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To the class of queuing networks analyzable by the method of Baskett, Chandy, Muntz, and Palacios, we add service centers whose scheduling is random. That is, upon completion of a service interval, the server chooses next to serve one of the waiting customers selected at random. As in the case of first-come first-served (FCFS) scheduling, all tasks must have the same exponentially distributed service time at such a center. We show that for purposes of this analysis, the results are identical to FCFS queuing. Example applications for random selection scheduling in computer system modeling are provided.