Алгоритмы формирования последовательности псевдослучайных чисел в натурном эксперименте при имитации процессов функционирования сложных информационных систем

Abstract

In this work is considered information systems: its structure and influencing factors of the external environment that allows to describe its simulation means. Elements for the description of similar systems are algebraic differential equations, Markov chains or similar of the Research objective consists in forming of conditions of carrying out a natural experiment not on the studied system, and on some other (with the known distribution parameters of the studied random variable, for example, of the distribution law), rather “similar” to given and such which experimental functioning will not lead to a little notable costs. Research methods. At simulation of processes of Markov the difficulties connected with need of input in memory of the machine of stochastic matrixes of infinite dimension very often meet. It is actually very difficult to present an infinite stochastic matrix in which all elements are selected “purely accidentally”, i.e. without any patterns. In practice there are always only such matrixes in which, since some line, a certain pattern in formation of elements is shown. The solution of the specified problem is based on this property. Results. The algorithm of finding of a random variable consists in the choice of that from expressions which at this value is true. Then the following implementation is on the formula corresponding to the selected expression. If at the same time the selected formula contains a random variable, then by means of already known receptions there is implementation of this random variable and is substituted in it. To be convinced of correctness of the offered algorithm and to understand reasons on the basis of which expressions are constructed it is enough to substitute all possible values of random variables and to compare result to received by means of a matrix. The considered logical reception is applicable also at simulation of behavior of the objects, more difficult, than a Markov chain. Its use in more difficult situations – a component of the idea of automatic modeling of information systems. Conclusion. The algorithms of forming of pseudorandom numbers received in work for simulation of components of an information system are rather adequate, however their efficiency is defined by the relation of a part of the square of a rectangle located under a curve to all its area. If this relation is not enough, then a considerable part of machine time is spent for unproductive receiving the accidental points lying under a curve and discarded in the course of calculations. From here follows, in particular, that for exponential distribution the specified method least, and for uniform is most effective. In practice it is reasonable to use such method when the specified relation exceeds value 0.3. In certain cases it can be applied and when this relation more than 0.1.