# Fine-Grained Boundary Conditions in Field-Based Routing
## 7 Conclusions and Future Work  
In this paper, we propose new fine-grained boundary conditions for field-based routing protocols as a promising enabler to enhance their applicability in both present and future industrial WMNs. These proposed boundary conditions include novel outer boundary conditions inspired by Robin boundary conditions in physics and inner boundary conditions reinterpreted from Dirichlet boundary conditions in physics. Additionally, we introduce the concept of virtual nodes to implement these new fine-grained boundary conditions. Ultimately, our proposed boundary conditions significantly improve routing performance. Rigorous simulations conducted on various network topologies, including practical examples like Google WiFi mesh networks, as well as grid regular network topologies, demonstrate that field-based routing with these fine-grained boundary conditions outperforms existing protocols using coarse-grained boundary conditions. Regarding the outer boundary conditions, in the grid regular network topology scenario, a maximum performance difference of 48% in the overall packet delivery ratio was observed. In the non-grid regular topology scenario, gains of 200 Kbps and 17% were observed in overall packet delivery ratio and aggregate throughput, respectively. In the case of Google WiFi network topology, significant improvements of over 1000 times in terms of the same metrics were observed. On the other hand, regarding the inner boundary conditions, an approximate increase of 10% in overall packet delivery ratio and 130 Kbps in aggregate throughput was achieved.  
However, it is important to recognize the limitations of our study. One of the key limitations is the absence of an explicit method to determine the optimal value of \(\eta\), which represents sensitivity to the number of packets in the queue of mesh nodes. Currently, this parameter tuning heavily relies on empirical results obtained through extensive simulations. Moreover, it is noteworthy that dealing with this challenge is not unique to our study, but is a common issue in algorithms with tuning parameters.  
Moving forward, in the context of future research directions, we recognize the imperative need to explore alternative methods for determining the optimal value of \(\eta\) without solely relying on empirical results obtained through extensive simulations. One possible avenue of exploration involves investigating heuristic configurations that assign varying weights based on network traffic load or queue lengths. This approach, although it may seem immature, may lead to more advanced research efforts aimed at discovering superior methodologies for parameter optimization.  
Figure 9: Performance according to the kind of inner boundary conditions in the non-grid regular topology. (**a**) Overall packet delivery ratio; (**b**) Aggregate throughput.  
**Author Contributions:** Conceptualization, J.S.; methodology, J.S.; validation, J.S.; formal analysis, J.S. and Y.K.; investigation, J.S. and Y.K.; resources, J.S. and Y.K.; data curation, J.S. and Y.K.; writing--original draft preparation, J.S.; writing--review and editing, J.S. and Y.K.; visualization, J.S.; supervision, Y.K.; funding acquisition, Y.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are contained within the article.  
**Conflicts of Interest:** The authors declare no conflicts of interest.