For a hierarchical cognitive radio network(CRN),the secondary users(SUs) may access the licensed spectrum opportunistically,whenever it is not occupied by the primary users(PUs).An important issue for this kind of CRN is the achievable qualityof-service(QoS) performance,such as traffic transmission delay,which is critical to the SUs’ traffic experience.In this paper,we focus on the delay performance analysis of the SU system and the design of the corresponding optimal access strategy for the case of SUs sharing multiple licensed channels.In our analysis,the transmission of PU and SU traffic is modeled as M/G/1 queues.By merging the PU and SU traffic,we propose the model of a priority virtual queue on the licensed channels.Based on this model,we obtain the expected system delay expression for SU traffic through M/G/1 preemptive repeat priority queuing analysis.For the case of multiple licensed channel access,the access strategy is further investigated with respect to the expected system delay for SU traffic.By minimizing the expected transmission delay,the optimal access strategy is modeled as a nonlinear programming problem,which can be resolved by means of the classic Genetic Algorithm(GA).Numerical results validate our analysis and design of an optimal access strategy.Meanwhile,by considering the time taken by the GA approach,we can also adopt the inverse proportional access strategy to obtain near-optimal results in practice. For a hierarchical cognitive radio network (CRN), the secondary users (SUs) may access the licensed spectrum opportunistically, whenever it is not occupied by the primary users (PUs) .An important issue for this kind of CRN is the achievable qualityof-service (QoS) performance, such as traffic transmission delay, which is critical to the SUs’ traffic experience. In this paper, we focus on the delay performance analysis of the SU system and the design of the corresponding optimal access strategy for the case of SUs sharing multiple licensed channels. In our analysis, the transmission of PU and SU traffic is modeled as M / G / 1 queues. By merging the PU and SU traffic, we propose the model of a priority virtual queue on the licensed channel. this model, we obtain the expected system delay expression for SU traffic through M / G / 1 preemptive repeat priority queuing analysis. For the case of multiple licensed channel access, the access strategy is further investigated with respect to the expected system delay for SU traffic. By minimizing the expected transmission delay, the optimal access strategy is modeled as a nonlinear programming problem, which can be resolved by means of the classic Genetic Algorithm (GA) .Numerical results validate our analysis and design of an optimal access strategy.Meanwhile, by considering the time taken by the GA approach, we can also adopt the inverse proportional access strategy to obtain near-optimal results in practice.