We present a novel resource allocation framework based on frame aggregation for providing a statistical Quality of Service (QoS) guarantee in high speed IEEE802.11 Wireless Local Area Networks. Considering link quality fluctuations through the concept of effective capacity, we formulate an optimization problem for resource allocation with QoS guarantees, which are expressed in terms of target delay bound and delay violation probability. Our objective is to have the access point schedule down-links at minimum resource usage, i.e., total time allowance, while their QoS is satisfied. For implementation simplicity, we then consider a surrogate optimization problem based on a few accurate queuing model approximations. We propose a novel metric that qualitatively captures the surplus resource provisioning for a particular statistical delay guarantee, and using this metric, we devise a simple-to-implement Proportional–Integral–Derivative (PID) controller achieving the optimal frame aggregation size according to the time allowance. The proposed PID algorithm independently adapts the amount of time allowance for each link, and it is implemented only at the Access Point without requiring any changes to the IEEE802.11 Medium Access Control layer. More importantly, our resource allocation algorithm does not consider any channel state information, as it only makes use of queue level information, such as the average queue length and link utilization. Via NS-3 simulations as well as real test-bed experiments with the implementation of the algorithm over commodity IEEE 802.11 devices, we demonstrate that the proposed scheme outperforms the Earliest Deadline First (EDF) scheduling with maximum aggregation size and pure deadline-based schemes, both in terms of the maximum number of stations and channel efficiency by 10–30%. These results are also verified with analytical results, which we have obtained from a queuing model based approximation of the system. Applying actual video traffic from HD MPEG4 streams in both simulations and real test-bed experiments, we also show that our proposed algorithm improves the quality of video streaming over a wireless LAN, and it outperforms EDF and deadline based schemes in terms of the video metric, Peak Signal to Noise Ratio.