## 7 Results and Discussion
### Impact of Client Pool Size on Accuracy, Battery, and Privacy  
To assess how the size of the client pool influences FL performance under real-world conditions, we examined training behavior on four datasets (MNIST, EMNIST, Fashion-MNIST, and CIFAR-10) using heterogeneous client groups only. In all configurations, the total number of clients remained 100% heterogeneous, with device proportions preserved across:  
* 10 clients: approx. 3 smartphones, 3 edge, and 4 IoT;
* 100 clients: 33 smartphones, 33 edge, and 34 IoT;
* 1000 clients: 330 smartphones, 330 edge, and 340 IoT.  
All results reported below are measured at round 90, to ensure consistency across settings. Table 6 summarizes the results.  
As shown in Table 6 and Figure 15, increasing the total number of heterogeneous clients leads to a decrease in model accuracy at a fixed round, such as round 90. For  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Dataset** & **Clients** & **Accuracy (\%)** & **Battery Usage (\%)** & **Avg. Privacy Loss** \\ \hline \multirow{3}{*}{MNIST} & 10 & 94 & 18.0 & 0.40 \\  & 100 & 89 & 12.0 & 0.25 \\  & 1000 & 64 & 7.0 & 0.12 \\ \hline \multirow{3}{*}{EMNIST} & 10 & 90 & 19.0 & 0.44 \\  & 100 & 85 & 13.0 & 0.27 \\  & 1000 & 60 & 8.0 & 0.13 \\ \hline \multirow{3}{*}{Fashion-MNIST} & 10 & 91 & 17.0 & 0.38 \\  & 100 & 86 & 11.0 & 0.22 \\  & 1000 & 61 & 6.5 & 0.11 \\ \hline \multirow{3}{*}{CIFAR-10} & 10 & 80 & 20.0 & 0.47 \\  & 100 & 75 & 14.0 & 0.29 \\ \cline{1-1}  & 1000 & 50 & 9.0 & 0.14 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Performance summary at round 90 for heterogeneous client pools (adjusted for realistic battery usage).  
Figure 14: Accuracy, energy consumption, and privacy loss across different heterogeneous client distributions (100 clients; 300 rounds).  
instance, MNIST accuracy drops from approximately 94% with 10 clients to 89% with 100 and 64% with 1000. This trend holds across EMNIST, Fashion-MNIST, and CIFAR-10. The accuracy reduction is primarily due to the lower probability of each individual client being selected in larger pools. As fewer updates are aggregated per round, the global model receives less information, slowing convergence. Figure 16 highlights a benefit of this reduced selection frequency: lower battery consumption per device. In small pools, devices such as smartphones are selected frequently and experience high battery drain (up to 10-11% per round). In contrast, in larger pools, individual clients are chosen less often, reducing average battery usage to around 4-5% and allowing devices to participate longer. Figure 17 shows a similar effect in terms of privacy. In smaller pools, high-sensitivity devices are exposed repeatedly, leading to rapid privacy degradation. Larger pools distribute participation across a wider population, decreasing the likelihood of repeated selection and reducing cumulative privacy loss. For example, in CIFAR-10, the average privacy loss per smartphone falls from 0.47 with 10 clients to just 0.14 with 1000. This analysis demonstrates that while larger client pools may reduce accuracy at a fixed round, they significantly improve battery efficiency and privacy protection by lowering per-device selection probability. These trade-offs highlight the importance of balancing pool size with training duration when designing scalable FL systems.  
Figure 16: Effect of client pool size on battery usage (%).  
Figure 17: Effect of client pool size on privacy loss.  
Figure 15: Effect of client pool size on model accuracy.