In a communication switch with input and output queueing, which handles different priority classes of traffic (e.g. video and audio applications with a high priority, and file transfers and e-mail as low priority traffic), the invention provides a timed shut-off mechanism at each input queue. This mechanism is activated when an input queue attempting to transmit low-priority traffic gets a backpressure signal. The mechanism interrupts further attempts to transmit low priority traffic for a predetermined period of T switching cell cycles. Hence, during the shut-off periods, the output queue is only used by the high priority traffic. Therefore, the performance of the high priority traffic is preserved.