2.1 Modeling and Simulation
13
as simple models are developed quicker, are more flexible, require less data and
can be executed faster.
There are several options to classify models 3 of which three are depicted here.
Models can be static or dynamic, deterministic or stochastic, and discrete or continuous. While static models are used to constitute a system in which time is no
longer a factor, dynamic models depict a system as it evolves in the course of
time. As the experimentation with static models only depicts a point behavior 4 , it
can only be used very limited for computer simulation [KSZ2002, p. 9; Ör2009,
p. 19; MC2007, pp. 3.8–3.9]. Therefore, static models are not relevant for this thesis. The second dimension differentiates models according to the randomness of a
system. A deterministic model does not involve any probabilistic components, the
behavior is completely predictable, and the output is determined. If a system has
random input components, it is referred to as a stochastic system. Manufacturing
and inventory systems are generally described in a stochastic simulation model
[Ba+2005, p. 11–12; La2007, p. 5–6]. The third dimension distinguishes between
the system dynamics. Systems are hybrid by nature, only a “few systems in practice are wholly discrete or wholly continuous; but since one change predominates
for most systems, it will usually be possible to classify a system as being either
discrete or continuous” [LK2000, p. 3]. For discrete models, the state variables
change only at separated points in time (time-stepped) or on the occurrence of
state-affecting events (event-stepped) [Ba1998, p. 8; He2008, p. 18] while a continuous model concerns the modeling over time with the state variables changing
continuously with respect to time, having an infinite number of states [La2007,
p. 70]. Depending on the object of study, both, the continuous time-advancement
and the discrete event state jumps might be important for the simulation purpose [Lu2002, p. 3] 5 . Depending on the type of model performed, simulations
can be subdivided into discrete, continuous or hybrid approaches. After a short
introduction on discrete and continuous simulation in section 2.1.1, the hybrid
3 The ‚pieces of a simulation model‘ (e.g., entities, attributes, (global) variables, resources,
cues, events, etc.) are assumed to be basic knowledge and will not be described here. The
interested reader is referred to Kelton, Sadowski and Randall [KSZ2002, pp. 24–29] as
well as to Banks et al. [Ba+2005, pp. 8–9], who have worked out the basics in great detail.
4 “Most mathematical and statistical models are static, in that they represent a system at a
fixed point in time. Consider the annual budget of a firm. The budget resides in a spreadsheet.
Changes can be made in the budget and the spreadsheet can be recalculated but the passage
of time is usually not a critical issue” [Ba1998, p. 7].
5 Readers are referred to ‘Banks’ Handbook of Simulation [Ba1998, pp. 6–13, pp. 31–36 and
pp. 47–49], Discrete-Event System Simulation [Ba+2005, pp. 3–12] and LAW’s Simulation
Modeling and Analysis [La2007, pp. 1–6, pp.] for further reading on the definitions of system,
model and simulation in general.
13
as simple models are developed quicker, are more flexible, require less data and
can be executed faster.
There are several options to classify models 3 of which three are depicted here.
Models can be static or dynamic, deterministic or stochastic, and discrete or continuous. While static models are used to constitute a system in which time is no
longer a factor, dynamic models depict a system as it evolves in the course of
time. As the experimentation with static models only depicts a point behavior 4 , it
can only be used very limited for computer simulation [KSZ2002, p. 9; Ör2009,
p. 19; MC2007, pp. 3.8–3.9]. Therefore, static models are not relevant for this thesis. The second dimension differentiates models according to the randomness of a
system. A deterministic model does not involve any probabilistic components, the
behavior is completely predictable, and the output is determined. If a system has
random input components, it is referred to as a stochastic system. Manufacturing
and inventory systems are generally described in a stochastic simulation model
[Ba+2005, p. 11–12; La2007, p. 5–6]. The third dimension distinguishes between
the system dynamics. Systems are hybrid by nature, only a “few systems in practice are wholly discrete or wholly continuous; but since one change predominates
for most systems, it will usually be possible to classify a system as being either
discrete or continuous” [LK2000, p. 3]. For discrete models, the state variables
change only at separated points in time (time-stepped) or on the occurrence of
state-affecting events (event-stepped) [Ba1998, p. 8; He2008, p. 18] while a continuous model concerns the modeling over time with the state variables changing
continuously with respect to time, having an infinite number of states [La2007,
p. 70]. Depending on the object of study, both, the continuous time-advancement
and the discrete event state jumps might be important for the simulation purpose [Lu2002, p. 3] 5 . Depending on the type of model performed, simulations
can be subdivided into discrete, continuous or hybrid approaches. After a short
introduction on discrete and continuous simulation in section 2.1.1, the hybrid
3 The ‚pieces of a simulation model‘ (e.g., entities, attributes, (global) variables, resources,
cues, events, etc.) are assumed to be basic knowledge and will not be described here. The
interested reader is referred to Kelton, Sadowski and Randall [KSZ2002, pp. 24–29] as
well as to Banks et al. [Ba+2005, pp. 8–9], who have worked out the basics in great detail.
4 “Most mathematical and statistical models are static, in that they represent a system at a
fixed point in time. Consider the annual budget of a firm. The budget resides in a spreadsheet.
Changes can be made in the budget and the spreadsheet can be recalculated but the passage
of time is usually not a critical issue” [Ba1998, p. 7].
5 Readers are referred to ‘Banks’ Handbook of Simulation [Ba1998, pp. 6–13, pp. 31–36 and
pp. 47–49], Discrete-Event System Simulation [Ba+2005, pp. 3–12] and LAW’s Simulation
Modeling and Analysis [La2007, pp. 1–6, pp.] for further reading on the definitions of system,
model and simulation in general.