# 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
After outputting all shortest paths by the multi-path routing algorithm based on the improved breadth-first search, we use path selection based on the available bandwidth method and the GraphSAGE-based performance optimization algorithm for optimal path selection, respectively, and compare the network performance between the two selection methods at different data sending rates. The experimental results are shown in \[u_{ij}=\frac{1}{\sum\limits_{k=1}^{c}{\left(\frac{d_{ij}}{d_{k}}\right)^{\frac{ 2}{m-1}}}} \tag{4}\]7 The figure shows that there is little difference between the two methods when the data-sending rate is low. This is because the amount of data has not reached the bandwidth capacity. When the data sending rate is higher, the GraphSAGE-based performance optimization algorithm has a lower average end-to-end delay and packet loss rate, and greater throughput. The GraphSAGE-based performance optimization algorithm considers multiple network performance metrics and can select transmission paths more accurately. Overall, the GraphSAGE-based performance optimization algorithm can effectively evaluate the network status, optimize the selection of transmission paths, and improve the network performance. In order to verify the actual performance of the proposed GraphSAGE-based multi-path reliable routing algorithm, the proposed algorithm is evaluated from the effects of data sending rate, topology size, and channel environment on the network performance, respectively. The traditional shortest path routing algorithm and the Equal-Cost Multi-Path routing (ECMP) [27] are selected as the comparison algorithms to evaluate the performance of the proposed algorithm. To study the effect of data sending rate on algorithm performance, the data sending rate is increased from 10 packets/s to 100 packets/s. The experimental results are shown in Figures 7-9. Figure 7 explains the average end-to-end delay at different data-sending rates. The figure indicates that the average end-to-end delay is increasing as the data-sending rate increases. Figure 8 illustrates that as the data-sending rate increases, the packet loss rate also increases. Figure 9 shows the relationship between throughput and data sending rate, where throughput increases and then levels off as the data sending rate increases. When the data sending rate is low, there is no significant difference in the performance of the three algorithms because the amount of data has not yet reached the bandwidth capacity and the network status is good. However, when the data sending rate is higher, the proposed algorithm outperforms the two comparison algorithms in terms of network performance metrics such as average end-to-end delay, packet loss rate, and throughput. \[u_{ij}=\frac{1}{\sum\limits_{k=1}^{c}{\left(\frac{d_{ij}}{d_{k}}\right)^{\frac{ 2}{m-1}}}} \tag{4}\]8 (**a**) Average end-to-end delay at different data sending rates. (**b**) Packet loss rate at different data sending rates. (**c**) Throughput at different data sending rates. This is because the traditional shortest path routing algorithm can select only one shortest path for data transmission, which is prone to network congestion. Although the EMCP algorithm can perform multi-path transmission, it only spreads the traffic to different paths for transmission, which is likely to worsen the congestion for the paths that have already been congested. Instead, the proposed algorithm can not only obtain all the shortest paths from the source to the destination, avoiding the limitation that the traditional shortest path algorithm can select only one path for transmission but also dynamically select the optimal path according to the network performance, effectively alleviating network congestion. Moreover, as the data-sending rate increases, the performance improvement of the proposed algorithm becomes larger and larger, which effectively improves the network performance, reduces average end-to-end delay and packet loss rate, and increases throughput.