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In this paper, stochastic network calculus is relied on to analyze the guaranteed quality of service in a cognitive radio network, mainly from the viewpoint of delay. Each user is assumed to carry an ON-OFF source with same average rate but random phase. Then the aggregated flow can be approximated by a Gaussian process, based on which specific delay distribution bound is derived. Numerical results are obtained and discussed from different aspects, including the capacity under certain delay constraint, impact of sensing error probability, and system admission region.