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
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