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Supporting the quality of service of unlicensed users in cognitive radio networks is very challenging, mainly due to the dynamic resource availability induced by the licensed users' activities. In this paper, we derive the optimal admission control and channel allocation decisions in cognitive overlay networks to support delay sensitive communications of unlicensed users. We formulate it as a Markov decision process problem, and solve it by transforming the original formulation into a stochastic shortest path problem. We then propose a simple heuristic control policy, which includes a threshold-based admission control scheme and and a largest-delay-first channel allocation scheme, and prove the optimality of the largest-delay-first channel allocation scheme. We further propose an improved policy using the rollout algorithm. By comparing the performance of both proposed policies with the upper-bound of the maximum revenue, we show that our policies achieve close-to-optimal performances with low complexities.