## 3 Relative Literature
### Process Modelling and Simulation  
The main objective of a process model is to develop a scientific understanding through quantitative expressions of knowledge of a system by displaying what we know, but may also reveal things that we do not know. It is also ideal for testing the effects of changes in a system, making predictions and helping in decision making, including both tactical decisions by managers as well as strategic decisions by planners. In order to underline the significance and the widespread application of the process modelling and simulation approaches in the present industrial and social systems, some of the most popular and promising application areas, as specified from our extensive research and academic activity on the domain of digital twins and applications, are highlighted. * **Smart Industries**: Cyber physical systems manage processes and monitor each other, while interconnected software manages the local operating and interacting parts (entities) of a company. * **Global Virtual Factories**: Network of businesses from multiple regions that resolve the issues of processes, dependencies and interrelations, data and material flows between companies and between customers and suppliers. * **Asset Performance Management**: Improved reliability and performance of equipment and assets is achieved through better visibility, availability and predictability enabled from tools and algorithms from different scientific fields. * **Process and Quality Improvement**: Yield and productivity of manufacturing operations is optimized, covering the operations from design through warranty support. * **Resource Efficiency Optimisation**: Optimising energy efficiency, facility productivity, product reliability, quality, safety and yield, while reducing costs, resource idleness and production time. * **Supply Chain Optimisation**: Improving visibility and insights to build a dynamic supply chain that accelerates innovation, efficiency and performance taking advantage of resources and state-of-the-art technologies. * **Predictive Maintenance**: The condition of in-service equipment is monitored and evaluated in order to estimate when maintenance should be performed with the intention to minimize the consequences from equipment disorders (such as loss of productivity). * **Anomaly Detection**: Patterns, events, behaviours or observations which raise suspicions by differing significantly from the normality of the observed and stored data. To model any system, we first need to define its state space, i.e., the variables that govern the behaviour of the system with respect to the metrics being estimated. If the variables continuously change with time, it is called a continuous system. If the system state instantaneously changes at discrete points in time instead of continuously, it is called a discrete system. It is important to define and detect all the critical parameters that govern the behaviour of the system in order to understand it and set an efficient study mechanism. In the modelling and simulation procedure, there are three basic entities: the model, the simulator and the experimental frame. The model is the system specification, defining the static and dynamic structure and behaviour needed to generate data comparable to real-world data. Typically, the structure of a model represents all the entities involved in its operation as well as a set of possible states in which the physical system can be found after the appearance of certain sequences of events. Practically different levels of detail can be considered in a model in order to make it applicable in alternative cases, and for this, certain entities can be neglected (this can be done for reduction in the model complexity or for the study of certain aspects of the system). The selection of the best model comes down to the problem of choosing the appropriate level of detail, and it is considered one of the most difficult aspects of the modelling process. A model that is too simple will be unrealistic, and its results will be of little use.