## 3 Proposed Framework  
The queuing theory is a useful analytical tool that can be utilized in the process of designing and optimizing admission-control systems in cognitive radio networks (CRNs) [13]. In the context of CRNs, where dynamic spectrum access and effective resource usage are of the utmost importance, queuing theory makes it possible to conduct a systematic examination of the queuing dynamics, service rates, and user arrivals in the network [14]. It is possible to conduct an analysis of the performance indicators that are essential for admission control by modeling the network as a queuing system [15]. These metrics include queue lengths, waiting times, and levels of system utilization. This technique makes it possible to gain a thorough understanding of how admission decisions affect network performance. This, in turn, makes it possible to build effective strategies that optimize spectrum usage, decrease interference, and assure efficient exploitation of available resources in cognitive radio environments. Overall, the utilization of queuing theory in admission control for cognitive radio networks makes a contribution to the improvement of overall network efficiency and the fulfillment of quality-of-service standards [16]. In the workflow of a cognitive radio network, requests from both PUs and SUs are managed by the server to optimize spectrum utilization and minimize interference, as presented in Figure 1. Upon arrival, requests are queued and prioritized, with PUs given precedence over SUs to access spectrum bands for communication [17]. Once PU requests have been serviced, the server addresses SUs, allowing them to exploit the unused spectrum opportunistically. Responses indicating request status are provided to both PUs and SUs, facilitating efficient \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Authors** & **Models Used** & **Contributions** & **Limitations** \\ \hline [PERSON] and [PERSON] [7] & Correlated retry queueing architectures & Showcases two-way interaction with two customer classes without disruptions & N/A \\ \hline [PERSON] et al. [8] & Queueing framework for cognitive radio networks with reactive-decision spectrum handoff & Introduces blocking probability, average number of sensing SUs, and transmission time metrics & Finite orbit size assumption \\ \hline [PERSON] et al. [11] & Multi-objective optimization framework for resource allocation in cloud systems logic & Proposes weighted-sum-based multi-objective optimization framework utilizing fuzzy logic & - \\ \hline [PERSON] et al. [12] & Multi-point algorithm in heterogeneous networks for RAT selection & Introduces combination of techniques for best RAT selection using biogeography-based optimization & Implementation scheme focused on RAT selection probabilities from MDP \\ \hline Proposed framework & Priority-based M/D/1 queue (with preemption and non-preemption) & Effective in mitigating SU spectrum outage in CRNs. Provides insight into priority-based admission of request-estimation of real-time system constraints. & Scalability with increasing users and implementation complexity. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
The performance of the various proposed methods is assessed by examining the average total waiting times for both the PU and the SU under different scenarios. Initially, performance was assessed for a delay model based on PUs that has already been developed. The study in [4] focuses on analyzing the priority queuing models to improve the Quality of Service (QoS) for the SU. These methods, which have an infinite buffer size, are suggested for the purpose of performance assessment. Subsequently, identical designs are proposed, albeit with a limited buffer capacity [18, 19]. The M/D/1 model is considered for both the PU queue and the SU queue in all schemes.