A method and apparatus are provided for implementing hierarchical scheduling of oversubscribed virtual paths with underutilized bandwidth that works for both ATM (cell) and IP (frame) scheduling. A scheduler includes a first calendar for pipes and autonomous flows and a second calendar for pipe flows. A winner of a pipe or an autonomous flow is identified from the first calendar. Responsive to an identified winner pipe, a pipe queue is checked for an associated pipe flow for the winner pipe. Responsive to identifying an empty pipe queue for the winner pipe, a pipe win credit is assigned to the pipe without reattaching the winner pipe to the first calendar. Then a next winner is identified from the first calendar. When a winner pipe flow is identified from the second calendar and the pipe win credit is assigned to the pipe for the winner pipe flow, then the winner pipe flow is serviced without delay.