Recently, a quality-of-service (QoS) extension of the IEEE 802.11 standard (known as IEEE 802.11e) for wireless LANs has been proposed. We present a versatile and accurate performance model to study how these new QoS enhancements can be used to improve the performance of wireless nodes competing for bandwidth in a multi-hop ad hoc network. The paper presents the QoS enhancements, and shows how they can be modeled using a simple, yet effective, parameterized quasi-birth-death model. The model is developed hierarchically, in that results at packet level (e.g., as developed by Bianchi and others) are used in our flow-level model, in which a single bottleneck station interacts with a time-varying number of traffic sources. Thus, we are able to study the impact of the QoS enhancements on the flow-level performance. This has not been done before. The results of our analyses are compared with extensive simulations (using Opnet), and show excellent agreement for throughput, mean number of active sources and mean buffer occupancy at the bottleneck station. An important asset of our model is that it allows for very quick evaluations: where simulations require up to an hour per scenario, our model is solved in seconds.