2 APPROACHES TO THE DECOMPOSITION OF COMPOUND HIERARCHICAL STOCHASTIC-SYSTEMS

Two approaches are considered for a solution of the problem of decompo sing the processes of operation of compound hierarchical systems. The approaches rely on the conditions of interaction between their subsyst ems. The first approach dealt with in this article (Part 1) involves s tudying the systems composed of continuously interacting subsystems. C omputer communication networks are a typical Example of such systems. It is customary to investigate these systems with the aid of queueing network models for which the decomposition problem is solved in the fr amework of the multiplicative representation in regard to the stationa ry probability distribution of system states. By extending the method of additional variables, the proof is given of the admissibility of th e multiplicative representation in the case of the hierarchical networ k with dependent service lime lengths, which is specific to data trans mission, systems.