning of the distributed information processing system, created in the AnyLogic software environment. A method for constructing models with self-similar traffic is described. The article also presents a method for obtaining real (reference) indicators of the average response time of the system to user requests. The results of numerical experiments on the created models of the functioning of distributed information processing systems with self-similar traffic are presented. The main conclusions about the performed experiments are presented.

Keywords: distributed information processing system, self-similar flow, average system response time, simulation, object-oriented concept, agent-based and discrete-event modeling

• ## Solving the problem of ensuring optimal efficiency of distributed information processing systems

The paper presents a formalized statement of the problem for conducting a comparative analysis of the efficiency of distributed information processing systems. Reliability, technical-operational and technical-economic indicators of the distributed information processing systems functioning were selected as the main efficiency criteria. At the conceptual level, this problem was reduced to the problem of vector optimization, the solution of which is associated with significant difficulties. An alternative approach to solving this problem is proposed.

Keywords: distributed information processing system, vector optimization, availability factor, average system response time, fault tolerance coefficients, total downtime cost

• ## The problem of determining the optimal fault-tolerance of distributed information processing systems

In this article, in terms of the language queueing networks, the problem of finding the optimal values for average system response time for requests from all users for distributed information processing systems that are implemented based on the architecture "file-server", double-tier and three-tier architecture "client-server" at a fixed downtime cost, including the cost of idle users the value of the idle transmission channel, and the cost of downtime service nodes. An algorithm for solving this optimization problem is presented.

Keywords: Distributed information processing system, file-server architecture, two-level client-server architecture, three-level client-server architecture, state space, average system response time, loss cost, stationary probabilities

• ## The task of determining the optimal reactivity distributed information processing systems at a fixed cost of their downtime

In this article, in terms the language of queuing networks, the problem is formulated finding the optimal value the average response time of the system to the requests all users for distributed information processing systems implemented on the basis of the file-server architecture, two-level and three-level client-server architecture with a fixed cost of downtime, including the cost downtime for users, the cost of downtime for a data transmission channel and the cost downtime for service nodes. An algorithm for solving this optimization problem is presented.

Keywords: distributed information processing system, file-server architecture, two-level client-server architecture, three-level client-server architecture state space, average system response time, loss cost, stationary probabilities

• ## Software complex of simulation modeling of the influence of the main integrated indicators of the distributed information processing system on its reactivity

This article describes a software complex simulation, which allows you to evaluate the impact of the main integrated indicators of the distributed information processing system on its reactivity, taking into account the properties of self-similarity of traffic, TCP/IP data transfer Protocol, and various architectures. The software package consists of software-implemented mathematical models of distributed information processing systems based on file-server, two-level client-server and three-level client-server architecture, as well as the algorithm of distributed information processing system objects distribution. The platform AnyLogic PLE was used as a software tool.

Keywords: a distributed information processing system architecture "file-server", two-tier architecture "client-server", three-tier architecture "client-server", simulation, self-similar traffic, agent-based modeling, discrete event simulation, system dynamics

• ## Analytical and numerical simulation of the operation of distributed information systems with self-similar input traffic

This article formulates the main stages of the process of constructing analytic-numerical models of functioning of distributed information systems with non-exponential (self-similar) input traffic of requests. Each separate stage of modeling, at the conceptual level, is reduced to solving a certain class of mathematical problems. The basis of the mathematical apparatus for obtaining the basic integral characteristics of the quality of distributed information systems functioning lies in the method of analyzing the average values ​​of networks of queues. The basic relationships for calculating the reactivity of distributed information systems operation are given.

Keywords: distributed information system, discrete self-similar process, Hurst parameter, Pareto distribution, queuing network, Kendall classification, Polacek-Khinchin formula, average system response time

• ## Mathematical model of evaluation reactivity of distributed information processing system using the decomposition approximation method

In this article, using the decomposition approximation based on Norton's theorem, the authors present a mathematical model of the distributed information processing system based on the local computer network on file-server architecture with arbitrary functions of the distribution of service time of requests in the network nodes. A conceptual model of an equivalent two-node Queuing network is constructed, in which the first center of the network coincides with the i-th center of the original network with an arbitrary law of distribution of the duration of requests maintenance, and the second (composite), which is the equivalent of the rest of the network, has exponentially distributed service time, which depends on the number of messages in it. The basic mathematical expressions for calculating the intensity of service in the composition center, as well as expressions for calculating the average response time of the system to user requests are also presented.

Keywords: distributed information processing system, file-server architecture, decomposition approximation, queueing network, compositional center, intensity of service, the average response time of the system to user requests, conceptual model, normalizing constan

• ## Software implementation modeling tasks of the main integral indicators of economic information systems functioning

This article describes a software package to solve the problem of optimal placement of information resources-fragments of a distributed database on the nodes of a distributed economic information system by the criterion of the minimum average response time of the system to user requests. The software complex consists of software-implemented mathematical models of distributed systems of processing economic information on the basis of file-server, two-level client-server and three-level client-server architecture, as well as optimization algorithm. The developed software product also allows to make experiments for obtaining and subsequent analysis of the dependence of the reactivity of distributed systems on such integral characteristics as the dimension of the problem, the intensity of the formation of requests by users, the speed of message transmission through communication channels, the speed of reading, the speed of writing and processing in the nodes, which allows to implement a more rational organization of the computational process in the system. The software was implemented in C#, the NetFramework 4.6.1 platform, using the Microsoft Visual Studio 2017 Community development environment.

Keywords: economic information system, distributed information processing system, architecture "file-server", two-level architecture "client-server" three-level architecture "client-server", the global balance equation, a closed exponential queueing network