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Fair scheduling algorithms are an important component of most QoS mechanisms designed to support the performance guarantees required by real-time applications. In this paper, we present greedy fair queueing (GrFQ), a novel scheduler based on a greedy strategy of reducing the maximum difference in normalized service received by any two flows at each transmission boundary. We prove that the GrFQ scheduler achieves a better bound on the normalized lag than other known schedulers. We further propose a simplified version of the scheduler, called GrFQ-lite, which avoids the emulation of a fluid flow system and has a per-packet work complexity of O(1) in the computation of the timestamps. Borrowing from the field of economics, we use the Gini index as a measure of instantaneous fairness. Using real gateway traffic traces, we show that the GrFQ scheduler achieves better fairness than any other known scheduler at virtually all instants of time. We further show that the GrFQ-lite scheduler achieves equivalent or better fairness than other known schedulers including those that are significantly more computationally intensive in their emulation of the ideally fair fluid flow system.