# Heuristic Routing Algorithms for Time-Sensitive Networks in Smart Factories
## 6 Performance Evaluation
### Non-TT Flow Routing Experiment  
In order to verify the effectiveness of Algorithm 2, as proposed in this paper, we developed a non-TT routing test program, which is available online at [57]. The simulation  
Figure 14: Convergence curves of the four algorithms when solving the same MTSP problem.  
Figure 13: The effect of changing the number of salesmen on \(min(T)\) when using Algorithm 1.  
parameters are shown in Table 3. Likewise, we performed each experiment 30 times and took the average result as the final result to minimize misguidance caused by randomness.  
We simulated a case of sending \(m\) non-TT flows from industrial sensors to a data server and compared the AACO to two other routing algorithms, as depicted in Figure 15. To make the visualization more intuitive, we chose the smaller \(m\) value of 5 and set the starting and end nodes as the two farthest nodes within the network. The starting node was labeled with a diamond and the end node with a pentagram. The route of each non-TT flow was represented by a line segment, which were distinguished from each other by color.  
We developed a routing program based on the SPB algorithm proposed by [20] and the route obtained is depicted in Figure 15a. Since the routes planned by SPB for each non-TT flow are always the shortest solution, when the source node and the destination node were the same for all \(m\) flows, the obtained multiple paths completely coincided. In addition, we made appropriate modifications for our problem model based on the LB-DRR method proposed by [PERSON] et al. [19]. The results of the LB-DRR algorithm are depicted in Figure 15b. For LB-DRR, the routes never overlapped with other routes when there were other options. In contrast, the route scheme generated by Algorithm 2 from this paper was more balanced and reasonable.  
When a flow chose to detour, the more SWs the route passes through, the longer the processing and propagation delays. We defined the sum of processing and propagation delays as the detouring delay. In addition, from the simulation results presented in Section 6.1, we obtained the correspondence between queuing delay and the number of queuing flows, so we could estimate the queuing delay. We counted the average total delay from multiple experiments to evaluate the algorithm performances, as depicted in Figure 16. The results showed that the SPB, which pays attention to the shortest path, had  
Figure 15: Comparison of the three algorithms for non-TT routing: (**a**) routes assigned by the SPB; (**b**) routes assigned by the LB-DRR; (**c**) routes assigned by the AACO.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline Symbol & Value & Description & Remarks \\ \hline \(n\) & 100 & The number of SWs in the non-TT network & Can be selected by the user \\ \(Z\) & 80 & The number of ants in each colony & Parameter of the algorithm \\ \(Q\) & 2 & The pheromone increment constant & Parameter of the algorithm \\ \(C_{0}\) & 2 & The initial pheromone constant & Parameter of the algorithm \\ \(I_{max}\) & 800 & The maximum number of iterations & Parameter of the algorithm \\ \(\alpha\) & 1 & The pheromone impact factor & Parameter of the algorithm \\ \(\beta\) & 5 & The heuristic impact factor & Parameter of the algorithm \\ \(\rho\) & 0.5 & The pheromone volatile factor & Parameter of the algorithm \\ \(\gamma\) & 0.05 & The stronger ant colony impact factor & Parameter of the algorithm \\ \hline \hline \end{tabular}
\end{table}
Table 3: The non-TT routing simulation parameters.  
the best detouring delay but the queuing delay was too long, resulting in the longest total delay. The LB-DRR, which focuses on load balancing, had the best queuing delay but due to too many detours, results were also unsatisfactory. The AACO algorithm proposed in this paper comprehensively considered a balanced distribution along with the optimization of routes; thus, the total delay was the shortest and the optimization effect was the best.