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In recent years, access-points have been densely placed at public spaces. Users can each select an access-point from among such access-points so as to enhance communication quality. Access-point selection methods have thus become an important technical issue. This paper proposes a new access-point selection method using Markov approximation, which adapt to dynamic changes in network conditions. Markov approximation is a distributed optimization framework, where a network is optimized by individual behavior of users forming a time-reversible continuous-time Markov chain. Our proposed method provides an optimal channel and access-point selection strategy according to a time-reversible continuous-time Markov chain, aiming at maximizing the total throughput of users. Simulation experiments demonstrate the effectiveness of the proposed method.