Towards an orientation framework in multi-paradigm
modeling
Aligning purpose, object and methodology in
System Dynamics, Agent-based Modeling and Discrete-Event-Simulation
Tobias Lorenz
University of Stuttgart
DaimlerChrysler AG, Research and Technology
System Dynamics Group Bergen
Nordbahnhofstr. 179, 70191 Stuttgart, Germany
Tobias.Lorenz @ gmail.com
Andreas Jost
DaimlerChrysler AG, Research and Technology Strategy
Andreas.Jost @ daimlerchrysler.com
Keywords: Agent-based Modeling, Discrete-Event-Simulation, Paradigmata, Multi-
Paradigm-Modeling, Hybrid Modeling
Abstract
Methodologies are built upon fundamental assumptions (called paradigms) which are
rarely questioned within a respective community. When applying a methodology without
being aware of these assumptions we risk accepting wrong conclusions (abduction
risk). Therefore this paper proposes that the development of valuable simulation models
strongly depends on the sound alignment of purpose, object and methodology. In order
to align these dimensions and in the light of upcoming tools capable of multi-paradigm-
modeling a clear conception of the available methodologies, their differences and
suitability becomes a necessity. In the context of modeling and simulating of socio-
technical systems three methodologies seem reasonable. Next to System Dynamics (SD)
these are Agent-based Modeling (ABM) and Discrete-Event-Simulation (DES). The
following paper analyzes and compares all three approaches in order develop an initial
concept idea for an orientation framework which aligns purpose, object characteristics
and methodology for choosing and/or combining suitable modeling approaches.
Introduction
Reviewing System Dynamics literature, a clear problem definition or model purpose is
the initial starting point of a successful modeling process.! Only with a clear purpose the
modeler is able to focus on key aspects, define adequate model boundaries and choose
an appropriate level of abstraction. Mostly overlooked however is the fact, that also the
choice of a suitable modeling and simulation approach is an essential success factor that
needs to be integrated in the early stages of the modeling process. Due to familiarization
and (early) association with a specific modeling paradigm modelers tend overlook other
paradigms or simply are not able to adequately differentiate and apply alternative
approaches. The latter is about to change with the availability of tools capable of multi-
paradigm modeling. However, the ability to differentiate is still a success factor these
tools simply cannot provide.
Purpose — Object - Methodology
Based on the fact that any given methodology comes along with a set of (implicit or
explicit) assumptions (called paradigms”) it is the central hypothesis of this paper that
only by finding the best fit of the three dimensions: purpose, object and methodology, a
suitable modeling approach can be found.
Object
What?
Methodology
How?
Purpose
Why?
Figure 1: Purpose - Object - Methodology
Purpose refers to the motivation of the intended modeling effort which can include
solving a given problem or finding effective leverages to change or optimize a given
behavior. Let alone the fact that a correct problem definition already includes a clear
‘ Compare Sterman, Business Dynamics. Systems Thinking and Modeling for a Complex World, Boston, 2000, page 89 "A clear
purpose is the single most important ingredient for a successful modelling study”
* Compare Meadows, The unavoidable A Priori, p. 24 in Randers, Elements of the System Dynamics Method, Cambridge/ London,
1980, "Different modeling world views, or in Thomas Kuhn’s terminology, paradigms (Kuhn, 1970), cause their practitioners to
define different problems, follow different procedures, and use different criteria to evaluate their results.”
purpose, a modeling purpose can also be to gain insight into a broader not yet
understood problem context. Therefore the term purpose is not equal to a problem
definition but can and should nevertheless lead to an exact problem definition. Both
purpose and/or problem definitions are not only important for the identification of
adequate model boundaries but also hold key aspects for the selection of a suitable
modeling methodology.
Object refers to the real world context under investigation. Since models refer to
selected aspects of the real world, examining the characteristics of the respective real
world objects provides important indications for the selection of an appropriate
modeling approach. E.g. the structure and level of detail of available information
about investigated objects can already favor certain modeling approaches.
Methodology is defined as ,,a comprehensive, integrated series of techniques or
methods creating a general systems theory of how a class of thought intensive work
ought to be performed‘. Therefore a methodology consists of a set of individual
methods and/or techniques. In the example of SD the methodology includes methods
and techniques such as boundary diagrams, causal loop diagrams and stock & flow
diagrams. In other approaches techniques such as state charts, workflow diagrams are
applied. Through its set of methods a modeling and simulation methodology defines
how the object is being approached in order to achieve the intended purpose. As no
model can reflect a one-to-one representation of reality, choices of what aspects to
include are to be made. Since all methods come along with strengths and weaknesses,
the application of a certain methods already presets a tendency which aspects are
likely to be included and which are likely to be left out. This effect is frequently
associated with the paradigm of a modeling methodology. Different paradigms favor
different object and purposes. Therefore the methodology needs to be chosen in
accordance with the real world objects and the purpose of the modeling effort.
Paradigms
The term “paradigm” has been frequently used to capture the aforementioned set of
assumptions and is characterized by the fact that it is to a large extent not questioned
within its scientific community. Meadows and Robinson for example postulate that
“Different modeling paradigms cause their practitioner to define different problems,
follow different procedures, and use different criteria to evaluate the results.”* Some
concepts from theory of science may clarify the problems that come along with
preliminarily accepting paradigms.
Generally, three distinct methods are discriminated in scientific research. These are
induction, deduction and abduction. If we conceptualize science as consisting of
causality statement about observable phenomena, these statements have the logical
form:
C— +E (If C then E)
3 Standard Glossary of Software Engineering Terminology* of the Institute of Electrical and Electronics Engineers (IEEE) defines
methodology as ,,a comprehensive, integrated series of techniques or methods creating a general systems theory of how a class of
thought intensive work ought be performed [IEEE 1990] -> therefore a methodology consists of individual methods and/or
techniques.” IEEE Standard Glossary of Software Engineering Terminology. IEEE Computer Society. IEEE Std 610.121990. New
York 1990.
* Meadows/Robinson, The electronic oracle, Chichester, 1985, p. 20
Induction finds validated regularities by the observation of a certain number of
regularities between causes and effects and the abstraction of a general statement
(Having observed a glass break when hitting the ground with a certain impulse for
several times one could postulate: If “glass hits the ground with a certain impulse” then
“glass breaks”).
Deduction builds upon existing regularities in order to deduce the effect for observed
causes (given the aforementioned regularity and observing a glass hitting the ground,
one could postulate that “it will break’).
Abduction on the other hand, attempts to explain an observed effect with a given
regularity (Observing a broken glass and assuming that it had fallen by referring to the
aforementioned regularity). Acknowledging that there might be other reasons which
might cause a glass to break (e.g. CE) this is logically a relative weak method of
reaching conclusions. Abduction finds causes for a certain effect by assuming a specific
regularity (e.g. C —» E) to be adequate. Therefore this logical weakness persists no
matter how certain the assumed regularity (C—*E) is for itself, because it arises out of
the uncertain application of the regularity to an observed effect (C—»E where C; E
might as well be applicable).
Coming back to modeling and simulation we argue that methodologies already build
upon certain C—E statements, which are implicitly accepted within a certain paradigm.
Therefore by approaching a problem with a given methodology without confirming
inherent assumptions already holds the risk of uncertain conclusions (abduction risk).
Looking at simulation models themselves, they add numerous assumptions on top of
these fundamental statements, adding up to a complex system of C—>E statements.” But
fortunately (and in contrary to underlying assumptions of a paradigm) the assumptions
in a simulation model are mostly (and ideally) stated explicitly. Therefore they can be
questioned, which reduces the risk of drawing uncertain conclusions. The lower level of
a modeling paradigm on the other side include statements that are understood to be
generally relevant. These include the expected dominant sources of complex system
behavior as well as methods and techniques how these underlying concepts are to be
transformed into computable models.
Core assumptions of SD, DES and ABM
In the following the assumptions of the three competing simulation modeling
techniques (Agent-based Modeling, System Dynamics and Discrete-Event-Simulation)
will be discussed. This discussion is based on the idea that major difference can be
found in the abduction of assuming underlying causes for complex system.° Morecroft
and Robinson formulate this as follows: “Rather than focus on technical and conceptual
differences, we compare the nature of explanations and insights these two approaches
have to offer about puzzling dynamics. Our premise is that the modeling style you
choose affects the way you represent and interpret phenomena from the real world”
a) Differences between Discrete-Event-Simulation and System Dynamics
5 Compare Magnani, Model-Based Creative Abduction in Magnani/ Nersessian/ Thagard, Model-based reasoning in scientific
discovery, New York, 1999
© Also compare Morecroft, John/ Robinson, Stewart, Explaining Puzzling Dynamics: Comparing the Use of System Dynamics and
Discrete-Event Simulation, Proceedings of System Dynamics Conference 2005,
7 Morecroft, John/ Robinson, Stewart, Explaining Puzzling Dynamics: Comparing the Use of System Dynamics and Discrete-Event
Simulation, Proceedings of System Dynamics Conference 2005, p.5
Morecroft and Robinson deliver an exquisite analysis of the different worldviews held
by System Dynamicists and Discrete-Event-Modelers respectively. Before we turn
towards the main issue - the assumed roots of behavior - some technical details will be
regarded en passant. System Dynamics is generally viewed to be computed
continuously whereas DES is computed discretely. A model can be called discrete if
“[...] the state variable(s) change only at a discrete set of points in time”. Taking a
closer look SD models are also computed in a series of discrete time steps, nevertheless
the focus lies on continuous policies in contrast to the focus on individual events in
DES. A DES-model consists of entities, attributes and activities, which constitute
defined states and can be changed by events. The focus lies on the entities in contrast to
the focus on aggregates in System Dynamics. “An entity is an object of interest in the
system. An attribute is a property of an entity. An activity represents a time period of
specified length.”
Whereas in System Dynamics aggregates are linked through aggregated mechanisms
implemented as flows, in DES the activities of the individual entities are modeled and
then linked through interconnecting events. 0
The perspective in DES is on multiple events, where an event is an “[...] instantaneous
occurrence that may change the state of the system.”"!, whereas the perspective in SD is
again an aggregated one, where these multiple events are aggregated into rates.
Nevertheless, we need to keep in mind, that in reality there are also discrete events
within a SD model when the system does react with a sudden state change e.g. upon the
introduction of a new control policy. This fact is once in a while forgotten within SD
through the attempt to smooth everything out and look at the system from a highly
aggregated view.
Typical applications of DES are so-called queuing models, where “[...] customers
arrive from time to time and join a queue, or waiting line, are eventually served, and
finally leave the system. The “term” customer can be transferred to any type of entity
that is requesting “service” from a system. Therefore, many service facilities,
production systems, repair and maintenance facilities, communications and computer
systems, and transport and material handling systems can be viewed as queuing
systems.””~
The main difference has been assumed to lie in different assumptions regarding the
roots of complex behavior. Whereas in System Dynamics these are assumed to “[...]
arise from endogenous, deterministic and structural properties of the system [ows in
DES behavior is assumed to “[...] arise from the interaction of (random) processes
coupled together by endogenous structure.” '*
Another approach has been to claim that the methodologies pursue different kinds of
complexity, which is “dynamic complexity” in the case of SD, and “detail complexity”
® Banks, Carson, Nelson, Nicol, Discrete-Event System Simulation, New Jersey, 3rd edition, p.12
° Banks, Carson, Nelson, Nicol, Discrete-Event System Simulation, New Jersey, 3rd edition, p.10
'" “tn order to build a model suitable for discrete event simulation, it is necessary to: Identify the important classes of entity;
Consider the activities in which they engage; Link these activities together.” (Michael Pidd, Computer Simulation in Management
Science, Chichester, 2004, Sth edition, p.66)
"' Banks, Carson, Nelson, Nicol, Discrete-Event System Simulation, New Jersey, 3rd edition, p.10
" Banks, Carson, Nelson, Nicol, Discrete-Event System Simulation, New Jersey, 3rd edition, p.204
8 Morecroft, John/ Robinson, Stewart, Explaining Puzzling Dynamics: Comparing the Use of System Dynamics and Discrete-Event
Simulation, Proceedings of System Dynamics Conference 2005, p.7
' Morecroft, John/ Robinson, Stewart, Explaining Puzzling Dynamics: Comparing the Use of System Dynamics and Discrete-Event
Simulation, Proceedings of System Dynamics Conference 2005, p.7
in the case of DES: “Detail complexity arises from the existence of multiple variables,
which may have many different attributes and which therefore give rise to an enormous
number of possible inter-connections and effects. Such detail can swamp users wishing
to grasp its ramifications and is a central concern of DES. Dynamic complexity arises
because variables influence each other in ways which involve non-linearities, delays and
accumulative or draining relationships. Such complexity produces counterintuitive
behavior which can confuse problem owners and is the focus of SD.” Lane proposes
the following table for discrimination:
Perspective
Resolution of models
Data sources
Problems studied
Model elements
Human agents represented in
models as
Clients find the model
Model outputs.
DES
Analytic, emphasis on detail
complexity
Individual entities, attributes,
decisions and events
Primarily numerical with some
judgmental elements
Operational
Physical, tangible and some
informational
Decision makers
Opaque/ dark, grey box,
nevertheless convincing
Points predictions and detailed
performance measures across a
range of parameters, decisions
SD
Holistic,
complexity
emphasis on dynamic
Homogenized entities, continuous
policy pressures and emergent
behavior
Broadly drawn
Strategic
Physical, tangible, judgmental and
information link
Boundedly rational policy
implementers
Transparent/ fuzzy glass _ box,
nevertheless compelling
Understanding of structural source
of behavior modes, location of key
performance indicators and effective
tules and scenarios policy levers
Table 1: Comparison of Discrete-Event-Simulation and System Dynamics!°
Applying a given Methodology (accepting a certain set of general assumptions) also
leads to a different perspective on a system. E.g. looking for structure within a system
requires a longer time horizon, whereas a collection of events can be discussed within
shorter periods.'”
b) Differences between Agent-based Modeling and System Dynamics
Both System Dynamics and Agent-based Modeling are regularly utilized to explain
socio-technical phenomena but differ significantly in the way they approach their
explanandum. Whereas System Dynamics typically looks for a reference mode for a
'SLane, David, You just don’t understand me: Modes of failure and success in the discourse between system dynamics and discrete
event simulation, LSE OR Working Paper 00.34, 2000, p. 16
‘Lane, David, You just don’t understand me: Modes of failure and success in the discourse between system dynamics and discrete
event simulation, LSE OR Working Paper 00.34, 2000, p. 16
" Compare also: “Thus, events have a short, possibly immediate, timescale whereas system behaviour represents the observed
fluctuations over a longer time period.” (Michael Pidd, Computer Simulation in Management Science, Chichester, 2004, 5th
edition, p.250)
central variable (which is to be reproduced and explained), Agent-based Modeling takes
a contrary approach. It models an agent with individual behavior and observes the
emergent behavior out of the interaction of a population of those agents. Due to the
complications arising in tracing back the emerging behavior to the agents properties,
which don’t arise in the tighter causal linkage of a SD model, the Agent-based approach
might be called explanatory. The approach of SD might be called exploratory. Phelan
uses the descriptions confirmatory and exploratory" to discriminate System Theory
from Complexity Theory, but Systems Theory is capable of more than consistency
checking as it normally integrates several theories into one model and implements the
assumptions of the modeler through the links. Nevertheless both techniques can be
described as “abductive”, since they attempt to develop models to explain given effects.
In Agent-Based Modeling, “the individual members of a population such as firms in
an economy or people in a social group are represented explicitly rather than as a single
aggregate entity.”’”. “This massively parallel and local interactions can give rise to path
dependencies, dynamic returns and their interaction.””°
By focusing on the individual entity, three characteristics of Agent-based approaches
can be identified. They are suitable to
a) describe and demonstrate how the interaction of independent agents create
collective phenomena;
b) identify single agents whose behavior has a predominant influence on the
generated behavior;
c) — identify crucial points in time, at which qualitative changes occur.”!
Schieritz and Milling developed the following table in order to pin down some distinct
differences between System Dynamics and Agent-Based Modeling.
System Dynamics Agent-based Simulation
Basic building block Feedback loop Agent
Unit of analysis Structure Rules
Level of modelling Macro Micro
Perspective Top-down Bottom-up
Adaptation Change of dominant structure Change of structure
Handling of time Continuous Discrete
Mathematical formulation Integral equations Logic
Origin of dynamics Levels Events
Table 2: Comparison of System Dynamics and Agent-Based Modeling”
'S Phelan, Steven, A Note on the Correspendence Between Complexity and Systems Theory, Systemic Practice and Action
Research, Vol. 12, No. 3, 1999
Sterman, Business Dynamics. Systems Thinking and Modeling for a Complex World, Boston, 2000, p. 896
* Grebel/ Pyka, Agent-based modelling — A methodology for the analysis of qualitative development processes, 2004 in: Lombardi/
Squazzoni, Saggi di economia evolutiva , Franco Angeli, Milano, Italy (forthcoming). p. 10
> Grebel/ Pyka, Agent-based modelling — A methodology for the analysis of qualitative development processes, 2004 in: Lombardi/
Squazzoni, Saggi di economia evolutiva , Franco Angeli, Milano, Italy (forthcoming).
® Schieritz/ Milling, Modeling the Forest or Modeling the Trees, Proceedings of the 21st International Conference of the System
Dynamics Society, 2003
These points of departure between the two methodologies seem to be a good starting
point for the analysis of the underlying assumptions. Nevertheless, a central point in our
conception, the primary hypothesized cause of the problem to be explained, is
missing.”* Other directions to discriminate both methodologies can be found in the
diverging approach to individuals and observables” or the concept of emergence”.
As hypothesized above, we regard the assumed origins of dynamic behavior as the
central difference inherent to the two methodologies. This set of assumptions is central
for the explanation of a problem, whereas the practices of the methodology (e.g. if a
model is implemented in continuous or discrete time) are technical details following
from the choice of the basic assumptions. As those assumptions are crucial, they will be
made more explicit in the following as a clear perception of them might lead to refined
discussion. Two assumptions are regarded as central in System Dynamics:
a) Feedback is central in generating behavior (“All dynamics arise from the
interaction of just two types of feedback loops, positive (or self-reinforcing) and
negative (or self-correcting) loops.””°; “..the concept of feedback is central to system
dynamics.””’)
b) Accumulations are central in generating behavior (“Stocks and flows, along with
feedback, are the two central concepts of dynamic systems theory.””*; “To capture
disequilibria in a system, however, stocks must be explicitly represented since they
accumulate the imbalances between inflows and outflows.””’)
Analyzing Agent-Based Modeling, we find a different set of basic
ssumptions:
a) Micro-Macro-Micro feedback is central in generating behavior
b) Interaction of the systems elements is central in generating behavior. (“In its
broadest perspective, the work can be seen as part of the study of emergent organization
through “bottom-up” processes. In such “bottom-up” processes small units interact
according to locally defined rules, and the result is emergent properties of the system
such as the formalization of new levels of organization.” 0. “At the simplest level, an
agent-based model consists of a system of agents and relationships between them. Even
a simple agent-based model can exhibit complex behavior patterns and provide valuable
information about the dynamics of the real-world system that it emulates”*', “One of the
basic premises of complexity theory is that much of the apparently complex aggregate
2 For a detailled critique of the Schieritz/ Milling approach compare Lorenz/ Bassi, Comprehensibility as a discrimination criterion
for Agent-Based Modelling and System Dynamics: An empirical approach, in Sterman et al., Proceedings of the 23 rd International
Conference of the System Dynamics Society, Boston, 2005
* Parunak/ Savit/ Riolo, Agent-Based Modeling vs. Equation-Based Modeling: A Case Study and Users’ Guide, Proceedings of
Workshop on Modeling Agent Based Systems, 1998
* Compare Casti, Would-Be Worlds: How simulation is changing the frontiers of science, New York, 1997, p. 91, “A surprise-
generating mechanism dependent on connectivity for its very existence is the phenomenon of emergence. This refers to the way the
interactions among system components generates unexpected global system properties not present in any of the subsystems taken
individually
*° Sterman, Business Dynamics. Systems Thinking and Modeling for a Complex World, Boston, 2000, p. 12
* Radzicki, Michael/ Sterman, John, Evolutionary Economics and System Dynamics in England, Richard, Evolutionary Concepts in
Contemporary Economics, p. 67
* Sterman, Business Dynamics. Systems Thinking and Modeling for a Complex World, Boston, 2000, p.191
® Radzicki, Michael/ Sterman, John, Evolutionary Economics and System Dynamics in England, Richard, Evolutionary Concepts in
Contemporary Economics, p. 68
* Axelrod, A model of the emergence of new political actors, in Gilbert/ Conte, Artificial Societies, London, 1995, p. 19
* Bonabeau, Eric, Agent-Based modeling: Methods and techniques for simulating human systems in PNAS, 2002, Vol. 99
behavior in any system arises from the relatively simple and localized activities of its
9932
agents.””"”)
Purpose-oriented modeling
Having identified some major differences between these three paradigmata, the crucial
question remains how to deliver sound models. As recommended above one of the first
steps of modeling after having defined a problem context should be a reflection upon
which modeling paradigm and methodology suit purpose and object best. At this stage
the modeler has two options: he can either focus on one paradigm gaining the advantage
of a stringent set of methods of one established methodology, or he can try to combine
suitable methodologies and turn towards multi-paradigm modeling. The latter tend to be
closer to reality as they can combine best-fit methods of different methodologies but
may lose some explanatory power. In both cases practitioners need criteria that provide
orientation for when to apply which methodology.
In order to find the most suitable method for a modeling project it seems useful to
identify the impact of different causes to the problem. The most important impacts need
to be categorized into the main assumptions of the available methods.
This idea has already been addressed against System Dynamics in a very early critique
of Ansoff: “Another major characteristic in determining areas of application of
Industrial Dynamics is the specific model structure incorporating concepts of levels and
flows built around the concept of tight loop information feedback. Forrester, in his
book, makes a point that industrial systems are inherently information feedback
systems. Granting the point, it does not necessarily follow that all aspects of the firm are
best studied by means of information feedback systems. This suggests that the
appropriateness of the information feedback viewpoint should be determined on the
basis of the relative influence of the feedback information on the decision in any given
situation.”
The main point is, if the feedback of a system (and it is argued that there is feedback
almost everywhere) has only a minor effect on the problem to explain then of course the
importance of this feedback should not be overstated by using System Dynamics
methodology. If a system is characterized by discrete jumps, which form the core
problem, then these jumps should not be smoothed out by a SD model. If the problem
seems to be caused by the interaction of heterogeneous agents, then ABM seems most
suitable. Of course if several effects interact a mix of methodology can be useful.
Nevertheless it has to be considered, that a clear focus on a small number of
interrelations is the differentiating advantage of computer simulation in approaching
“messy systems”. The major problem seems to be found in comparing the strengths of
the different causes in order to identify the most suitable method. Up to now (if
alternative methodologies are considered at all) this is mostly done intuitively. A
method or framework in order to determine the most suitable modeling methodology is
still missing.
* Phelan, Steven, A Note on the Correspendence Between Complexity and Systems Theory, Systemic Practice and Action
Research, Vol. 12, No. 3, 1999, p. 239
® Ansoff, Igor/ Slevin, Dennis, An appreciation of Industrial Dynamics, in Management Science, Vol. 14, No. 7, 1968, p. 392
A final list of criteria for the choice of the right modeling paradigm seems out of
reach. Nevertheless there are criteria at hand that might serve as rules of thumb. Some
criteria for the usage of Agent-based Modeling have been proposed by Bonabeau™:
e When the interactions between the agents are complex, nonlinear,
discontinuous, or discrete
e When space is crucial and the agents’ positions are not fixed
e¢ When the population is heterogeneous, when each individual is (potentially)
different
e¢ When the topology of interactions is heterogeneous and complex
e¢ When the agents exhibit complex behavior, including learning and adaptation
Discrete models seem appropriate if the discreteness of the object has some reflection in
the purpose. “Discrete-event models are appropriate for those systems for which
changes in system state occur only at discrete points in time.”>
Considerations regarding the application of Agent-Based Simulation seem to be driven
predominantly by the object-side of the triangle (spatialty and heterogeneity can not be
modeled very elegantly in SD). The criterion for choice between SD and DES on the
other hand seems to lie more on the purpose-side. For DES-models it seems to be more
short-term, operational logistics problems, which are to be optimized and require a
shorter time horizon. The discussion of long-term strategic policies favors SD: “Hence,
most discrete event simulations are microscopic in their focus and involve considerable
detail. They may include appropriate probability distributions if the system behavior is
stochastic. It is, though, possible and often useful to model system behavior at the rather
more macroscopic level. This is the usual focus of the system dynamics approach [...].
System Dynamics is less concerned with detail than discrete event simulation and
focuses, instead, on the ways in which system structures affect tem behavior.”*° In
accordance with the criteria that Lane proposes in his table which seem to reflect more
upon the purpose side than onto the object-side the thesis defended here would be that
the choice of the modeling paradigm depends upon the purpose if it is to decide between
SD and DES. If the decision has to be taken between SD and AB, the object-side
becomes more relevant. Then the key-indicator would be whether the problem is caused
by feedback or interaction between heterogeneous elements.
Some authors propose “uncertainty” and “probability” as a key criterion for the choice
of modeling a paradigm:
“For example, SD is particularly well suited to studying systems containing a complex
web of feedback loops, while discrete system simulation is preferred when the system
contains a high degree of uncertainty. A key strength of ABS is its ability to incorporate
spatial as well as probabilistic aspects of the system.”*”
™ Bonabeau, Eric, Agent-Based modeling: Methods and techniques for simulating human systems, in PNAS, 2002, Vol. 99, page
7287
* Banks, Carson, Nelson, Nicol, Discrete-Event System Simulation, New Jersey, 3rd edition, p.163
* Michael Pidd, Computer Simulation in Management Science, Chichester, 2004, Sth edition, p.249
*’ Wakeland/ Gallaher/ Macovsky/ Aktipis, A comparison of System Dynamics and Agent-Based Simulation Applied to the Study
of Cellular Receptor Dynamics, Proceedings of the 37th Hawaii International Conference on System Science, 2004, p.1
Nevertheless stochastic elements can be included in SD-models as well. Another rule
might suggest itself in that context: With an increase in uncertainty in the available data,
the degree of aggregation should increase aswell.*®
An approach to choose the right paradigm which takes into account only
“idiosyncratic combinations of factors to do with the personal styles and preferences of
analysts and clients, the time available, gross characteristics of the ‘perceived issues’,
past experiences of all concerned, organizational cultures, financial and academic
pressures inhibiting or encouraging collaborative working, and so on”*” seems
inappropriate and tends to result in the loss of credibility.
Multi-Paradigm Modeling
In addition to the selection of suitable paradigms a next step would be to build multi-
paradigm-models consisting of interacting modules orientated at best-fit paradigms for
the respective sub-problems. This effort makes the preliminary task to identify the right
methodology for a sub-problem even more necessary in order to avoid unnecessary
work by trying different methodologies. Experiments with models integrating ABM and
SD have already been studied. Main areas were the Bass model“? and the modeling of
supply chains"’,
For the integration of the two methodologies it is necessary to clearly identify possible
links. In this context two main approaches for implementing SD into Agent-based
modeling are reasonable. The first possibility is to create entities out of SD structures.
The second possible way includes creating a dynamic environment for the agents, which
would be provided by an SD model. In this context three categories of environments can
be distinguished in an Agent-based model:
Alternative environments in AB-modeling
a) “Zero” environment
- Environment does not effect agents in any way
- Environment may just hold some aggregate values
b) Passive environment
- Agents only interact with some variables or structures in the environment
- Environment does not have any inherent dynamics
c) Active environment
- Environment has its own dynamics and therefore is an active player in the
AB model
Table 3: Alternative environments in Agent-based Modelling
** Compare Rahmandad/ Sterman, Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and
Differential Equation Models (to appear), downloadable from http://web.mit.edu/jsterman/www/Heterogeneity.html, p. 24, “The
results suggest extensive disaggregation may not be warranted unless detailed data characterizing network structure are available,
that structure is stable, and the computational burden does not limit sensitivity analysis or the inclusion of other key feedbacks that
may condition the dynamics.”
* Bennett, Ackermann, Eden, Williams: Analysing Litigation and Negotiation: Using a combined methodology, in Mingers, Gill:
Multimethodology, Chichester, 1997, page. 86
"" Borshchev/ Filippov, From System Dynamics and Discrete Event to Practical Agent Based Modeling: Reasons, Techniqui
Tools, Proceedings of the 22nd International Conference of the System Dynamics Society, 2004
*' Schieritz/ Groessler, Emergent Structures in Supply Chains — A Study Integrating Agent-Based and System Dynamics Modeling,
Proceedings of the 36th Hawaii International Conference on System Sciences, 2001; Akkermans, Henk, Emergent Supply
stem Dynamics Simulation of Adaptive Supply Networks, Proceedings of the 36th Hawaii International Conference on
* Agent Based Modeling in AnyLogic downloadable from http://www.anylogic.jp/download/anySagentbasedmodeling.pdf, p.11
In the case of the zero environment clearly no SD structure is necessary, neither in the
case of a passive environment. In the case of an active environment on the other hand it
seems very useful to use System Dynamics as the dynamics are constituted by aggregate
values gained out of the Agent-based model.
It remains questionable how useful this approach is after all. Two ways of generating
dynamics, first by interaction of individual entities and second by feedbacks are
combined, which leaves the analysis of the evolving model even more challenging.
Whether this approach is beneficial strongly depends on the model purpose. In any case
the combination leads to a higher flexibility as the stock-and-flow-notation is enriched
with additional syntax. This would hint towards the idea that stocks can easily be
isaggregated into individual agents without the loss of information (Nevertheless
possibly loosing computational speed).
One of the major advantages that can be gained through the integration of Agent-
based Modeling into System Dynamics models is the spatiality which is easily
implemented by giving each agent a distinct x and y variable. There are different types
of concepts in ABM in order to add information of space. One is the concept of discrete
space which could also be represented within stock and flow notation. However it
remains unanswered whether this would still be consistent with the traditional concept
of stock and flow.
Interaction of paradigms
“While the conventional wisdom suggests that reality is causally prior to theories that
attempt to explain it, it is clear that causality runs in both directions. Theories and
beliefs, once widely accepted, shape behavior in ways that make reality consistent with
the theory, even when it was not initially the case.”*
As discussed above methodologies assemble a distinct set of hypothesis regarding the
underlying sources of dynamic in a system. Repenning* illustrates that it is risky to
assume those sets for a given problem unreflectively. The challenge is to stay aware of
those sets and to apply them adequately.
The most promising approach of a reflection upon the underlying assumptions of a
modeling paradigm is a lively discussion with experts of the other fields (in this case
Agent-Based Modeling or Discrete-Event Simulation). In addition it seems valuable to
foster the integration with Agent-Based Modeling as it is increasingly being integrated
into the social sciences. Two fields which are particular interesting are the so-called
socionic, which evolves out of sociology, based on the first steps made by Axelrod
and the Agent-Based computational economics, promoting the application of Agent-
Based Modeling to economic questions. As those fields are both still relatively young,
they might profit from the insights gained in System Dynamics. Once the assumptions
of both methodologies have been clearly formulated as assumptions, which is a
legitimate process, a collection of arguments for these assumptions could be started
within the fields. A starting point might be Phelan:
Repenning, Nelson, Selling system dynamics to (other) social scientists, System Dynamics Review, Vol. 19, No. 4, p.325
“ Repenning, Nelson, Selling system dynamics to (other) social scientists, System Dynamics Review, Vol. 19, No. 4
* Axelrod, The evolution of cooperation, London, 1984
“Tt is something of an article of faith with systems theorists that a combination of
positive or negative feedback (including self-referential behavior) is a useful way of
characterizing interactions in a system. One of the weaknesses of the approach is that
stocks and flows invariably refer to the quantity rather than to the quality (or any other
characteristic) of an element (or its attributes).’*°
Conclusion
Based on the basic principles of how to reach conclusions in science theory it must be
acknowledged that by crude application of modeling methodologies we risk wrong
conclusions through the implicit acceptance of underlying assumptions in established
paradigms (abduction risk). Therefore this paper proposes to integrate the discussion
and selection of suitable modeling methodologies into the early stages of any modeling
process.
By discussing and comparing underlying assumptions as well as technical differences
of the three paradigms (SD, ABM and DES) this paper provides important indications
which aspects need to be taken in account. These aspects can be categorized in the
dimensions purpose, object and methodology.
Purpose refers to the initial motivation of the modeling effort and can include aspects
such as:
- Tracking individual behavior’?
- Understanding aggregate values
~ Gaining insight in a specific (not yet understood) problem context
= Reproducing a given system behavior
- Optimizing specific system values
- Evaluation of long term policies
= Ete.
Object relates to the real world characteristics of the problem context and includes
aspects such as:
- Level of detail of available information
- Uncertainty of available information
- Continuous or discrete system behavior
= Number of relevant entities
- Importance of interaction
- Differentiability of entities (individual properties such as entity history and
spatiality)
“© Phelan, Steven, A Note on the Correspondence Between Complexity and Systems Theory, Systemic Practice and Action
Research, Vol. 12, No. 3, 1999, p. 240
*” Compare Sterman, Business Dynamics. Systems Thinking and Modeling for a Complex World, Boston, 2000, p.208, “When the
purpose of the model requires tracking the individual people, for example modeling the behavior of people entering the line at the
supermarket to determine the optimal number of checkout counters, then people can be modeled as discrete individuals arriving at
discrete points; this is a classic modeling paradigm in queuing theory.”
- Etc.
Methodology refers to the general approach, the underlying assumptions and
suggested methods and techniques of a given modeling paradigm. Methodology aspects
include:
= Perspective (top down vs. bottom up)
- Predominant source of dynamics (e.g. feedback, coupled events, interaction
of agents, ...)
- Perception of time (discrete events, time slicing, continuous, etc. )
- Available methods and tools
- Validation techniques
~ Etc.
This paper argues that only by aligning these three dimensions (purpose, object and
methodology) the best suitable methodology for a given problem or sub-problem can be
identified. This argumentation of course also applies to the combination of
methodologies for different sub-problems in multi-paradigm modeling efforts. The
ability to link purposes and objects with alternative methodologies will hopefully
overcome a typical phenomenon that practitioners of a specific methodology “define
different problems, follow different procedures, ..2"8. Our vision is to select the most
suitable methodology for a given purpose and object.
*S Meadows, The unavoidable A Priori, p. 24 in Randers, Elements of the System Dynamics Method, Cambridge/ London, 1980
Methodology
Purpose Object
Methodology
Vision: Purpose
Beyond the abduction trap
Figure 2: Vision of Multi-Paradigm Modeling
Concluding the discussion of this paper it must be admitted, that there is still a way to
go in order to provide the wanted orientation framework that can be applied by
modeling practitioners independently. First steps will now be made in the form of
criteria hinting towards a specific methodology, which is proposed for discussion. These
criteria correspond to the underlying assumptions of the methodologies and form
guidelines to the choice of the adequate methodology in a specific modeling task.
-Interacting entities
-Spatial distribution
-Heterogeneity
Agent-Based
Modeling
-Strategic problems
S “a
-Feedback
-Stochastic variation . a
-Nonlinearities
-Linear relationships
Discrete-Event ] System
Simulation 7 Dynamics
-Logistic problems I -Strategic problems
-Quantitative optimization -Long-term policy development
-Aggregated perspective
Figure 3: Criteria for adequate modeling methodologies
Together with the developed categories and the discussion above these criteria form a
first step towards an orientation framework in multi-paradigm modeling. Further
research is necessary in subsequent steps in order come closer to this declared goal.
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