## 1 Introduction  
The trend of using AGVs for material handling in Flexible Manufacturing Systems (FMS) has recently increased, and it is expected to grow in the coming years [1]. Hence, Multi-AGV (MAGV) fleets are playing a vital role in enhancing the efficiency and robustness of the logistic processes in factories and, consequently, their study has become a major research interest [1, 2]. MAGV systems require a coordinated motion of their components to guarantee a timely and deadlock-free completion of all transportation tasks. Those in charge of keeping this so-called liveness [3] of the system are traffic control algorithms, which may achieve this major goal following three basic approaches [4, 5]: (i) conflict avoidance, where AGVs plan conflict-free routes; (ii) conflict prevention, where specific rules are applied during route executions to ensure a conflict-free operation, and (iii) detection and resolution, where conflicts are resolved when they occur. In turn, the traffic control implementation is centralized, when it is managed by a single computer, or decentralized, with decisions taken by the different system components [6]. Centralized strategies may lead to high computational loads on the central controller when the system is scaled up, while decentralized ones may result in sub-optimal solutions [1, 6]. Among the different types of traffic control algorithms (see, for example, the thorough classifications in [7, 8]), zone control has emerged as the prevailing traffic management technique [9]. In zone control approaches, the workspace is divided into a number of zones, also known as resource points [10] or tiles [11]. Then, AGVs traverse through these zones supervised by the traffic control algorithm, which gives the permissions to move from one zone to the next one, adjacent to it, on their planned paths. This discretizationallows to model the layout as a graph, which simplifies not only route planning tasks but also route execution. This is because the traffic controller awards permissions to resume according to the occupancy level of the zones, now graph nodes, in order to prevent collisions and deadlocks. Zone partitioning in irregular layouts has been studied in [12], where a zone control algorithm considering AGV geometry and guidepath topology that efficiently handles collision and deadlock avoidance is proposed. However, most zone control algorithms are presented for grid-like layouts and assume that AGVs fit within the tiles [5; 7; 10; 13; 14; 15; 16], which is taken as the starting point of this work. Notice, firstly, that the same grid layout allows different discretizations. This is illustrated in Figure 1: the layout on the top left can be discretized in a basic way, just taking crossings as nodes, as shown in the top-right figure, or using a denser discretization, as depicted in the bottom plots. Therefore, since permits can be neither requested nor given instantaneously, and waiting states may take place farther or closer to troubled nodes depending on the discretization level, the performance metrics of the system may be affected by the type of discretization. This is even more relevant in industrial scenarios, where aisles between crossings may be tens of meters long. Take, for example, the situation in Figure 2. In the sparse discretization depicted on top, an AGV moving from \(A\) to \(B\) has to wait at \(A\) till \(B\) is cleared, and moves straightforward to it when allowed. Instead, in the case of a denser discretization, such as that on the bottom, the motion is from \(A\) to \(C\), then from \(C\) to \(D\), and, finally, from \(D\) to \(B\), which requires calling the traffic controller at each step in order to obtain the corresponding permit. This scales up not only the permit requests, but also the amount of communications in the network and the deceleration and acceleration maneuvers when arriving and leaving a zone, thus yielding extra power consumptions for the AGVs.