# Offloaded Computation for QoS Routing in Wireless Sensor Networks
## 5 Theoretical and Experimental Evaluation
### Experimental Evaluation
#### 5.4.1 Experimental Setup  
This subsection presents the experimental configuration used to evaluate the proposed approach. The setup includes the routing algorithms, simulation environment, and the variable parameters used across different scenarios.  
**Compared Methods.** Three routing strategies were evaluated:  
* **EX**: The proposed offloaded computation framework constructs QoS-compliant conflict-free DODAGs based on centralized multi-constrained path computation.
* **H\({}_{1}\)**: A heuristic baseline inspired by [46], where auxiliary weights are derived and a shortest-path tree is constructed using additive metrics.  
* **H\({}_{2}\)**: A heuristic approach based on [17], in which each node selects its parent based on the minimum cumulative non-linear path length to the BR. All three strategies were implemented in C++ using the LEDA graph library [63]. This ensured consistent data structures, path models, and execution environments across all the experiments for fair comparison.  
**Network and QoS Settings.** The simulations were conducted on synthetic WSN topologies under the following assumptions:  
* Node coordinates were randomly distributed within a square region.
* Communication links were created between nodes within a fixed communication range.
* Each link was assigned \(k\) uncorrelated additive QoS parameters uniformly drawn from the interval \((0.0,5.0)\).
* The number of QoS parameters \(k\) and the threshold vector \(\vec{L}=(L_{1},L_{2})\) were varied to simulate different levels of constraint tightness and metric dimensionality.
* The number and placement of BRs were modified across experiments to explore topological effects on feasibility and coverage.
* **Definition of Path Length.** In this context, _path length_ refers to the **non-linear additive cost** of a routing path, not the simple hop count. Specifically, this metric is computed by aggregating multiple QoS parameters (e.g., delay and ETX) in a weighted or non-linear fashion, as described in our methodology. Consequently, the resulting values may be fractional even though the underlying topology is discrete. This allows us to more accurately represent the performance of different routing strategies under multi-constrained QoS formulations.  
For example, in one scenario, two additive QoS parameters (\(k=2\)) were used with threshold vectors such as \(\vec{L}=(9.0,11.0)\) and \(\vec{L}=(12.0,14.0)\), representing tight and relaxed constraint configurations, respectively.  
**Interpretation of Thresholds.** It is important to emphasize that the values in \(\vec{L}\) represent end-to-end cumulative constraints over an entire path, not per-link limits. Since link metrics are additive, as formally defined in RFC 6551 [49], the total cost of a path is the sum of its individual link values. Therefore, even though each link metric lies within \([0.0,5.0]\), a feasible path comprising 3 to 6 hops can naturally yield an aggregate QoS cost between 9 and 30. For example, a 4-hop path with an average per-link delay of 3.5 will accumulate an end-to-end delay of approximately 14. This threshold model aligns with the multi-constrained routing formulations used in the SAMCRA and TAMCRA algorithms [52], which verify path feasibility based on cumulative metric sums. Similar additive thresholding strategies are employed in recent work by [PERSON] et al. [17; 59], where constraints represent total end-to-end limits rather than per-hop boundaries.  
This setup enables a comprehensive analysis of the performance and scalability of the proposed method under diverse and realistic WSN operating conditions.