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It is crucial to save power and prolong the runtime of mobile stations (STAs) in wireless local area networks (WLANs). In an infrastructure WLAN, a STA cannot be connected until it is associated with an access point (AP), which is responsible for buffering frames for all the associated STAs operating in the power saving mode. Hence, efficient memory utilization is critical for an AP to accommodate as many power-saving STAs as possible. The basic power management (BPM) scheme introduced in the IEEE 802.11 standard achieves power saving by allowing STAs not engaging in data delivery to operate in doze mode, but it does not consider the efficient use of the memory in the AP. To tradeoff power consumption for memory usage, we present an AP-priority timer-based power management (APP-TPM) scheme and develop a novel model for stochastic analysis of the proposed scheme. Based on this model, the probability distributions of the numbers of frames buffered at the AP and the average numbers of frames buffered at the AP are obtained. Moreover, a power-aware buffer management scheme (PBMS), which is based on the derived statistics, is proposed to accommodate as many STAs as possible given a fixed amount of memory in the AP while maintaining low power consumption. Simulation results show that the proposed scheme performs better than BPM in terms of memory usage in the AP.