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This paper considers designing an optimal policy for deadline-constrained access in cognitive radio networks, where a secondary user needs to complete a packet transmission over the vacant spectrum within a delivery deadline. To minimize the total access cost, it is desirable to design an optimal opportunistic access policy by utilizing channel dynamics and sensing outcomes. We take non-negligible switching overheads, a state-dependent overtime penalty, and practical switching operations into consideration in the Markov decision process formulation of such an access problem under wide-band sensing. Moreover, we establish the existence of monotone optimal decision rules to reduce the complexity of computing an optimal policy. Simulation results verify our theoretical studies and the cost advantage over other policies.