# GraphSAGE-Based Multi-Path Reliable Routing Algorithm for Wireless Mesh Networks
## 3 Multi-Path Routing Algorithm Based on the Improved Breadth First Search
### Multipath Output
\[u_{ij}=\frac{1}{\sum\limits_{k=1}^{c}{\left(\frac{d_{ij}}{d_{k}}\right)^{\frac{ 2}{m-1}}}} \tag{4}\]9 Packet loss rate at different data sending rates. \[c_{i}=\frac{\sum\limits_{j=1}^{n}{{u_{ij}}^{m}x_{j}}}{\sum\limits_{j=1}^{n}{{u_ {ij}}^{m}}} \tag{5}\]0 Average end-to-end delay at different data-sending rates. To study the effect of topology size on algorithm performance, the data sending rate is fixed at 70 packets/s and the number of topological nodes is increased from 4 to 28. The experimental results are shown in Figures 10-12. Figure 10 explains the average end-to-end delay with a different number of topological nodes. The figure illustrates that as the number of topological nodes increases the average end-to-end delay of the shortest path algorithm first increases and then levels off, while the ECMP algorithm and the proposed algorithm first decrease and then level off. Figure 11 shows the packet loss rate with a different number of topological nodes. In this figure, the variation of packet loss rate with topological nodes follows the same trend as the average end-to-end delay in \[c_{i}=\frac{\sum\limits_{j=1}^{n}{{u_{ij}}^{m}x_{j}}}{\sum\limits_{j=1}^{n}{{u_ {ij}}^{m}}} \tag{5}\]1 Figure 12 indicates that the throughput of the shortest path algorithm decreases first and then levels off as the number of topological nodes increases. The results show that the shortest path routing algorithm gives the worst network performance due to selecting only one shortest path for data transmission, which is prone to network congestion. When the number of topological nodes is small, the available shortest paths are also very few, so the proposed algorithm cannot exert its ability to dynamically select the optimal path and the network performance is poor. However, the ECMP algorithm can spread the traffic to different paths for transmission, with better network performance, which is more suitable for simple topologies with a small number of nodes. When the number of topological nodes is bigger, the network performance of the proposed algorithm is better and less volatile compared with the ECMP algorithm. The proposed algorithm analyses multi-attribute parameters such as traffic, packet loss rate, and transmission delay, which can dynamically select the optimal path according to the network performance, effectively alleviate network congestion and improve network performance. \[c_{i}=\frac{\sum\limits_{j=1}^{n}{{u_{ij}}^{m}x_{j}}}{\sum\limits_{j=1}^{n}{{u_ {ij}}^{m}}} \tag{5}\]2 Throughput at different data sending rates. \[c_{i}=\frac{\sum\limits_{j=1}^{n}{{u_{ij}}^{m}x_{j}}}{\sum\limits_{j=1}^{n}{{u_ {ij}}^{m}}} \tag{5}\]3 Packet loss rate at different topology sizes. \[c_{i}=\frac{\sum\limits_{j=1}^{n}{{u_{ij}}^{m}x_{j}}}{\sum\limits_{j=1}^{n}{{u_ {ij}}^{m}}} \tag{5}\]4 Throughput at different topology sizes. \[c_{i}=\frac{\sum\limits_{j=1}^{n}{{u_{ij}}^{m}x_{j}}}{\sum\limits_{j=1}^{n}{{u_ {ij}}^{m}}} \tag{5}\]5 Average end-to-end delay at different topology sizes. To study the effect of channel environment on network performance, WiFi5, and WiFi6, the two latest WiFi protocols, are used as the physical layer protocol of WMN for simulation, respectively. In terms of modulation mode, WiFi6 supports 1024-QAM and WiFi5 supports 256-QAM. In the simulation, the two protocols both operate in a 5 GHz frequency band. As shown in Figure 13, there is no significant difference in network performance for the two-channel environments at different data-sending rates. This shows that the proposed algorithm has good performance in different channel environments and can be applied to various channel environments. ## 6 Conclusions

This paper proposes a reliable routing algorithm to address the problems that traditional routing algorithms have low network resource utilization and are difficult to guarantee the reliability of transmission in real networks.