## 5 Proposed Methodology
### Process Modelling Methodology
#### 5.3.2 Model Synthesis and Operation Procedure
* Representation of system topology. In particular, the way models of the specific entities are interconnected in order to represent the flows of information, materials and other resources in the system is defined according to the topology and the geometry of the real system. The interactions between entities are important for the simulation, as they increase modelling power, controllability, represent realistic cases and through the addition of randomness may lead to different outputs through the reach of different states. This step mainly allocates the structure of the overall system model, using as structural components the individual models of the entities composing it and defines the flows of material and data in the system. Flows of information are critical for the operation of the model as a digital twin, as the different services exchange different types of information in real time. * Split of the system in subsystems with common production and operation characteristics (e.g., transfer lines, and parallel machines). Each subsystem may consist of multiple entities (for example, process stages) and in this stage, the internal structure of each subsystem is confirmed, and the operational limits of each subsystem are defined. This is an iterative process that splits the overall system in subsystems with common operational characteristics. * Definition of the industrial system type. Not all subsystems share common characteristics and these characteristics play significant role on the way system is analysed and studied. In the current research, two major types of production systems are considered, transfer lines and parallel machines in production stages. In the case of a  
Figure 2: Petri net model building procedure. transfer line, scheduling is common for all machines composing it and all parts visit machines mandatorily and with the same sequence. In this case, only the schedule for the first machine has to be provided. When in certain production stages there are parallel machines, that can perform the same operation (with constraints or not), the sub-schedule should be provided per machine (since parallel machines share the parts they have to process). For simplicity reasons, in the current research, production systems can be considered parts (segments) of the above-mentioned types and for each part, the respective strategy will be followed. Generally, the problem can become more complicated when routing flexibility is considered, as in this case, the schedule per machine can be totally individualized. * Construction of the Petri net models of the individual entities. In order for this to become possible, the complexity and the exact structure of the models has to be defined with respect to the events that occur in the system and changes of its state as well as of their characteristics. For example, the number of different types of processes performed in an entity as well as their sequence has to be defined in this stage. For this reason, the applied policies and strategies, such as the schedules calculated from optimisation algorithms, or rules or heuristic methods, have to be taken into account. Orders should be fed to the respective machines or lines in given sequences. Generally, the events considered can be of different categories, as some of them are fully controllable (e.g., change of process performed in a machine, and machine setup), some are partially controllable (preventive maintenance that should be considered in a given time window), while others are not at all controllable (e.g., machine breakdowns, raw material shortage or external to the system events) and change the state of system not in the direction of improving its performance. Non-controllable events cannot be modelled accurately and are approached using distributions that give partially satisfactory results with respect to previous data. * Construction of the structure of the overall system Petri net model with respect to the respective models of the entities. This is a typical bottom-up modelling approach.