# Fine-Grained Boundary Conditions in Field-Based Routing
## 6 Performance Evaluation
### Simulation Scenarios and Parameters  
We utilize NS-2 [19] for performance evaluation, covering both outer and inner boundary conditions. We use two metrics for performance evaluation: overall packet delivery ratio (i.e., the ratio of the total number of successfully received packets at all the gateways to the total number of sent packets from all the sources) and aggregate throughput (i.e., the aggregated amount of traffic flowing from all the sources to all the gateways within a given period of time). The focus primarily lies on assessing outer boundary conditions, with performance evaluations for inner boundary conditions as a secondary aspect of our study. This approach considers that the varying potential values at inner boundary nodes, which act as drainage points for the potential field under various circumstances, can cause negatively impact field convergence, as discussed in Section 4. First, to assess the performance of the proposed outer boundary conditions inspired by the Robin boundary conditions, we consider three distinct topologies: grid regular, non-grid regular, and the practical Google WiFi network [20] topologies. Additionally, we consider scenarios where network holes, which can frequently occur in real-world network environments, are present. Specifically, for the grid regular and non-grid regular topologies, we intentionally create network holes, while for the practical Google WiFi network topology, we leverage network holes that are inherently present within the topology itself, without artificially creating new ones. It is worth noting that conducting performance evaluations for networks with holes allows us to derive results that are more representative of real-world conditions. Regarding potential values, we assign 0 as the lowest potential value to gateways, following the convention in conventional ALFA. This is because we aim to purely assess the performance improvement by the proposed outer boundary conditions. In the existing ALFA using the Dirichlet boundary conditions, a +1 potential value is assigned only to outer boundary nodes within the outermost area, indicating their highest potential value. Additionally, the highest potential value is allocated to mesh nodes where potential value calculation is not feasible due to the absence of full enclosure by triangles formed with their neighboring nodes. However, in the new version of ALFA using the proposed Robin boundary conditions, a +1 potential value is assigned to the generated virtual nodes. The new version of ALFA, with the proposed outer boundary conditions, is then compared to the existing ALFA, which utilizes the conventional Dirichlet boundary conditions traditionally used in existing field-based routing in terms of packet delivery ratio and throughput. Second, we conduct performance evaluations of the proposed inner boundary conditions. We use the non-grid regular topology as a representative case to highlight the impact on performance evaluation. The new version of ALFA, incorporating the proposed inner boundary conditions that allow each inner boundary node to have a different potential value, is compared to the existing ALFA, which utilizes the conventional boundary conditions traditionally used in existing field-based routing. In existing field-based routing, the same potential value is assigned to all the gateways acting as inner boundary nodes. As our simulation parameters, we set the maximum queue size to 100, and \(\eta\) is set to \(1\times 10^{-4}\), which is empirically obtained when the best performance is observed through various simulations. All data packets are UDP packets with 1000 bytes, and the packet generation follows a Poisson distribution with a rate under the channel bandwidth of 2 Mbps. While it is possible to set arbitrary numbers directly as the packet generation rate without any specific qualitative meaning, we introduce an offered load expressed as a percentage to determine the rate in the Poisson distribution.