## 6 Numerical Results
\begin{table}
\begin{tabular}{r r r r r r} \hline
**AGVs** & **IDRR** & **IDRRP** & **DRR** & **DRR-2m** & **DRR-1m** \\ \hline
1 & 20,139 & 29,627 & 29,651 & 31,166 & 32,293 \\
2 & 10,668 & 15,833 & 15,973 & 16,524 & 16,911 \\
3 & 7818 & 10,881 & 12,992 & 13,644 & 13,991 \\
4 & 6022 & 8427 & 13,027 & 13,812 & 14,192 \\
5 & 5249 & 6989 & 14,952 & 14,326 & 14,203 \\
6 & 4732 & 6025 & 15,118 & 15,213 & 15,289 \\
7 & 4404 & 5403 & 14,224 & 15,438 & 15,974 \\
8 & 4068 & 4985 & 14,990 & 14,953 & 14,941 \\
9 & 3979 & 4759 & 16,080 & 15,601 & 15,528 \\
10 & 3957 & 4677 & 15,306 & 15,889 & 16,143 \\ \hline \end{tabular}
\end{table} 
Table 1: Benchmark layout—Test 1: Ending times (in [s]) for \(T=1\) s, for 1 to 10 AGVs. These results are further confirmed by the data in Tables 3-5. Namely, Table 3 contains the waiting time, i.e., the fraction of time (in %) in which AGVs have been in a waiting state during the overall task execution. Higher waiting times indicate a worse utilization of AGVs and, consequently, higher ending times. As expected, IDRR has the lower numbers; the % waiting time increases for IDRR, as AGVs have to add the extra path from drop-off to parking stations after each trip, but it is still under that of DRR because of the traffic \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 & 20,139 & 29,646 & 29,651 & 31,166 & 32,293 \\  & 0.5 & 19,508 & 28,713 & 28,717 & 29,207 & 29,394 \\  & 0.2 & 19,428 & 28,594 & 28,598 & 28,690 & 28,779 \\  & 0.1 & 19,133 & 28,152 & 28,155 & 28,180 & 28,214 \\  & 0.05 & 19,018 & 27,978 & 27,982 & 27,988 & 27,998 \\  & 0.02 & 18,980 & 27,924 & 27,925 & 27,924 & 27,932 \\ \hline
2 & 1 & 10,668 & 15,833 & 15,973 & 16,524 & 16,911 \\  & 0.5 & 9961 & 14,787 & 15,258 & 15,335 & 15,362 \\  & 0.2 & 9642 & 14,342 & 15,001 & 15,067 & 15,090 \\  & 0.1 & 9587 & 14,230 & 14,937 & 14,975 & 14,996 \\  & 0.05 & 9563 & 14,189 & 14,915 & 14,939 & 14,943 \\  & 0.02 & 9560 & 14,180 & 14,900 & 14,904 & 14,907 \\ \hline
3 & 1 & 7818 & 10,881 & 12,992 & 13,644 & 13,991 \\  & 0.5 & 7301 & 10,180 & 12,885 & 13,038 & 13,098 \\  & 0.2 & 7043 & 9836 & 12,798 & 12,916 & 12,965 \\  & 0.1 & 7015 & 9794 & 12,743 & 12,772 & 12,801 \\  & 0.05 & 6993 & 9752 & 12,725 & 12,744 & 12,755 \\  & 0.02 & 6982 & 9721 & 12,713 & 12,724 & 12,729 \\ \hline
4 & 1 & 6022 & 8427 & 13,027 & 13,812 & 14,192 \\  & 0.5 & 5617 & 7876 & 12,979 & 13,266 & 13,338 \\  & 0.2 & 5434 & 7582 & 12,894 & 13,105 & 13,163 \\  & 0.1 & 5398 & 7564 & 12,859 & 12,932 & 12,979 \\  & 0.05 & 5384 & 7534 & 12,798 & 12,853 & 12,887 \\  & 0.02 & 5365 & 7504 & 12,770 & 12,789 & 12,803 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Benchmark layout—Test 2: Ending times (in [s]) for different \(T\) and 1 to 4 AGVs. Figure 10: Benchmark layout—Test 2: Percentage (%) of relative improvement in ending times for \(T=0.5\) s (black), \(0.2\) s (dark grey), \(0.1\) s (grey), \(0.05\) s (light grey), \(0.02\) s (white) with respect to \(T=1\) s, and \(1\) to 4 AGVs. management policy. In turn, the more densely discretized DRR-2m and DRR-1m have slightly worse results than DRR because of the extra permission requests, which are not compensated by the time saved in conflict resolutions. In turn, the waiting time percentage decreases with the control period, \(T\), showing a tendency to stabilization around \(T=0.02\) s.