## 1 Introduction
However, in case \(B\) is busy but \(C\) and \(D\) are available, the AGV can advance till \(D\) and wait there for the permit to resume towards \(B\); hence, the resuming motion is initiated much closer to \(B\) than in the sparse discretization (top) case, which shortens the overall time taken when moving from \(A\) to \(B\). Figure 1: (**Top**): A grid layout (**left**) and the graph model corresponding to a sparse discretization (right). (**Bottom**): A denser discretization of the layout (**left**) and the corresponding graph model (**right**). Therefore, understanding how layout discretizations affect the performance is essential for an efficient implementation of traffic control systems in real industrial scenarios; denser discretizations can improve the time response to certain conflicts, but also result in a software overload that may hinder the overall system performance. Nevertheless, despite its criticality, to the best of the authors' knowledge, there are no studies in the zone control literature dealing with layout discretization and its effect. In fact, besides assuming that a block can entirely contain an AGV, most works just mention in the simulation section the dimensions of the zones, where squares of side 1 m [5,10,13,14] or 2 m [7] are often taken. Others, instead, indicate the number of nodes of the selected graph, but not the size of the corresponding zones [15]. Finally, ref. [16] uses a basic discretization with nodes representing crossings, workstations, and parking/charging slots, while edges stand for the aisles in between them. Intrinsically linked to the discretization effects is the control period, i.e., the time interval of activation of the traffic control algorithm loop that issues commands to the AGVs. This is because denser discretizations scale up the number of permit requests from the AGV fleet to proceed; so, dealing promptly with them using lower control periods should have a beneficial influence on the time completion of tasks. This article deals with the effect of layout discretization on the overall system performance of zone control-based traffic controllers. The analysis is conducted using two representative traffic management strategies: the Dynamic Resource Reservation (DRR) approach [10], and the recently published Improved Dynamic Resource Reservation (IDRR) algorithm [16]. The study takes into account both the density of the discretization and the control period of the traffic manager. Interestingly, realistic numerical simulations run on two different layouts reveal that denser discretizations do not result in significant performance improvements while, as intuitively expected, shorter control periods yield substantial reductions in task completion times. The remainder of the paper is organized as follows: Section 2 includes basic modeling details and concepts that are common to DRR and IDRR traffic control algorithms. The main features of DRR and IDRR are presented in Sections 3 and 4, respectively. The experimental setup, including a description of the prescribed task, is presented in Section 5. The numerical results are gathered and discussed in Section 6. The contributions of the paper, together with some suggestions for further research, are discussed in Section 7. Finally, conclusions are drawn in Section 8.