Two approaches to the decomposition of compound hierarchical stochastic systems (Q1281063)

In the paper, devoted to the problems of decomposition of complex systems, the generalization of multiplicative representation for stationary state probabilities of queueing network on the case of dependent durations of message transmission on channels is given. It is assumed that the messages have the random volumes, which, however, remain constant in process of their transmission on network, and the transmission durations on various channels depend on the speeds of work of channels with regard to their distinctions and are proportional to these volumes. Using the generalized method of additional variable the admissibility of multiplicative representation in the case of hierarchical network is proven.