A switch at a transmission end of a system including a number of memory devices defining queues for receiving traffic to be switched, each queue having an associated predetermined priority classification, and a processor for controlling the transmission of traffic from the queues. The processor transmits traffic from the higher priority queues before traffic from lower priority queues. The processor monitors the queues to determine whether traffic has arrived at a queue having a higher priority classification than the queue from which traffic is currently being transmitted. The processor suspends the current transmission after transmission of the current minimum transmittable element if traffic has arrived at a higher priority queue, transmits traffic from the higher priority queue, and then resumes the suspended transmission. At a receiving end, a switch that includes a processor separates the interleaved traffic into output queues for reassembly of individual traffic streams from the data stream.