## 5 Discussion  
The analysis of two distinct algorithms for managing cross-domain redundancy in RED/BLACK communication systems reveals important insights into the reliability and efficiency of these critical infrastructure systems. Our results demonstrate that both cross-domain redundancy strategies offer significant improvements in reliability compared to traditional isolated architectures. However, the comparative performance between the two algorithms reveals nuanced trade-offs between resource efficiency, operational complexity, and security considerations. While the term \"algorithm\" is used to describe these strategies, it is important to note that these are conceptual frameworks rather than computational procedures. The analysis presented focuses on the theoretical evaluation of these strategies through Markov chain modeling, providing insights into how they can enhance system reliability. Future work could involve the development of more detailed procedural algorithms that implement these strategies in practical applications, offering step-by-step guidelines for their deployment in real-world systems. Figure 4 illustrates the relative performance of the two algorithms by showing the reliability improvement factor \(B\) as a function of the number of reserve elements in both the RED (\(n\)) and BLACK (\(m\)) domains for a system with the number of channels \(h=8\) in the BLACK domain and \(k=10\) in the RED domain. This factor \(B\) represents the ratio of unavailability between the unified pool algorithm (\(A_{RD1}\)) and the separate pools algorithm (\(A_{RD2}\)), effectively quantifying how much more reliable the separate pools approach is compared to the unified pool approach:  
\[B=\frac{1-A_{RD1}}{1-A_{RD2}}=\frac{U_{RD1}}{U_{RD2}}\]The graph in Figure 4 depicts several key insights:  
* The reliability improvement factor \(B\) generally increases as the number of reserve elements in both domains increases, indicating that the separate pools algorithm becomes increasingly advantageous as more backup resources are available. * The improvement is showing diminishing returns as the number of reserve elements grows, particularly in the RED domain. * The impact of increasing reserve elements in the BLACK domain (\(m\)) appears more pronounced than increasing reserves in the RED domain (\(n\)), especially when \(n\) is small. This suggests that leveraging BLACK domain resources can be particularly effective for improving RED domain reliability. * There are noticeable \"steps\" in the improvement factor, particularly visible as m increases. * The complex interplay between RED and BLACK domain reserves emphasizes the importance of considering both domains holistically when designing redundancy strategies. This visualization underscores the potential benefits of the separate algorithm, particularly in scenarios where a high number of reserve elements can be allocated in both domains. However, it also hints at the need for careful optimization, as the gains from additional reserves are not uniform and may need to be balanced against increased system complexity and cost. To quantify the reliability improvement achieved by the second strategy (separate pools with cross-domain access) compared to the classical approach (RED domain using only its own reserves), we introduce the factor of channel availability improvement \(V\):  
\[V=\frac{1-A_{R}}{1-A_{RD2}}=\frac{U_{R}}{U_{RD2}}\]  
where \(A_{R}\) represents the availability of the system with only RED domain reserves (classical approach), and \(A_{RD2}\) is the availability of the system using the second strategy with cross-domain redundancy. The value of \(A_{RD2}\) is determined using Equation (2), while \(A_{R}\) was derived in previous studies [33]. Figure 5 illustrates the reliability improvement factor \(V\) as a function of the additional standby radio stations \(m\) in the BLACK domain that can be accessed by the RED domain. The graph shows multiple curves, each representing a different reliability parameter \(\gamma\) of the radio stations.