МОДЕЛИРОВАНИЕ МНОГОКАНАЛЬНЫХ СИСТЕМ МАССОВОГО ОБСЛУЖИВАНИЯ КАК КОМПОНЕНТОВ СОЦИОТЕХНИЧЕСКИХ СИСТЕМ

Abstract

For a multichannel queuing system, in which all calls have individual characteristics of arrival and maintenance in accordance with their characteristics in the required socio-technical system and switching from one call to another are performed in accordance with a specified switching function determined by the resolution policy adopted in the socio-technical system of conflict situations, recurrence relations have been obtained for the queue lengths, for the list of free instrument changes, for the list of call numbers waiting for service, and for a number of other characteristics at successive call termination services. The procedure of sequential calculation of all specified characteristics of the system is described taking into account their internal interrelation. In accordance with this procedure, in a strictly defined sequence, eleven characteristics of the system are calculated on the basis of recurrence relations. To increase the efficiency of the process of practical implementation of the modeling procedure, it is proposed to replace the initial distribution functions of random variables by their approximate values, which are mixtures of gamma distributions whose values can be calculated significantly faster than the values of the initial distributions. The problem of finding a set of exponential distributions for a given simulated distribution function is formalized, the mixture of which approximates the distribution function with a given accuracy.