A packet scheduling system for use in a switching node of a high speed packet switching network. Incoming packets are enqueued in connection queues. Each connection is classified as red (exceeding traffic profile) or green (within traffic profile). QOS priority is also identified for each connection. Packets are dequeued for transmission as a function of priority class and connection class. Higher priority class connections have priority over lower priority class connections. Within a given priority class of connections, green connections have priority over red connections. Round robin scheduling is used for packets from connections in the same priority and connection class. In addition, a dynamic priority coupling mechanism is provided to prevent red higher priority traffic from blocking green lower priority traffic.