Abstract: In a switching device coupled to a computer network, a method for enqueing data packets for transmission over the computer network according to a priority scheme. Initially, the switching device is configured to define a hierarchy of priority levels. A number of queue buffers are reserved for each of the priority levels. Furthermore, each application program is assigned a particular priority, depending its relative importance and time-criticalness. When the application program generates an outbound packet, that packet is assigned a corresponding priority. The CPU checks the number of buffers in the queue which are currently available and compares it with the sum of the buffers which were reserved for all priority levels which are higher than the priority of the outbound packet. If the number of available buffers exceeds the sum of the buffers reserved for the priority levels higher than that of the packet, then the packet is stored in the queue. Otherwise, the packet is discarded.