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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

• ## Mathematical model of functioning distributed infomatione systeme on the base "fale-server" architecture with cosidering the influence of blocings

Using a device of close homogeneous exponential queueing networks (QN) a mathematical model of an information system functiouning with 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: 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