validation then would be (2.4). To test hypothesis (2.4) a t statistic can be used and the the null-hypothesis – that the responses are not correlated or negatively correlated – is rejected and therefore the model accepted as valid if there is strong evidence that the simulated and the real responses are positively correlated.
H0: β0= 0, β1= 1 (2.3)
H0: β1≤ 0 (2.4)
Though operational validation is possible only for existing systems where the necessary system output, that is compared to the model output, can be acquired, a way to achieve valid models for different system configurations is to model the existing system and validate this model and then change the model to reflect proposed changes in the system, assuming that this does not undermine model validity. So for existing systems where the aim of the simulation study is to gain new insights about the systems operations or to compare different policies or configurations for the system to determine and implement the best, both types of validation conceptual and operational validation can be performed as existing data on the system’s output can be compared to the output of the simulation of the conceptual model. However, when completely new systems are studied by simulation only the components of the simulation model and their links can be validated, in the hope that the final result still remains satisfactory. For the validation of these components and their relations only conceptual validation is applicable as there exists no real system and therefore no real system’s output against which one could compare the output from simulations of the conceptual model (Pidd, 1992). There are, however, some sources of output data against which the model’s output can be compared, like for example already validated simulation models or results of analytic models for simpler problems (Sargent, 2005).
2.4
Conceptual model
A model is a purpose oriented, simplified representation of an real-world system and therefore a system too (as can be seen from Figure 2.4). In the modeling phase the system is abstracted to a model in representing the entities and relations – important for the intention and purpose of the simulation study – in a changed way. For conceptual models that are studied by simulation through computer experimentation this means transformation in a form that can be understood by a computer i.e. in form of procedures and mathematical or logical relations. The aim of studying a conceptual model is to gain information and insights about the original system it represents (Page, 1991; M¨uller, 1998). Conceptual models for simulation can be determined verbally, graphically by flowcharts, or mathematically by equations and logical rules (Law and Kelton, 1991), the documentation of the conceptual model, besides its implementation in a computer program is part of the simulation process.
Figure 2.4: Model and system characteristics (Balci, 1994, p. 122)
Models can be classified along diverse dimensions: (i) the method used for their investigation – separating analytic models for analytic solutions and simulation models for simulation –, (ii) the medium of representation, which leads to material or immaterial models8, (iii) if and how their
states change over time9, and (iv) their purpose10(Page, 1991).
The most important distinction for models, when applied for simulation, is the way in which the system states change over time, as this builds the basis for two quite distinct simulation approaches i.e. discrete-time simulation and continuous time simulation – also called system dynamics.11 As automated negotiation belongs more to the realm of systems with discrete state
changes over time, which is discussed in more detail in Chapter 4, and due to the major differ- ences between these two simulation approaches we will focus on discrete-time models.12 Law and
Kelton (1991) call models studied by means of simulation ’simulation models’ and distinguish such models depending on: (i) the concept of time used, (ii) the use of probabilistic compo- nents, and (iii) status transitions, into static versus dynamic, deterministic versus stochastic, and discrete versus continuous simulation models:
8Where immaterial models can be further subdivided depending on whether they are formal or informal and
whether they are written or drawn into: (a) informal verbal descriptions (e.g. natural language models), (b) informal graphical descriptions (e.g. flow charts), (c) formal mathematical descriptions (e.g. equation systems), and (d) formal graphical descriptions (e.g. petri-nets).
9In static and dynamic models, where dynamic models can be further subdivided depending on how they change
over time and their ambiguousness into: (a) continuous-time deterministic, (b) continuous-time stochastic, (c) discrete-time deterministic, and (d) discrete-time stochastic models.
10Separating descriptive – to describe the behavior of the system –, prognostic – to forecast future system output
under alternative assumptions–, decision support – to evaluate alternative policies and system configurations –, and optimizing models – to derive a system configuration that maximizes or minimizes some target function.
11Furthermore note, that with respect to the other classification criteria, a simulation program is an immaterial,
formal, and written (in computer code) model, while the conceptual model can be any kind of immaterial model. Both the conceptual model and the simulation program can serve any of the mentioned purposes.
12In general system dynamics simulations are common in natural science and best modeled using differential
equations to model relationships between dependent and independent variables – usually time – so that the state of the system at some point of time in the future can be calculated from a known initial configuration (Bratley et al., 1987). A detailed discussion can be found for example in (Pidd, 1992, part III). A well-known example are ecological ’predator-prey’ models, where the population size development of both, the predator and the prey, is calculated from the initial population sizes and birth/dead rates for a particular point in time by numerically integrating the differential equations (Law and Kelton, 1991).
2.4. Conceptual model 27
• (i) Concept of time – static vs. dynamic simulation models: In static simulation models the system representation is provided for one particular point in time only, while dynamic simulation models represent the system as it evolves over time.
• (ii) Probabilistic components – deterministic vs. stochastic simulation models: Determinis- tic simulation models have no probabilistic components, so that the output of the simulation given a certain input is always the same. So simulation models that experience random inputs and operate them deterministically are classified as deterministic simulation mod- els, while simulation models with inherent stochastic elements that govern the operations belong to the class of stochastic simulation models.13
• (iii) Status transitions – discrete vs. continuous simulation models: If the simulation model is dynamic – i.e. changes over time – a distinctive feature to further differentiate types of simulation models – which is important to the field of simulation as it discriminates the two major classes of simulation discrete and continuous or system dynamics simulation – is the nature of state transitions in the simulation model, measured by the changes in its state variables – the variables used to describe a system at a particular time – over time. In discrete simulation models the state variables change instantaneously at separate points in time (an example of a discrete simulation model would be the queue in front of a bank counter – where the length of the queue would be a state variable of the simulation model – that changes only if a customer is finished or a new enters the bank). In continuous simulation models state variables change continuously with respect to time (here an example would be an airplane moving through the air where the position, velocity, and height – as state variables – change continuously over time).
Though the distinction between discrete and continuous simulation models is straightforward given the operations of the simulation model, it is not easy at all to decide which type of model to use for studying a given real world system, as systems in general are neither purely discrete nor purely continuous, but in most cases combine both aspects. For discrete systems, such as the production, transportation, and logistics systems that are studied in operations research and management science and where changes in the state of a system mainly are due to certain discrete events, discrete-event simulation is appropriate. On the other hand in physical, biological, and medical systems studied in the natural sciences the continuous change of these systems over time, following physical or biological rules, can be of particular interest and in this case such systems are best studied by system dynamics simulation (Page, 1991). However, discrete events may cause a discrete change in the value of an otherwise continuous state variable or cause the relationship governing a continuous state variable to change at a particular time. Furthermore, continuous state variables reaching a threshold value may cause a discrete event to occur. In such cases it has to be decided which type of simulation model is the more appropriate for the focal system and the purpose of its analysis or if a combination of both classes is a viable approach (Law and Kelton, 1991; Liebl, 1992).
13A well known example of a deterministic simulation is Conway’s game of ’Life’ Gardner (1970), for which a
number of implementations can be found on the Internet – e.g. on www.bitstorm.org/gameoflife/ last accessed 23.03.09. In this simulation simple rules lead to short-lived, constant, or oscillating patterns depending on the start pattern.