We consider networks with a very large or infinite number of nodes, linked by cable channels. The request which comes to a node is ordered to occupy a certain route of successive channels. The functioning of the system is regulated by the reserving of channels in order of the arrivals of the requests. Under some general conditions the existence of an ergodic region for such networks is proved. The practical value of the result lies in the fact that these conditions do not depend on the size of the graph.
