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A closed cyclic queueing system with multiple classes is analyzed numerically. The queueing system was originally motivated by a need to model circuit switching traffic in a data multiplexing scheme which provides both circuit and switching capabilities. The queueing system consists of two nodes, a primary and a secondary node. Customers in the primary node may require a random number of servers simultaneously. The secondary node simply provides the means of modeling the arrival process to the primary node. An efficient numerical procedure is used to obtain performance measures such as throughput, queue-length distribution, and utilization.