# Offloaded Computation for QoS Routing in Wireless Sensor Networks
## 5 Theoretical and Experimental Evaluation
### Experimental Evaluation
#### 5.4.4 Impact of Border Router Number and Placement  
More sensors can transmit data when multiple BRs are available while satisfying QoS constraints. Optimal BR placement significantly improves coverage, resembling a special case of the area coverage problem. If the BRs are placed carefully, the number of sources covered by QoS-aware paths linked to at least one BR can be considerably increased. Careful sizing of data collection involves a thorough analysis of the network geometry (the number and placement of sensors, communication ranges, and existing links). Based on these elements and the QoS requirement, the number and position of the BRs needed can be determined. Methods such as the well-known K-means and/or the distance-based decomposition of Voronoi can be useful. Figure 7 illustrates the effect of BR placement:  
* In Figure 7a, the first BR covers a limited set of sensors, and adding a second BR provides minimal improvement. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Number \(k\)** & **Feasible** & **Feasible** & **Nodes in** & **Feasible** & **Unfeasible** & **Feasible** & **Unfeasible** \\
**of** **Parameters** & **Paths** & **Nodes (EX)** & **DODAG** & **Nodes (\(H_{1}\))** & **Nodes (\(H_{1}\))** & **Nodes (\(H_{2}\))** & **Nodes (\(H_{2}\))** \\ \hline
2 & 2490.2 & 43.65 & 39.85 & 40.85 & 15.95 & 42.55 & 14.25 \\
3 & 666.5 & 36.95 & 32.9 & 31.9 & 24.15 & 35.35 & 20.7 \\
4 & 404.5 & 34 & 30.6 & 30.45 & 25.55 & 33.05 & 22.95 \\
5 & 382.65 & 31.35 & 28 & 27.85 & 29.1 & 29.45 & 27.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Number of feasible and unfeasible nodes/paths by varying the number of parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number \(k\) of** & **Feasible** & **Average NL** & **Average NL** & **NL with \(H_{1}\)** & **Average NL** & **Max NL** \\
**Parameters** & **Paths (EX)** & **with EX** & **with H\({}_{1}\)** & **with H\({}_{2}\)** & **with H\({}_{2}\)** & **with H\({}_{2}\)** \\ \hline
2 & 43.65 & 0.86887645 & 0.76564 & 1.6954283 & 0.73822055 & 1.60968735 \\
3 & 36.95 & 0.86503695 & 0.88879065 & 1.809788 & 0.8404888 & 1.737761 \\
4 & 34 & 0.85768205 & 0.9211531 & 1.842404 & 0.88596795 & 1.727532 \\
5 & 31.35 & 0.85400845 & 1.08513055 & 2.2432795 & 1.04401305 & 2.0862665 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Non-linear length (NL) depending on the number \(k\) of QoS parameters. Figure 6: Number of feasible/unfeasible nodes depending on the number \(k\) of QoS parameters. * In Figure 7b, strategically placed BRs enable better coverage, as shown by the Voronoi diagram (dotted lines). Our simulations explored two scenarios: 1. _Sixty sensors with a communication range of 25_:
* BRs were initially placed at the center, and additional BRs were equitably distributed. * The first BR covered approximately _50 feasible nodes_, while multiple BRs increased coverage to 57-59 _nodes_ (out of 59). * The improvement from adding more BRs was slight since the first BR already covered most feasible nodes. 2. _One-hundred-twenty sensors with a smaller communication range (12)_:
* Initially, only _20-25 nodes_ were feasible out of 120. * Adding _2 to 4 BRs_ significantly increased feasible nodes and improved coverage in the first computed DODAG. The results are visualized in Figures 8 and 9. **Key Observations:**
* Adding BRs increases the number of feasible nodes, especially in low-connectivity settings (e.g., 120 nodes, range = 12). * Optimal BR placement leads to substantial coverage gains--up to 82 out of 120 nodes become feasible with four BRs. * For denser topologies (e.g., 60 nodes, range = 25), marginal gains are observed since the first BR already covers most nodes. * Table 9 summarizes these effects, **Interpretation of Columns. ** In Table 9, the column _\"Number of BRs\"_ represents the total number of border routers (BRs) deployed in each scenario. In contrast, the column _\"Active BRs from 4\"_ indicates how many deployed BRs were utilized to serve at least one QoS-compliant source node in the resulting DODAGs.