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Traditional wireless sensor networks (WSNs) working in the license-free spectrum suffer from uncontrolled interference as the license-free spectrum becomes increasingly crowded. Designing a WSN based on cognitive radio can be promising in the near future in order to provide data transmissions with quality of service requirements. In this paper we introduce a cognitive radio sensor network (CRSN) and analyze its performance for supporting real-time traffic. The network opportunistically accesses vacant channels in the licensed spectrum. When the current channel becomes unavailable, the devices can switch to another available channel. Two types of channel switchings are considered, in periodic switching (PS) the devices can switch to a new channel only at the beginning of each channel switching (CS) interval, while in triggered switching (TS) the devices can switch to a new channel as soon as the current channel is lost. We consider two types of real-time traffic, i) a burst of packets are generated periodically and the number of packets in each burst is random, and ii) packet arrivals follow a Poisson process. We derive the average packet transmission delay for each type of the traffic and channel switching mechanisms. Our results indicate that real-time traffic can be effectively supported in the CRSN with small average packet transmission delay. For the network using PS, packets with the Poisson arrivals experience longer average delay than the bursty arrivals; while for the network using TS, packets with the bursty arrivals experience longer average delay.