## 3 Proposed w-SMNO
### Threshold Instances for w-SMNO  
In the process of selecting relays for our proposed system, some cases and subcases must be meticulously considered both for local groups and via the global leader to ensure optimal performance and reliability. A careful analysis of the relay's sensitivity and response time is crucial to guarantee its suitability for dissemination and routine operating scenarios. Different cases and subcases for relay selection through w-SMNO in VANET ensure optimal performance in dynamic vehicular environments. In some cases, it would be highly beneficial to select the \(LL\) with the next highest weighted score instead of the highest score. Let us consider two scenarios involving the mentioned case, one with the maximum score and the other with the next-to-maximum score, based on the population size in local groups and the number of neighbors to the local leader. For these scenarios, threshold is defined for factors, as shown below in Table 1. When both the population of the specific group \(Q\) is \(P_{LL_{Q}}\) and the number of neighbors in that respective group, \(N_{LL_{Q}}\), is greater than the population and local leader threshold, then the maximum weighted group using the dynamic parameter weight node from the learning model is considered to enhance the dissemination as the condition is to maintain a balance between groups and a leader, according to the population size. Similarly, if both the number of neighbors in that respective group, \(N_{LL_{Q}}\), is less than the threshold (\(LL_{Threshold}\)) and the population of \(Q\) subgroups, \(P_{LL_{Q}}\), is also less than the population threshold (\(P_{Threshold}\)), then the next maximum weighted group, \(Q^{\prime}\), is considered. For other conditions, the maximum weighted group is selected. An assumption has been made for the minimum neighbors' local leaders (\(LL_{Threshold}\)) with actual neighbors' local leaders (\(N_{LL}\)) and the dynamic population of a specific group (\(P_{LL}\)) with a population threshold (\(P_{Threshold}\)) for an efficient dissemination process, where \(LL_{Q}\) and \(LL_{Q}^{\prime}\) are, respectively, the maximum score and the next maximum score of local groups' leaders.  
Figure 8 illustrates a dynamic model depicting the threshold considerations for both local leaders' thresholds and each group population within a given total population size. The graph showcases the intricate relationship between these two entities as they navigate the challenges and opportunities inherent to their respective roles. The limitation to the number of local leaders for relay consideration demonstrates a distinct threshold that signifies the point at which their influence becomes the most impactful within their immediate community or region. Simultaneously, the graph represents the threshold for the group population at large, emphasizing the critical juncture at which the collective strength and cohesion of the entire population come into play. This figure serves as a valuable tool for understanding the nuanced interplay between local leaders and the broader group population, offering insights into the optimal points of engagement and coordination to maximize positive outcomes within the larger framework.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Instances**} & \multicolumn{1}{c}{**Group (Order of Score)**} & **Relay Node** \\ \hline
**Group Population** & **Neighbors (Qth Group LL)** & & LL\({}_{Q}\) & Maximum \\ \hline \((P_{LL})_{Q}>=P_{Threshold}\) & & LL\({}_{Q}\) & weight node \\ \hline \((P_{LL})_{Q}>=P_{Threshold}\) & & LL\({}_{Q}\) & (Machine \\ \hline \((P_{LL})_{Q}<P_{Threshold}\) & & LL\({}_{Q^{\prime}}\) & learning model) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Threshold instances (LL group).