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Rapid deployment of IEEE 802.11 wireless local area networks (WLANs) and their increasing quality of service (QoS) requirements motivate extensive performance evaluations of the upcoming 802.11e QoS-aware enhanced distributed coordination function (EDCA). Most of the analytical studies up-to-date have been based on one of the three major performance models in legacy distributed coordination function analysis, requiring a large degree of complexity in solving multidimensional Markov chains. Here, we expose the common guiding principle behind these three seemingly different models. Subsequently, by abstracting, unifying, and extending this common principle, we propose a new unified performance model and analysis method to study the saturation throughput and delay performance of EDCA, under the assumption of a finite number of stations and ideal channel conditions in a single-hop WLAN. This unified model combines the strengths of all three models, and thus, is easy to understand and apply; on the other hand, it helps increase the understanding of the existing performance analysis. Despite its appealing simplicity, our unified model and analysis are validated very well by simulation results. Ultimately, by means of the proposed model, we are able to precisely evaluate the differentiation effects of EDCA parameters on WLAN performance in very broad settings, a feature which is essential for network design.