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Abstract-Cognitive Radio (CR) is a promising technology for overcoming the lack of available communication bands. However, in Cognitive Radio Networks (CRN), available spectrum changes due to the user mobility. In this paper, we investigate dynamic spectrum planning and allocation in CRN, which considers the mobility of the cognitive users. The on-line dynamic spectrum planning and allocation problem under conventional model is a NP-hard one, which is generally hard to solve due to the unacceptable computational complexity. We propose a model design in a stochastic geometry approach and an off-line dynamic spectrum planning scheme based on this model. Specifically, to evaluate the robustness performance of the cognitive radio networks, we derive the average collision time T in closed form under this model. Further, the value of T will be used to select the best scheme of spectrum utilization. The rationality of this dynamic spectrum planning approach is also verified through computer simulations.