Abstract--Proper admission control in cognitive radio networks is critical in providing QoS guarantees to secondary unlicensed users. In this paper, we study the admission control and channel allocation problem in overlay cognitive radio networks under the maximum cumulative delay constraint. We formulate it as a Markov decision process problem, and then solve it by transforming the original formulation into a stochastic shortest path problem. We further simulate the performance of a class of threshold-based admission control with the largest-delay-first channel allocation policy, and show its advantage over other two benchmark policies.