Hierarchical packet fair queueing algorithms

Hierarchical Packet Fair Queueing (H-PFQ) algorithms have the potential to simultaneously support guaranteed real-time service, rate-adaptive best-effort, and controlled link-sharing service. In this paper, we design practical H-PFQ algorithms by using one-level Packet Fair Queueing (PFQ) servers as basic building blocks, and develop techniques to analyze delay and fairness properties of the resulted H-PFQ servers. We demonstrate that, in order to provide tight delay bounds in a H-PFQ server, it is essential for the one-level PFQ servers to have small Worst-case Fair Indices (WFI). We propose a new one-level PFQ algorithm called WF2Q+ that is the first to have all the following three properties: (a) providing the tightest delay bound among all PFQ algorithms; (b) having the smallest WFI among all PFQ algorithms; and (c) having a relatively low implementation complexity of O(log N). We show that practical H-PFQ algorithms can be implemented by using WF2Q+ as the basic building block and prove that the resulting H-WF2Q+ algorithms provide similar delay bounds and band-width distribution as those provided by a H-GPS server. Simulation experiments are presented to evaluate the proposed algorithm.