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

Abstract

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

Scoba A.N.,Mikhaylov V.K.,Nazarov S.A.,Skorik N.S.

Incoming article date: 06.11.2018

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