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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

• ## 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

• ## Mathematical model of optimal placing information resources is solved on distributed information systeme on the basis of three-lewel client server arhitecture without cosidering the influence of blocings

Using a device of close homogeneous exponential queueing networks (QN) a mathematical model of an distributed information system functiouning for solving the problem of getting integral indexis on the basis of local computing network on the basis of three- level client server arhitecture. The base correlation for transitione matrix probabilities constraction and intensitiese of service at the network nodes are given.The peculiarity of the model being worked out is in making a selective choice of information at the database servers and via the channel of communication not the full data base is transmitted but some separate parts of it, which satisfy the conditions of SQL-request search.

Keywords: Distributed information system, distributed data base, local computing system, mass service network, conceptual model, exponential law of distributing the random value, stationary probability, mark process, the global balance equation, system reaction tim

• ## Software implementation of models of optimal allocation of information resources

This article describes the stages of implementing the program to solve the task of calculating the average response time of a distributed information processing system to user requests and an algorithm for the optimal distribution of information relations over the nodes of a distributed information processing system implemented on the basis of a file server architecture and a two-tier client server architecture, with and without locks. The procedure for constructing the initial data for modeling is described: the elements of the matrix of the initial distribution of information resources (relations) over the nodes of the distributed information processing system, the elements of the matrix of information interrelation between the requests of users of the distributed information processing system and the information resources themselves, the elements of the matrix of probabilities for generating queries by users. A procedure has been developed and programmed to significantly simplify the calculation of the normalizing constant, and accordingly the average response time of the system to user requests. The results of numerical experiments are presented

Keywords: Distributed information processing system, file-server architecture, two-level client-server architecture, nonlinear combinatorial optimization, generator of equiprobable choice, Jordan-Gauss method, normalized constant, average reaction time of the syste

• ## Heuristic algorithm for solving the problem of optimal allocation of information resources .

In this article to solve the problem of optimal distribution of information resources over the nodes of distributed inorganic system according to the criterion of minimum of the medium time, the response of the system to the requests of the users an original heuristic algorithm is proposed that uses the notion of databases as points of a mulltidimensional space, but about nodes in which these bases are placed as clasters. The resuts of numerical experiments are presennted depending on the architecture of the distributed system used and on the method of ensuring data integrity. Numerical experiments showed rather high efficiency of the proposed algorithm.

Keywords: Distributed information system, distributed data base, local computing system, mass service network, non-lineare combinatorial optimization, query generation, a matrix of probabilities for generating queries by users, a matrix for distributing relations a

• ## Mathematical model of functioning distributed infomatione systeme on the basis of three-lewel client server arhitecture .

Using a device of close homogeneous exponential queueing networks (QN) a mathematical model of an distributed information system functiouning for solving the problem of getting integral indexis on the basis of local computing network on the basis of three- level client server arhitecture. The base correlation for transitione matrix probabilities constraction and intensitiese of service at the network nodes are given.The peculiarity of the model being worked out is in making a selective choice of information at the database servers and via the channel of communication not the full data base is transmitted but some separate parts of it, which satisfy the conditions of SQL-request search.

Keywords: Distributed information system, distributed data base, local computing system, mass service network, conceptual model, exponential law of distributing the random value, stationary probability, mark process, the global balance equation, system reaction tim

• ## Use of the device of queueing networks for analytical and numerical modeling of an information system without considering the influence of blockings

Using a device of close homogeneous exponential queueing networks (QN) a mathematical model of an information system functiouning without considering influence of blockings was worked out. A proccessor and the united resourse "channel - external memory" are considered as shared resources. All the users' requests are assumed to be single and homogeneous and the servicing discipline "First Come First Served" is used for sequence of their execution. Analytic expressions are given for calculation of the integral characteristics of the system: the distribuition law of number of messages in a system, the average number of messages at a node, the average sojourn time of a message at a node, the average sojourn time of a message in a system.

Keywords: data base, blocking, queueing network, servicing discipline for messages, exponential distribution law, conceptual model, state space, the global balance equation, normalizing constant, stationary probability, the distribuition law of number of messages

• ## Mathematical model of optimal placing distributed data base onto Local Computing Network knots on the basis of two-level client-server architecture

Using a device for close exponential networks of mass service a mathematical model for solving the problem of getting integral indexes of distributed information system on the basis of local computing network using two-level architecture “client-server” was worked out. The peculiarity of the model being worked out is in making a selective choice of information at the server and via the channel of communication not the full data base is transmitted but some separate parts of it, which satisfy the conditions of SQL-request search. Using the developed earlier heuristic algorithm the problem of optimal placing the distributed data base onto the local computing system knots according to the criterion of minimal average time of system reaction for users’ requests was solved. The results of numerical experiments are given.

Keywords: Distributed data base, selective information choice, SLQ-request, transaction, system conditions space, stationary probability, transitive probability, service intensity in network knots, information volume matrix, system reaction time

• ## Mathematical model of optimal placing distributed data base onto Local Computing Network knots on the basis of file-server architecture

Using a device for close exponential networks of mass service a mathematical model for solving the problem of getting integral indexes of distributed information system on the basis of local computing network using file-server architecture was worked out. The heuristic algorithm of optimal placing the distributed data base onto local computing network knots according to the criterion of minimal average time of system reaction for users’ requests is represented. This algorithm uses the understanding of data bases as the points of multidimensional space and the knots in which those data bases are placed as clusters or classes. The results of numerical experiments are given.

Keywords: Distributed information system, distributed data base, local computing system, mass service network, conceptual model, exponential law of distributing the random value, stationary probability, mark process, the global balance equation, system reaction tim