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IEEE 802.11e EDCA induces service differentiation by appropriate joint tuning of four adjustable contention parameters. Existing and emerging work has devoted considerable attention to the nonsaturated performance of EDCA networks due to the difficulty of predicting the joint influence of the four parameters. However, most existing nonsaturated EDCA models adopt complex extensions of a Markov-chain approach. In sharp contrast, this paper invokes an extension of a renewal-reward approach. Our extension has the following unparalleled advantages: good scalability, ease of understanding, fast computation speed, high accuracy, models joint differentiation of all four parameters, captures the impact of an arbitrary buffer size, and predicts a wide range of performance indicators including the buffer overflow probability and the MAC access delay distribution. Our nonsaturated EDCA model is a nontrivial augmentation of our previously proposed nonsaturated DCF model. Our results indicate that if we accurately model the nonsaturated collision probability, the same formulas used for the saturated performance descriptors can produce accurate results for nonsaturated operation, and therefore it is unnecessary to construct specific formulas for nonsaturated performance descriptors, as done in previous work. To illustrate the utility of our model, we also develop an admission control policy based on the proposed EDCA model for a CWmin-differentiation system. Simulations validate that this policy enables the system to run slightly below a critical point, beyond which the system performance deteriorates drastically.