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To achieve a long run-time for battery-operated portable electronic devices that incorporate wireless transceivers, efficient power management of the radio is a critical requirement. The power management function of IEEE 802.11 wireless local area networks (WLANs) allows stations (STAs) to operate in the doze mode so that their power consumption is significantly reduced. Hence, efficient algorithms to manage when and how often a STA enters and exits doze mode are crucial to battery-operated STAs. We address this problem by developing a novel model for stochastic analysis of timer-based power management in infrastructure IEEE 802.11 WLANs. Based on this model, the probabilities that a STA is active, idle, or dozing are derived, and the power consumption of the STA, number of frames buffered, and average delay per frame are obtained. These results enable an efficient power management algorithm that optimizes the idle timer and doze duration at the STA and the frame buffer at the access point. Moreover, similar statistics for the basic power management method in the IEEE 802.11 standard are derived as a special case of the proposed timer-based power management scheme. Numerical results are presented to demonstrate the effectiveness of the proposed algorithms.