## 7 Discussion and Future Work  
The numerical results show that, although it may be tempting to use denser discretizations hoping that this would yield a reduction in waiting times associated with conflict prevention and detection and resolution, it turns out that this is compensated by the cumulative waiting times associated with the higher number of permission requests inherent to node-to-node displacements, up to the point that no significant benefit is observed from the use of denser discretizations. As denser discretizations also require higher energy consumptions because of the scaling up in communications and acceleration/deceleration maneuvers, sparse discretizations should be prioritised in industrial implementations of zone control approaches. In turn, a noticeable improvement arises when using faster control periods for the allocation mechanism loop. However, this may increase the computational burden and require better and more expensive hardware, so a trade-off should be required. Interestingly, a practical control period can be determined according to the hardware used for localization of the AGVs; since knowing the position of AGVs is an integral part of the system, the control period can be calculated, setting it some 5 to 10 times slower than the sensor data measuring frequency. Usually, localization sensors work in the range of \([20,50]\) Hz, so a control period of 0.2 s seems to be practically achievable in real manufacturing systems. Current limitations when implementing zone control-based approaches stem from the common assumption that the workspace is able to accommodate the AGV kinematic constraints. In real scenarios, issues may arise if the motion trajectories followed by the AGVs do not consider either self-kinematics or those of potential nearby AGVs. This is usually solved when modeling the layout while setting up the system, but a \"kinematic-aware\" approach [12] can further improve the system performance. Another restriction is linked to the fact that these strategies are mainly devised for point-to-point displacements; in cases where there exist tasks with complex interdependency, specific rules have to be taken into account at the task allocation level without hampering the traffic management \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**AGVs** & **T** & **IDRR** & **IDRRP** & **DRR** & **DRR-2m** & **DRR-1m** \\ \hline \multirow{3}{*}{\(1\)} & 1 & 45.0 & 36.4 & 36.4 & 33.4 & 33.2 \\  & 0.5 & 53.4 & 38.0 & 38.0 & 37.6 & 36.0 \\  & 0.2 & 55.6 & 39.0 & 39.0 & 38.8 & 37.6 \\  & 0.1 & 56.0 & 39.0 & 39.0 & 39.0 & 39.0 \\  & 0.05 & 56.2 & 39.2 & 39.2 & 39.2 & 39.2 \\  & 0.02 & 56.4 & 39.2 & 39.2 & 39.2 & 39.2 \\ \hline \multirow{3}{*}{\(2\)} & 1 & 43.4 & 32.4 & 32.2 & 30.2 & 29.6 \\  & 0.5 & 51.0 & 37.2 & 37.0 & 34.8 & 32.0 \\  & 0.2 & 53.0 & 38.2 & 38.0 & 36.0 & 33.2 \\  & 0.1 & 53.4 & 38.6 & 38.0 & 36.4 & 34.2 \\  & 0.05 & 53.4 & 38.8 & 38.2 & 36.6 & 34.4 \\  & 0.02 & 53.6 & 38.8 & 38.2 & 36.6 & 34.4 \\ \hline \multirow{3}{*}{\(3\)} & 1 & 39.6 & 30.4 & 29.0 & 27.0 & 25.6 \\  & 0.5 & 47.6 & 34.4 & 32.8 & 30.2 & 27.0 \\  & 0.2 & 52.4 & 35.8 & 33.8 & 31.4 & 28.6 \\  & 0.1 & 53.0 & 36.4 & 33.8 & 32.2 & 29.4 \\  & 0.05 & 53.2 & 36.8 & 34.0 & 32.6 & 30.0 \\  & 0.02 & 53.2 & 36.8 & 34.0 & 32.6 & 30.0 \\ \hline \multirow{3}{*}{\(4\)} & 1 & 38.4 & 29.8 & 27.8 & 24.2 & 22.2 \\  & 0.5 & 45.0 & 32.6 & 31.0 & 26.8 & 23.8 \\  & 0.2 & 47.8 & 33.6 & 32.4 & 28.0 & 25.2 \\  & 0.1 & 48.8 & 34.0 & 32.4 & 28.4 & 25.4 \\  & 0.05 & 49.2 & 34.2 & 32.6 & 28.6 & 25.6 \\  & 0.02 & 49.4 & 34.2 & 32.6 & 28.6 & 25.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Industrial layout—Test 2: Average throughput per AGV and per hour for different \(T\) and \(1\) to \(4\) AGVs. policy. Finally, the traffic control approach is closely linked to the geometric layout of the factory. In particular, IDRR is unable to handle non-grid-like layouts, as well as situations where WP stations have multiple CPs or are adjacent to each other.