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This paper introduces a finite load multi-class 802.11e EDCF model that is simple enough to be explicitly solvable. The model is nevertheless flexible enough to model the impact of 802.11e parameters on the prioritization of realistic traffic. We emphasize that a modeling framework which allows nonsaturated sources is essential in the study of realistic traffic. We apply the model to a situation of practical interest: competing TCP flows in an infrastructure network. The model allows us to make a principled selection of 802.11e parameters to resolve problems highlighted in this scenario. Model predictions and parameter selections are validated against simulation and experiment. The model is shown to be accurate and the parameters effective.