An improved method of hierarchical output queueing of packets for a network scheduler of a network gateway that determines delays needed to conform to applicable rate shaping, and enqueues the packets based on the delay. Queues are associated with different classes of service (CoS), and within each class, each queue has a different scheduled time upon which it becomes available for dequeuing. A single set of CoS queues can support a large number of devices, improving the efficiency of software-based queuing by reducing the number of queues and simplifying queue polling.