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We study problems of optimization of the topology of interconnected local computer networks using random access to a single channel. An approach to modeling of the system by a queueing network is proposed: the analytical solution of the model allows us to obtain global performance measures, which may be used as evaluation criteria in network topology optimization problems. A heuristic is proposed for the latter aspect for one class of problems. We also derive from the model the time needed, for a new user which joins the network, to transmit its number of messages.