## 6 Numerical Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**AGVs** & **Data** & **IDRR** & **IDRRP** & **DRR** & **DRR-2m** & **DRR-1m** \\ \hline
1 & \(R_{1}\) & 18,923 & 27,596 & 27,589 & 27,589 & 27,589 \\ \hline
2 & \(R_{1}\) & 9293 & 13,836 & 13,899 & 13,899 & 13,899 \\  & \(R_{2}\) & 9248 & 13,661 & 13,680 & 13,680 & 13,680 \\  & Avg & 9271 & 13,749 & 13,790 & 13,790 & 13,790 \\  & Tot & 18,541 & 27,497 & 27,579 & 27,579 & 27,579 \\ \hline
3 & \(R_{1}\) & 6737 & 9364 & 9437 & 9437 & 9437 \\  & \(R_{2}\) & 6528 & 9204 & 9203 & 9203 & 9203 \\  & \(R_{3}\) & 6543 & 8978 & 9030 & 9030 & 9030 \\  & Avg & 6603 & 9182 & 9223 & 9223 & 9223 \\  & Tot & 19,808 & 27,546 & 27,670 & 27,670 & 27,670 \\ \hline
4 & \(R_{1}\) & 4841 & 6929 & 7739 & 7739 & 7739 \\  & \(R_{2}\) & 4848 & 6832 & 7036 & 7036 & 7036 \\  & \(R_{3}\) & 4840 & 6724 & 6380 & 6380 & 6380 \\  & \(R_{4}\) & 4951 & 6689 & 6220 & 6220 & 6220 \\  & Avg & 4870 & 6793 & 6844 & 6844 & 6844 \\  & Tot & 19,480 & 27,174 & 27,375 & 27,375 & 27,375 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Benchmark layout—Test 2: Travel distances (in [m]) for 1 to 4 AGVs. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**AGVs** & **T** & **IDRR** & **IDRRP** & **DRR** & **DRR-2m** & **DRR-1m** \\ \hline
1 & 1 & 12.5\% & 15.1\% & 15.7\% & 16.7\% & 21.2\% \\  & 0.5 & 7.7\% & 8.7\% & 9.1\% & 11.6\% & 15.2\% \\  & 0.2 & 4.2\% & 4.7\% & 4.9\% & 6.2\% & 9.2\% \\  & 0.1 & 2.7\% & 2.8\% & 2.9\% & 4.2\% & 5.9\% \\  & 0.05 & 2.0\% & 2.0\% & 2.2\% & 3.0\% & 3.9\% \\  & 0.02 & 1.6\% & 1.7\% & 1.8\% & 2.4\% & 2.7\% \\ \hline
2 & 1 & 13.5\% & 16.9\% & 17.2\% & 19.1\% & 23.2\% \\  & 0.5 & 8.5\% & 10.7\% & 11.4\% & 13.1\% & 17.8\% \\  & 0.2 & 4.8\% & 6.7\% & 8.0\% & 9.1\% & 11.6\% \\  & 0.1 & 3.7\% & 4.6\% & 7.1\% & 8.2\% & 8.7\% \\  & 0.05 & 3.1\% & 3.6\% & 6.7\% & 7.2\% & 7.3\% \\  & 0.02 & 2.8\% & 3.1\% & 6.5\% & 6.5\% & 6.6\% \\ \hline
3 & 1 & 15.8\% & 18.7\% & 26.4\% & 29.8\% & 31.6\% \\  & 0.5 & 10.7\% & 12.6\% & 25.3\% & 27.1\% & 27.8\% \\  & 0.2 & 8.6\% & 10.2\% & 24.5\% & 25.6\% & 26.0\% \\  & 0.1 & 7.1\% & 8.6\% & 23.6\% & 24.0\% & 24.5\% \\  & 0.05 & 6.6\% & 7.9\% & 23.5\% & 23.6\% \\  & 0.02 & 6.2\% & 6.5\% & 23.3\% & 23.5\% & 23.6\% \\ \hline
4 & 1 & 17.2\% & 20.4\% & 33.2\% & 39.4\% & 39.5\% \\  & 0.5 & 13.1\% & 16.4\% & 31.4\% & 34.2\% & 35.8\% \\  & 0.2 & 9.3\% & 11.8\% & 30.1\% & 32.7\% & 33.0\% \\  & 0.1 & 9.1\% & 11.4\% & 29.9\%Table 4 shows the distances traveled by the AGVs during the experiment. Besides confirming that IDRR-controlled systems carry out the task with minimal traveled distance, IDRRP and DRR show similar results regardless of the scaling in the number of AGVs, as both algorithms require them to start and finish a task at their own parking places. Of course, the DRR-2m and DRR-1m data match those of DRR, as the traveled distance under the same traffic control algorithm is independent of the discretization density. Instead, it can be observed in Table 5 that the average velocities share the behavior of ending and waiting times already displayed in Tables 2 and 3, respectively, with respect to discretization and the control period variation. In this case, it is also worth noting that the average velocities of IDRR and IDRRP are very similar, which is due to the fact that, despite the parking policy difference, the traffic control algorithm is the same. The same tests were run on the industrial layout and for the task rationale also described in Section 5. In this case, the ending time was replaced by the average throughput, i.e., fully completed tasks per AGV and per hour, while the other metrics (waiting time, distance, and velocity) were kept. It is worth highlighting that the results are fully aligned with those already discussed for the benchmark layout. The average throughput per AGV and per hour for a control period of \(T=1\) s is depicted in Figure 11 from the data collected in Table 6. Notice that, as expected, it decreases as the number of AGVs in the layout increases because of the scaling up of the number of conflicts in the system.