# Offloaded Computation for QoS Routing in Wireless Sensor Networks
## 5 Theoretical and Experimental Evaluation
### Experimental Evaluation
#### Key Observations:  
* _Significant performance gain:_ As shown in Table 5, the proposed EX method consistently outperforms both heuristic baselines (H\({}_{1}\) and H\({}_{2}\)) across all tested QoS thresholds, achieving up to **1282.05%** gain in the number of feasible nodes, with an average improvement of **563.45%**.
* _Feasibility trend with relaxed constraints:_ Figure 5 confirms that the number of QoS-compliant nodes increases as the QoS bound \(L\) is relaxed, growing from approximately 42 nodes at \(L=9\) to 54 nodes at \(L=14\), validating the sensitivity of path feasibility to the constraint level.
* _Improved path efficiency:_ The EX approach achieves lower average and maximum non-linear path lengths than both heuristics (Table 6), contributing to more reliable and uniformly distributed routing paths.
* _Structural advantage with BRs:_ The effectiveness of multi-BR deployment is validated in Figure 8, which shows that optimal BR placement significantly boosts feasible coverage, especially under low-range settings. For example, in the 120-node case with range 12, the number of feasible nodes increased from 25 (1 BR) to over 80 (4 BRs), demonstrating the importance of both BR count and location.
* _General scalability:_ Across varying network sizes and link constraint dimensions, the centralized offloading model maintains high feasibility, adaptability, and topological flexibility. This reinforces its suitability for real-world constraint-sensitive WSN applications.  
These insights collectively validate that the centralized edge-assisted strategy yields structurally reliable and efficient routing topologies, making it a practical solution for real-world QoS-sensitive WSN deployments.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(L\)} & **Connected to** & **Feasible Nodes** & **Unfeasible Nodes (EX)** & **Nodes in the** & **Unfeasible Nodes Using** & **Unfeasible Nodes Using** \\  & **the BR** & **(EX)** & **Nodes (EX)** & **First DODAG** & **\(H_{1}\)** & **\(H_{2}\)** \\ \hline
9 & 55.85 & 41.9 & 13.95 & 35.9 & 17.25 & 15.3 \\
10 & 55.85 & 41.85 & 14 & 37.1 & 16.2 & 14.85 \\
11 & 56.1 & 49.1 & 7 & 40.75 & 10.9 & 8.5 \\
12 & 56.7 & 52.65 & 4.05 & 45.45 & 6.1 & 4.9 \\
13 & 55.85 & 50.95 & 4.9 & 43.25 & 6.5 & 5.85 \\
14 & 57 & 53.9 & 3.1 & 44.95 & 3.9 & 3.7 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Number of nodes with feasible and unfeasible paths by varying the QoS requirement \(L\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**QoS Threshold (L)** & **EX** & \(H_{1}\) & \(H_{2}\) & **Baseline Max** & **Preservation (\%)** \\ \hline
9 & 41.90 & 17.25 & 15.30 & 17.25 & 142.90 \\
10 & 41.85 & 16.20 & 14.85 & 16.20 & 158.64 \\
11 & 49.10 & 10.90 & 8.50 & 10.90 & 350.46 \\
12 & 52.65 & 6.10 & 4.90 & 6.10 & 763.11 \\
13 & 50.95 & 6.50 & 5.85 & 6.50 & 683.08 \\
14 & 53.90 & 3.90 & 3.70 & 3.90 & 1282.05 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Percentage improvement in the number of QoS-satisfying nodes preserved by the proposed method (EX) over the better-performing heuristic baseline (\(H_{1}\) or \(H_{2}\)) across varying QoS constraint thresholds.