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In a time-multiplex switching system, the incoming traffic must be scheduled to avoid conflict at the switch output (two or more users converging simultaneously upon a single output). Two scheduling algorithms, random scheduling and optimal scheduling, are explored in this paper. Random scheduling is computationally simple, whereas optimal scheduling is currently very difficult. We have found, using a traffic model appropriate for circuit switched traffic that increases of typically 10 to 15 percent in offered load can be obtained through optimal scheduling (as compared to the much simpler random scheduling algorithm). The improvement is a function of the number of time slots (or circuits) per time-multiplexed frame, and falls to zero for both very small and very large frame sizes. Thus, in many circuit switching applications, providing a computationally expensive optimal schedule may not be warranted. This conclusion has important ramifications for both electronic and emerging photonic switching systems since it reduces the importance of the costly design feature of optimal scheduling.