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Nonloopy network topologies are considered under the limitation that a channel can be utilized only if it is idle at all neighboring sites. Random channel selection is studied under a standard circuit-switched traffic model. Upper and lower bounds for blocking probabilities are determined via an auxiliary network process whose equilibrium distribution admits a computationally convenient form. By way of another approximate characterization, it is argued that random channel selection incurs vanishing loss of optimality as the number of channels and the traffic load increase in proportion.