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In recent years, a series of power saving (PS) protocols has been proposed in the family of 802.11 standards to save energy for mobile devices. To evaluate their performance, many works have been carried out on testbeds or simulation platforms. However, till now, there is a lack of accurate theoretical models to analyze the performance for these protocols. In an effort to fill this gap, we present a Markov chain-based analytical model in this paper to model these PS protocols, with its focus on multicast services in wireless LANs. The proposed analytical model successfully captures the key characteristic of the power saving system: the data delivery procedure starts periodically at the previously negotiated time, but ends at a rather random time with its distribution depending on the end time of data delivery in the last delivery period as well as the arrival rate of incoming traffic. In the situations with light to moderate traffic loads and under the Poisson assumption for incoming traffic, the amount of data delivered between consecutive delivery periods possesses the Markov property, which builds up our Markov chain-based model. For incoming traffic with long-range dependence (LRD), a multistate Markov-Modulated Poisson Process (MMPP) is used to approximate the traffic, making the analytical model valid in more general cases. We verify our model by simulations on ns2 and the results show that the model can faithfully predict the performance of these PS protocols over a wide variety of testing scenarios.