In this paper, performance analysis of a cognitive radio network is conducted. In the network, there is imperfect sensing and the wireless channel is a Gilbert-Elliott channel. The focus is on the network's capacity in serving traffic with delay constraints. Specifically, the maximum traffic arrival rates of both primary users and secondary users, which the network can support with guaranteed delay bounds, are investigated. The analysis is based on stochastic network calculus. A general relationship between delay bounds, traffic patterns and important characteristics such as spectrum sensing errors and channel fading of the cognitive radio network is derived. This relationship lays a foundation for finding the capacity under different traffic scenarios. Two specific traffic types are exemplified, namely periodic traffic and Poisson traffic. Analytical results are presented in comparison with simulation results. The comparison shows a good match between them, validating the analysis.