Hierarchical packet fair queueing algorithms

In this paper, we propose to use the idealized Hierarchical Generalized Processor Sharing (H-GPS) model to simultaneously support guaranteed real-time, rate-adaptive best-effort, and controlled link-sharing services. We design Hierarchical Packet Fair Queueing (H-PFQ) algorithms to approximate H-GPS by using one-level variable-rate PFQ servers as basic building blocks. By computing the system virtual time and per packet virtual start/finish times in unit of bits instead of seconds, most of the PFQ algorithms in the literature can be properly defined as variable-rate servers. We develop techniques to analyze delay and fairness properties of variable-rate and hierarchical PFQ servers. We demonstrate that in order to provide tight delay bounds with an H-PFQ server, it is essential for the one-level PFQ servers to have small Worst-case Fair Indices (WFI). We propose a newp PFQ algorithm called WF(2)Q+ that is the first to have all the following three properties: 1) providing the tightest delay bound among all PFQ algorithms; 2) having the smallest WFI among all PFQ algorithms; and 3) having a relatively low asymptotic complexity of O(log N). Simulation results are presented to evaluate the delay and link-sharing properties of H-WF(2)Q+, H-WFQ, H-SFQ, and H-SCFQ.