## 7 Comparison Between the Cloud Gaming Architecture Leveraging Fog and the Proposed Model  
The evaluation of the base model in the study [4] revealed the following results: the traffic load on each game server in terms of connected clients over time, along with the percentage of user coverage achieved in each cluster as a function of time in seconds. This model did not consider factors such as latency and variability in network conditions, the geographical location of servers, the geographical location of users, server permanence, the probability of movement between servers, and other aspects that were taken into account in the proposed model. To compare the two models, the proposed model was simulated under the same context as the base model, considering only the load, the number of servers, and using the same parameters as those used in the base model, as shown in Table 3.  
In the results of the base model, it is observed that the traffic load of the game servers, in terms of the number of connected clients over time, remains close to the maximum capacity. However, there are frequent drops in the number of connected clients, although these are quickly recovered in the following time interval. This behavior suggests that, although server capacity is not exceeded, disconnections or redirections to fog nodes cause frequent fluctuations in the load. In contrast, the proposed model shows a more balanced load distribution, with fewer abrupt drops compared to the base model. Although load balancing with fog nodes is also observed, this model manages to maintain a minimum load of around 135 clients, which is lower than the minimum observed in the base model (around 140 clients). This lower minimum load indicates that the proposed system better handles peaks in disconnection or traffic shifts, allowing for more efficient distribution without significant fluctuations. This is illustrated in Figure 8.  
Overall, the proposed model is more efficient because it maintains a more stable load distribution across the servers, even during times of variation, enabling better resource utilization. The less-abrupt fluctuations and the lower minimum load indicate that the proposed system manages disconnections better and optimizes load balancing, ensuring continuous server operation without negatively impacting the user experience. When comparing the user coverage results across clusters between the base model and the proposed model, the proposed model can identify key differences in their behavior and efficiency. Figure 8: The traffic load of each game server in terms of connected clients as a function of time in seconds. \begin{table}
\begin{tabular}{l l} \hline
**Input Data** & **Value** \\ \hline Simulation time & 1000 s \\ \hline Game Clusters/Servers & 4 \\ \hline Server’s maximum capacity & 150 \\ \hline Fog servers & 20 \\ \hline Fogs’ maximum capacity & 10 \\ \hline Game clients & 1000 \\ \hline Connectivity radius & 0.4 \\ \hline Connection probability & 0.8 \\ \hline Disconnection probability & 0.2 \\ \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters. In the base model, user coverage across different clusters ranges between 75% and 85%, demonstrating that the system achieves acceptable coverage despite capacity constraints. However, it is observed that the clusters exhibit relatively constant fluctuations and do not achieve consistent performance across the system. While most clusters remain within the mentioned range, there are more notable peaks and drops in some of them. On the other hand, in the proposed model Figure 9, clusters exhibit greater variability in user coverage, with some cases dropping as low as 68%. However, what makes the proposed model more robust is that it shows better control over peaks and variations, maintaining coverage within a broader range (68-85%) but with fewer abrupt drops and more controlled behavior. This suggests that the proposed model adapts better to extreme fluctuations, while the base model, though consistent, does not achieve the same level of adaptability.