2.1 Modeling and Simulation
15
y n+1 = ay n + b un
(2.2)
Does the simulation purpose require the parallel consideration of temporal and
spatial processes, partial differential equation (PDE) systems are used [Wi1998,
p. 15]. The independent variable in continuous simulation models is typically
the time. For the state variables that are described by explicit functional forms
or differential equations, a specified value for an initial point in time is defined,
using these values as an input to generate new values at the next point in time
[Pr1998, p. 43]. The continuous simulation has its origin in the “Industrial Dynamics” published by Forrester in the late 1950’s to investigate the dynamics of
industrial processes. „Industrial Dynamics is the study of information feedback
characteristics of industrial activity to show how organizational structure, amplification (in policies), and time delays (in decisions and actions) interact to influence
the success of the enterprise. It treats the interaction between the flows of information, money, orders, materials, personnel, and capital equipment in a company,
an industry, or a national economy“ [Fo1961, S. 13]. Due to its generality and its
applicability in other research areas, Industrial Dynamics was further developed
and later renamed into System Dynamics (SD) [Sc2004, p. 34]. In SD models, a
distinction is made between stock and flow parameters. The depiction of stocks,
feedbacks and flows in stock- and flow-diagrams is of central importance in the
SD concept. The stock-and-flow diagrams are formulated in a system of nonlinear
ordinary differential equations that calculate the change of each variable through
integration over time [St2000, p. 903].
Discrete simulation models have dependent state variables that change instantaneously at distinct points in time, the so-called event-times. Pritsker distinguishes discrete simulation models according to their world view describing the
system [Pr1995, pp. 52–60]. The event-oriented world view requires the definition
of all events that can possibly occur in a system and change its state. The state of
the model remains constant between single events, and the dynamic of a system
is portrayed by simulating time from one event to the next. The approach is therefore very efficient, as only the state changes in occurrence of events are modeled
[Wa2009, p. 11]. The event-oriented view functions as a basis for further world
views, the activity-oriented or activity scanning and the transaction-oriented world
view. For the activity scanning view the conditions for an event to start or end are
described, but the event’s start as well as the end is not scheduled. The conditions for each activity are tested while the simulation moves from event to event.
“To ensure that each activity is accounted for, it is necessary to scan the entire
set of activities at each time in advance” [PO1999, p. 25]. As a result, models
using the activity scanning approach cannot be implemented efficiently. Both,
15
y n+1 = ay n + b un
(2.2)
Does the simulation purpose require the parallel consideration of temporal and
spatial processes, partial differential equation (PDE) systems are used [Wi1998,
p. 15]. The independent variable in continuous simulation models is typically
the time. For the state variables that are described by explicit functional forms
or differential equations, a specified value for an initial point in time is defined,
using these values as an input to generate new values at the next point in time
[Pr1998, p. 43]. The continuous simulation has its origin in the “Industrial Dynamics” published by Forrester in the late 1950’s to investigate the dynamics of
industrial processes. „Industrial Dynamics is the study of information feedback
characteristics of industrial activity to show how organizational structure, amplification (in policies), and time delays (in decisions and actions) interact to influence
the success of the enterprise. It treats the interaction between the flows of information, money, orders, materials, personnel, and capital equipment in a company,
an industry, or a national economy“ [Fo1961, S. 13]. Due to its generality and its
applicability in other research areas, Industrial Dynamics was further developed
and later renamed into System Dynamics (SD) [Sc2004, p. 34]. In SD models, a
distinction is made between stock and flow parameters. The depiction of stocks,
feedbacks and flows in stock- and flow-diagrams is of central importance in the
SD concept. The stock-and-flow diagrams are formulated in a system of nonlinear
ordinary differential equations that calculate the change of each variable through
integration over time [St2000, p. 903].
Discrete simulation models have dependent state variables that change instantaneously at distinct points in time, the so-called event-times. Pritsker distinguishes discrete simulation models according to their world view describing the
system [Pr1995, pp. 52–60]. The event-oriented world view requires the definition
of all events that can possibly occur in a system and change its state. The state of
the model remains constant between single events, and the dynamic of a system
is portrayed by simulating time from one event to the next. The approach is therefore very efficient, as only the state changes in occurrence of events are modeled
[Wa2009, p. 11]. The event-oriented view functions as a basis for further world
views, the activity-oriented or activity scanning and the transaction-oriented world
view. For the activity scanning view the conditions for an event to start or end are
described, but the event’s start as well as the end is not scheduled. The conditions for each activity are tested while the simulation moves from event to event.
“To ensure that each activity is accounted for, it is necessary to scan the entire
set of activities at each time in advance” [PO1999, p. 25]. As a result, models
using the activity scanning approach cannot be implemented efficiently. Both,