## 1 Introduction
The comparisons and issues regarding unidirectional and bidirectional flow paths are described by [PERSON] and [PERSON] [6]. Flow paths based on loops can include single loop, multi loops, or segmented zones. In this case, the AGVs control is relatively simple. [PERSON] et al. [7] propose an integer programming formulation to design a loop material flow system. [PERSON] and [PERSON] [8] propose a tandem loop with multiple vehicles. The segmented flow path approach was proposed by [PERSON] and [PERSON] [9]. Transportation system layouts are very often arranged into regular shapes [4], e.g., at warehouses or container terminals. It can be described as a mesh-like path ([PERSON] and Hsu [10]) or a square topology ([PERSON] [11]). The most important issue to solve for any type of flow paths is to manage the AGVs deadlock states. There are three major approaches described by [PERSON] et al. [12]  
* deadlock detection and resolution by online detection and recovery from deadlock states;
* deadlock prevention by specifying online how a process can allocate resources;
* deadlock avoidance by online analysis of current state information to control how a process can allocate resources. Many authors have proposed different methods for the deadlock state resolution in the operation of AGVs. [PERSON] and [PERSON] [13] propose a centralized deadlock avoidance algorithm. This approach is based on a Petri net model of concurrent job flow and dynamic resource allocation. In this algorithm, the production sequences are divided into zones in which resources are shared or not. The deadlock avoidance problem is solved by defining a restriction policy. [PERSON] [14] introduces a structural online control policy for automated manufacturing systems which guarantees that the execution of an operation (an elementary step of a job) does not lead to a deadlock. [PERSON] et al. [15] propose a real-time and distributed algorithm for both collision and deadlock avoidance. [PERSON] et al. [16] present an algorithm for decentralized control of multiple AGVs. Conflict resolution is based on a vehicle priority scheme. [PERSON] et al. [17] propose a distributed approach to AGV system control. The vehicle team must autonomously reach a consensus on the division of the set of tasks in the approach to zone control. [PERSON] et al. [18] present a methodology for the implementation of a mobile robot in adaptive manufacturing environments. It is based on a mathematical model and a genetic algorithm-based heuristic. [PERSON] et al. [19] propose a collision and deadlock prevention method with a traffic sequence optimization strategy for the unidirectional guide-path network-based AGVs. This method is based on the semaphore theory and Internet of Things (IoT) positioning technology. To avoid cycle deadlocks an algorithm based on the digraph theory is developed. [PERSON] et al. [20] introduce a method based on the design of square topology, chains of path planning reservations, and dynamic task priority of the logistics workshop, which effectively utilizes environmental resources of the workshop to avoid collision and to solve deadlocks. [PERSON] et al. [21] provide a reference source in the robust supervisory control policies for automated manufacturing systems with unreliable resources that may fail. Robust control in the supervisory control area addresses deadlock when some reliable resources unexpectedly fail to work. [PERSON] et al. [22] focused their research on the modeling and fault-tolerant control of multiple AGVs in a high-storage warehouse. They developed a mathematical description of a set of multiple AGVs along with an algorithm that can generate an optimum sequence. [PERSON] et al. [23] propose a centralized control method for routing and scheduling a fleet of autonomously guided vehicles. This method maintains a central schedule, which ensures provably conflict-free control of a large fleet of vehicles in almost any layout. [PERSON] et al.