## 1 Introduction
### Related Work  
To solve the rerouting/rescheduling problem, one option is to use the alternate graph method [4; 5; 6]. This is a conflict detection and resolution technique with a fixed routes sub-problem [7]. The alternate-graph method can be implemented in a real-time traffic management system, called ROMA (railway traffic optimization by means of alternative graphs) [8] with the aim of branch and bound algorithm to solve the problem. The job shop scheduling problem also can be solved by the tabu search algorithm [9], where the delays can be minimized with computing the optimal train sequence. The conflict prevention strategy (CPS) can be solved by the dynamic impact zone (DIZ) heuristic [10].  
Other solutions can be taken with the aim of a mixed linear integer programming method. In this case, the solution can be even energy-optimized with decreasing the stops of a given train in the case of a disturbance [11; 12; 13; 14]. This solution can be implemented in an OpenTrack [15] or Treno [16] simulation. OpenTrack is a real-time railway microscopic simulator that allows the execution of different traffic scenarios. The program stores the railway infrastructure, the rolling stock, and the timetable in separate databases. It uses a directed double vertex graph to describe the infrastructure, in which the edges represent the track circuits, and nodes are generally signals, switches, etc. It is possible to give orders to the program during the real-time simulation via the application programming interface (API), such as stopping a train, decelerating a train or choosing another possible route. With the aim of this interface, the solution of the MADRL method can execute. Trenissimo is a synchronous, microscopic, and dispatcher-driven simulator for railway scheduling. This tool offers a flexible way to solve the traffic management problem based on research and project-specific data. It is possible to simulate the driver behavior, and different signaling systems can estimate the secondary delays in the case of disturbance.  
In this simulation, interlocking specific attributes can be considered, such as route setting time and switching time. Computing with the driver performances is also possible. This problem can also be written as a mixed nonlinear programming problem [17].  
The authors of [18] propose an off-line procedure utilizing the microscopic and stochastic simulation for managing disruption considering travel demand and service operation. The application of the proposed method on the Naples metro line showed improved service quality. Ref. [19] proposes a neighborhood search algorithm to find intervention strategies in the case of metro system failures. The results indicated the feasibility of the proposed method tested on a real-world metro system. For a more comprehensive study on the matter, see [20], which details the different models and algorithms used for solving the dispatching and rescheduling tasks.  
Besides the above-mentioned methods, artificial-intelligence-based solutions may help solve complex strategic tasks. For example, it can provide an effective way to solve the reordering and rescheduling problem. It can originate from a tree search procedure. With the aim of Monte Carlo tree search algorithms, it is possible to find a conflict-free solution in a fast way [21]. Due to the complexity of the railway infrastructure--properties, safety regulations, modeled vehicles--a simplified model can be used. The Flatland environment offers a simple grid model [22] with a multi-agent method. In the case of high-speed railways, the timetable rescheduling task--if there is disturbance--also can be solved with this method [23]. Dispatching problems using graph theory with a deep Q-network (DQN) for rescheduling also can be solved [24]. In some particular cases--e.g., closed subway systems--the Q-learning algorithm is appropriate to provide an energy-optimal solution [25].