Invariance of the stationary distribution of the states of modified Jackson and Gordon-Newall networks

Consideration is given to open and closed networks consisting of single-ser ver nodes. The incoming items are either quelled with a probability that de pends on the number of quelled items and the number of the preceding node o r bypass the node immediately and go further according to the route matrix. The item displaced from the server wedges itself in the Beginning of the q ueue, and as soon as it reaches the server, its servicing is completed. For open networks, the input flow is the simplest. For fixed first moments, th e stationary distribution of network states is proved to be invariant to th e form of distributions of servicing times.