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A number of emerging Internet applications, such as video-conferencing and live multimedia broadcasts, must rely on scheduling algorithms in switches and routers to guarantee performance and an acceptable level of quality of service. Fairness in packet schedulers is an intuitively desirable property with practical value; fair schedulers are a critical component of QoS mechanisms that seek to guarantee end-to-end delay bounds. Popular measures of the fairness achieved by packet schedulers are based on bounds, such as the relative fairness bound which captures the maximum possible difference between the normalized service received by any two flows. We argue that such measures do not capture the actual fairness achieved at most instants of time, and therefore, do not represent a true measure of the ability of a scheduler to successfully deliver end-to-end quality for real-time applications. We borrow from the field of economics and propose a new measure of fairness based on the Gini index. This measure captures the instantaneous fairness of a scheduler and, unlike other measures based on bounds, also captures the fairness of the scheduler in its handling of flows during idle periods. Using real traces of gateway and video traffic, we present a simulation-based evaluation of several well-known schedulers based on the Gini index. We also present a qualitative analysis of the phenomena underlying the observed results.