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Dynamic multichannel access is one of the most important issues in cognitive radio systems. Its major challenge is to make best use of the limited frequency bands while protecting the rights of primary users. In this paper, we propose a novel sensing scheme for dynamic multichannel access based on the restless multiarmed bandit process (RMBP). Specifically, we grant the RMBP model with a flexible ratio between transmission period and sensing interval, which is denoted as n. Whittle's index is applied as a sorting standard for secondary users to judge which channel to sense. Under Lagrangian relaxation, we compute the throughput and sensing cost in terms of n. Throughput is proved to converge to a fixed bound when n approaches infinity. Meanwhile, sensing cost is proved to diverge in some cases. We also prove that the interference percentage remains the same, regardless of the improvement on system performance. Finally, we offer recommendation on how to set the proper parameters according to the environment in practical use.