During the last decade, the wireless technologies have been developed. The actual spectral occupancy over some frequency bands studied was found to be virtually empty. In 1 spectrum measurement was conducted in rural and urban locations, covering 50 MHz–6 GHz bands, during the weekdays and weekends. A modified duty cycle metric is presented by introducing a space variable into the existing metrics available today. An adaptive energy detection threshold technique was employed, the results indicate the average spectral occupancy of 0.18%, and 5.08% in rural and urban locations respectively during weekdays and 1.45% on weekends for urban locations. It is very difficult to analyze the behavior of multi-server of the priority queue model when channel usage by primary and secondary users of different priority of multi-channels 2.Although the vast research on the analysis of priority queues with a single channel facility, efforts on the characterization of multi channel queues were not as extensive or fruitful due to their complications. This is essentially unfortunate since the modeling of many telecommunications problems can be suitably placed in the framework of a multi server system, such as multi channel cognitive radio networks 3.In 4 , the authors proposed M/M/1 queue which is represented by a two dimensional state transition graph. The authors proposed a queuing model for heterogeneous packets transmissions in underlay cognitive radio networks. In this model, safety or emergency related messages possess preemptive higher priority over nonemergency messages. This model has two classes; high priority for primary user and low priority for secondary user.In 5, Authors provide the comparison of 13 structured and simulated models systems (SSMS) which allow conventional users, not software designers, to create structured and simulated models without programming structured schemes of modeling objects. To compare SSMS structured, simulated and analytical models of queuing system of five channels have been used.In 6, priority based non-preemptive M/G/1 queuing model of spectrum handoff scheme was proposed in wireless cognitive radio networks. Channel bonding mechanism with starvation mitigation was proposed to increase spectrum handoff utilization. This model has two classes; high priority for primary user and low priority for secondary user.In 7, the authors proposed a Dynamic Spectrum Access (DSA) scheme for cognitive radio networks, where priorities for the bandwidth, the spectrum access, and spectrum handoff are considered for three types of traffics. Paper has adopted a multi-dimensional Markov chain with three state variables to analyze the state transitions of the dynamic spectrum access scheme which enables us to obtain the steady state distribution of the number of each kind of traffics in the system. Blocking probability and dropping probability have been derived for two classes of secondary traffic.The main contributions of this paper are as follows:1. Proposing queuing based spectrum access scheme for prioritized cognitive radio networks.2. Providing an accurate analytical model for spectrum access queuing based scheme priority service discipline.3. Proposed model can be applied for multi-priority secondary user.4. Proposed model consider general case of multi-channels.5. Evaluation of performance is given by four measures namely, expected waiting time in queue, expected waiting time in the system, expected number of users in queue, and expected number of users in the system.The rest of this paper is organized as follows: In Section 2, the proposed model has been introduced. The simulation results of the proposed model have been discussed in Section 3. Finally, Section 4 presents the conclusion of the proposed model.