## 2 Related Work
### Modeling and Simulation of Complex Systems  
The formalization of scientific theories is desirable to be explicit, standardized, and objective [13]. Therefore, the modeling of complex systems has become a proven method in many fields, especially in engineering and the mathematical and transportation sciences. Compared to laboratory or pilot plant experiments, it most often provides a relatively low-cost way of gathering information for decision making, especially since the size and complexity of real systems in the areas mentioned rarely allow for analytical solutions to provide the information [14]. For the modeling process, however, some terms and their delimitations need to be understood. The process of modeling, also referred to as model building, describes the realization of a planned or existing system in a model [15]. Such a system is a set of interrelated elements that are separated from their environment and can be characterized as follows [15]: First, and of utmost importance, by the definition of its borders with the environment and the respective interfaces for material, energy and information exchange as well as the definition of its elements and their sequence structures, denoted by rules and constant or variable attributes. Second, by the relations which connect the system elements among each other. Third, by the states of the elements which are each described by stating the values of all constant and variable attributes. However, generally only a small part of these is relevant to the investigation. Fourth, by the state transitions of the elements as continuous or discrete changes of at least one state variable due to the process running in the system. Furthermore, systems can be characterized by their variability, interconnectedness, and complexity [16]. Many systems are subject to variability, either predictable (e.g., manufacturing volumes) or unpredictable (e.g., machine breakdowns). Furthermore, systems are often interconnected, meaning elements of the system affect one another. Consequently, a change in one part of a system leads to a change in another part of the system. Regarding complexity, a system's combinatorial complexity and dynamic complexity can be distinguished. Combinatorial complexity is related to the number of elements in a system or the number of combinations of elements that are possible (e.g., order flows in job shops). Dynamic complexity arises from the interaction of components in a system over time and, therefore, is not necessarily related to size. However, systems that are highly interconnected (e.g., job shops) are likely to also display dynamic complexity with the following effects. First, an action has dramatically different effects in the short and long run. Second, an action has a very different set of consequences in one part of the system compared to another. Third, an action leads to non-obvious consequences (counter-intuitive behavior). A model on the other hand is a simplified reproduction of a planned or existing system [15]. It is characterized by the three criteria mapping, reduction and pragmatism [17]. Mapping describes that a model always represents a natural or an artificial original. However, a model does not capture all attributes of the original, but only those that seem relevant to the model creator or the model user--a reduction. Furthermore, as described by pragmatism, models are not uniquely assigned to their originals. They fulfill their replacement function for certain subjects, within certain time intervals and under restriction to certain mental or actual operations. We can distinguish between conceptual models and simulation models, also referred to as computer models [15; 16]. The conceptual model is a non-software-specific description of the model that is to be developed. It contains the objectives, inputs, outputs, content, assumptions and simplifications of the model [16]. In implementation, the conceptual model is, for the purpose of simulation, converted into an executable simulation model. Execution is not strictly limited to computers.