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Insight Maker: A general-purpose tool for web-based modeling & simulation

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A web-based, general-purpose simulation and modeling tool is presented in this paper. The tool, Insight Maker, has been designed to make modeling and simulation accessible to a wider audience of users. Insight Maker integrates three general modeling approaches – System Dynamics, Agent-Based Modeling, and imperative programming – in a unified modeling framework. The environment provides a graphical model construction interface that is implemented purely in client-side code that runs on users’ machines. Advanced features, such as model scripting and an optimization tool, are also described. Insight Maker, under development for several years, has gained significant adoption with currently more than 20,000 registered users. In addition to detailing the tool and its guiding philosophy, this first paper on Insight Maker describes lessons learned from the development of a complex web-based simulation and modeling tool.
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Insight Maker: A general-purpose tool for web-based modeling
& simulation
Scott Fortmann-Roe
University of California, Berkeley, Department of Environmental Science, Policy, and Management, 130 Mulford Hall, Berkeley, CA 94720-3114, United States
article info
Article history:
Received 29 April 2013
Received in revised form 23 March 2014
Accepted 26 March 2014
Keywords:
Modeling
Simulation
Web-based technologies
System Dynamics
Agent-Based Modeling
abstract
A web-based, general-purpose simulation and modeling tool is presented in this paper. The
tool, Insight Maker, has been designed to make modeling and simulation accessible to a
wider audience of users. Insight Maker integrates three general modeling approaches
System Dynamics, Agent-Based Modeling, and imperative programming in a unified
modeling framework. The environment provides a graphical model construction interface
that is implemented purely in client-side code that runs on users’ machines. Advanced fea-
tures, such as model scripting and an optimization tool, are also described. Insight Maker,
under development for several years, has gained significant adoption with currently more
than 20,000 registered users. In addition to detailing the tool and its guiding philosophy,
this first paper on Insight Maker describes lessons learned from the development of a com-
plex web-based simulation and modeling tool.
Ó 2014 The Author. Published by Elsevier B.V. This is an open access article under the CC BY
license (http://creativecommons.org/licenses/by/3.0/).
1. Introduction
The field of modeling and simulation tools is diverse and emergent. General-purpose modeling tools (e.g. MATLAB’s
Simulink or the Modelica language [1]) sit beside highly focused and domain-specific applications (e.g. [2] for modeling
network control systems, [3] for simulating the behavior of wireless network routing protocols, or [4] for the simulation
and control of turbines). Interest in and published works on such tools has grown over time. The ISI Web of Knowledge
reports a substantial growth in papers published on modeling or simulation tools with 299 such papers published in the span
of 1985–1989, 1482 published from 1995 to 1999, and 3727 published from 2005 to 2009.
1
For end-users, simulation and modeling tools are generally designed as executables to be run on a consumer operating
system such as Windows or Mac OS X. With the expansion of the Internet and the ubiquity of the World Wide Web, new
possibilities to harness this communication technology and platform to develop rich collaborative modeling tools have
become available. One major review of the opportunities and issues faced when utilizing web-based technologies as part
of a simulation or modeling application has been [5]. However, technology has advanced rapidly in the period since the pub-
lication of that review. Competition among technology companies such as Apple, Microsoft and Google has led to a rapid
increase in the availability of advanced features in web browsers and significant performance enhancements in these same
browsers (these improvements are documented at sites such as http://AreWeFastYet.com and http://html5test.com). Such
improvements have changed what is effectively possible in the browser. Where [5] note that web-based technologies were
http://dx.doi.org/10.1016/j.simpat.2014.03.013
1569-190X/Ó 2014 The Author. Published by Elsevier B.V.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).
E-mail address: ScottFR@berkeley.edu
1
The exact search query used was ‘’’modeling tool’’ OR ‘‘simulation tool’’’ in the Topic field.
Simulation Modelling Practice and Theory 47 (2014) 28–45
Contents lists available at ScienceDirect
Simulation Modelling Practice and Theory
journal homepage: www.elsevier.com/locate/simpat
not well suited to ‘‘local simulation and visualization’’ running all simulation code on an end-user’s machine that is no
longer the case as the work presented here demonstrates.
Other work on the intersection between simulation and modeling tools and web-based technologies includes but is not
limited to, [6] who develop a simulation–optimization platform for industrial applications, [7] who propose a framework for
online collaborative modeling and simulation an approach to environment construction adaptable across multiple domains,
[8] who study the execution of simulations in cloud-based platforms, and [9] who explore collaborative model integration in
a distributed environment. What is missing from earlier work, however, is a realization of a general-purpose simulation
environment developed using web-based technologies targeted first at a general audience.
Web-based technologies are especially beneficial to non-experts as they can significantly reduce the costs required for
a new user to experiment with and learn about a simulation and modeling tool. Simulation and modeling tools have been
shown to be useful instructional devices (e.g. [10] who used a simulation tool in the economics classroom or [11] for
examples of work in primary schools). By developing web-based simulation and modeling tools, the accessibility of these
tools can be increased both within the classroom and outside it. A layperson considering modeling may be adverse to
downloading and installing modeling and simulation software on a personal computer (due to fear of viruses and other
concerns). On the other hand, the same person may be more willing to open a simple web page that contains a simulation
model or embedded model construction interface. Lowering barriers to entry make it possible to engage more people in
modeling and simulation, potentially leading to societal benefits as a result of an increased usage and understanding of
modeling.
The rest of this paper presents the simulation and modeling tool Insight Maker (available at http://InsightMaker.com). It
is a free, open-source modeling and simulation tool developed using web-based technologies and supports graphical model
construction using multiple paradigms. The software is designed primarily to be as accessible to the layperson as possible,
but also contains significant advanced modeling tools such as embedded scripting capabilities and an optimization toolset.
Insight Maker was made public at the end of 2009 and has undergone continual development and evolution since then. Since
its release, the tool has gain over 20,000 registered users. The feedback from these users has helped set the course for the
direction and development of the tool.
The remaining sections of this paper first describe the philosophy and design principles of the simulation and modeling
tool. Next the architecture of the tool is detailed. As a web-based technology, the tool includes both server-side and client-
side components and this architecture is discussed. Particular attention is paid to the benefits offered and compromises
required to successfully implement a complex tool such as Insight Maker in a web-based environment. Finally, given that
the tool has undergone multiple years of iteration and development based on user feedback and benchmarks of user adop-
tion, conclusions and lessons learned from this evolution are also presented.
2. Guiding principles
It can be argued that three basic criteria should be used when assessing a tool or environment used to develop simulation
and models: performance, features, and accessibility. A high-performing environment is one that executes simulations
quickly with minimal resource requirements. Features are capabilities and high-level functionality in the simulation and
modeling tool. Accessibility indicates how easy it is to learn or use an environment. There are generally tradeoffs among
these criteria in the face of a fixed amount of development resources:
Performance versus features: Adding features to the simulation tool may often result in a negative impact on performance.
In addition to software ‘‘bloat’’, certain features may require computational overhead during simulations or make it more
difficult to implement some types of optimizations.
Performance versus accessibility: Making a simulation program accessible to users often requires utilizing higher-level
concepts divorced from the underlying machine hardware. An environment’s ability to convert higher-level concepts
to efficient machine code vary, but in general, accessible higher-level environments will have reduced performance when
compared to less accessible, lower-level environments.
Accessibility versus features: A baseline of features is important to make a simulation program accessible for users (e.g. a
Graphical User Interface). However, many features added to simulation software are targeted at specific subsets of users
and offer little value to the average user. Excess features that lead to ‘‘bloat’’ may result in user frustration or the feeling of
being overwhelmed [12].
Performance versus accuracy: One final tradeoff is between performance and accuracy, as they are often inversely corre-
lated. This tradeoff may often be exposed directly to users allowing them to determine how to balance these competing
goals.
Although tradeoffs may be mitigated through increased development time or resources, the choices developers make
about these tradeoffs are key in defining their simulation programs and environments (Fig. 1). As an example, models
and simulations may be developed in raw assembly as machine processor instructions. Such models should have excellent
performance, but their development would be highly difficult as assembly is inaccessible and has a minimal built-in feature
set. At the cost of some performance, higher-level development environments such as C++ are alternatives. Higher-level tools
S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
29
offer increased accessibility and features, but in exchange are often not able to match the performance of a highly optimized,
lower-level alternative.
Insight Maker prioritizes tradeoffs among performance, accessibility and features in the following way. Accessibility is
given primary priority, followed by features, with performance assigned the lowest priority. Accessibility is the primary goal
of Insight Maker and is central to the design of the tool from the perspective of the overall program architecture (namely, the
choice of implementation as a web application to increase application availability), to small language design choices (such as
the use of case-insensitivity in the language), to cosmetic choices.
The inclusion of a rich feature set is Insight Maker’s second priority. Many tools and capabilities are included in the
program such as a built-in optimizer and scripting language. In adding features, attempts are made not to significantly
increase the apparent complexity of the software; this has meant making those features available for users who desire them
but highlighting a basic set of functionality for newer users who are not immediately interested or able to use the more com-
plex features. An instance of this approach is Insight Maker’s support for measurement units. The simulation engine contains
the ability to associate units with each number in the simulation that are then automatically checked and validated when the
simulation runs. This useful capability can catch a class of equation errors and improve the reliability of models. However, it
can also decrease the accessibility of the software as it requires that users specify the units upfront when constructing a
model, which can be an unnecessarily complex burden for many applications. Thus, the simulator makes units a purely
optional feature in model construction, which the user can ignore or fully engage with depending on their individual skill
level and needs.
The priority that is least focused on in Insight Maker is performance. Significant work has gone into optimizing the
application. Nevertheless, choices made as a result of prioritizing accessibility first and features second make it impossible
to achieve speeds that would be possible if performance had been the primary priority. For instance, the choice of a web
application architecture imposes significant limitations on the application’s performance. As a pure web application, the sim-
ulator must use ECMAScript as its primary programming language
2
which has good, but not excellent, performance charac-
teristics, being roughly 2–8 times slower than C++ for numerical work [13]. Similarly, specific features may have a performance
cost. For instance, the support of units in Insight Maker requires an aggregate data object to be maintained representing the
results of calculations. This data object has significant performance costs compared to the usage of generic numbers.
3. The application
Insight Maker as a web application means that users run it by accessing a URL through their web browser. The application
provides a number of different services that both mirror what would be found in a traditional desktop application model
construction and model simulation but also extend beyond into areas more specific to a web environment user account
management as well as model searching and sharing. Although the latter services are important to the proper functioning of
the application, they serve a purely bookkeeping role and are not intellectually interesting in the context of modeling and
simulation. Instead, it is the novel simulation and modeling aspects of the application that are the focus of this section
and paper.
Fig. 2 illustrates the primary model construction interface of Insight Maker running within the Google Chrome web brow-
ser. The interface is divided into three primary components: the model diagram, the toolbar and the configuration panel. The
model diagram is an interactive illustration of the current model’s structure along with additional UI features such as textual
descriptions, pictures and interactive buttons. Users may select, position and resize elements in the model diagram using an
Fig. 1. Conceptual illustration of priority tradeoffs for simulation and modeling tools.
2
Other languages such as Java and Flash are often used in the browser. However, usage of these technologies require that users have plug-ins installed to
support them. Many users may not.
30 S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
input device such as a mouse or, on touch devices such as tablets, their finger. Each item in the model diagram has a set of
attributes associated with it that control its behaviors. The attributes can be configured in the configuration panel. The tool-
bar at the top of the window provides a number of functions. It contains a selector to add different types of objects to the
model diagram (both for simulation and for descriptive purposes), standard tools for document editing (undo/redo, copy and
paste, etc.), styling options to adjust the appearance of objects in the diagram (coloring and font characteristics), tools to
interface with the simulation, and buttons to save the completed model or start a simulation of the model.
The entire model building and simulation aspect of the application runs within a single web browser window. When a
simulation completes, results are displayed within the same browser window. A number of different display types for results
are available including time series charts, tables, histograms, scatterplots, and two-dimensional maps (Fig. 3). For offline
analysis, users can export results to CSV files. In addition to the display of results, a number of other windows and config-
uration dialogues open within this main window. By way of example, dialogues to configure an object’s mathematical equa-
tion, set simulation time settings, and carry out optimization runs or sensitivity tests all open within this primary window.
The entire contents of this window are defined using standard web technologies such as Hypertext Markup Language
(HTML) and Cascading Style Sheets (CSS).
4. System architecture
The application uses a client–server architecture (Fig. 4), where clients (user computing devices) are connected to the ser-
ver over the Internet. Users may use the web browser on their machine to connect to the server and load the model construc-
tion and simulation environment. The server-side components are responsible for managing user accounts, storing user data
and models, and providing search infrastructure. The client-side components provide model-editing capabilities along with
model simulation and analysis functionalities. Clients do not communicate with one another directly and instead all com-
munication happens through the centralized server.
It is important to note that the client-side code runs the simulation. An alternative would be to place the simulation logic
and code on the server and simply use the client for model construction and the reporting of results. This latter structure
was, in fact, how the application was originally designed. There are tradeoffs between these two approaches. In general,
optimized server-side simulations should be faster than client-side, ECMAScript-powered simulations. For small models,
however, the latency of sending data back and forth to the server may result in a server-side simulation effectively being
slower than client-side simulations. Other trade-offs between server-side and client-side simulations involve issues with
proprietary models (client-side simulation gives the client access to the model, making it impossible to release a model
Fig. 2. The primary model construction interface running within the Google Chrome web browser.
S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
31
without also releasing access to the model details) and the effects of software popularity (server-side simulations can
become costly and require the purchasing of additional servers, if the software experiences significant demand; client side
simulation reduces this pressure). Ideally, both server-side and client-side simulation options would be available for the user
to choose between. Unfortunately, this would most likely require maintaining two simulation code bases, which is currently
beyond the scope of the resources available to this project.
In terms of technological choices, the tool uses standard open-source technologies and runs on a generic Linux/Unix
server. As much as possible, existing open-source technologies and solutions were used to minimize costs and increase
the portability of the system. Data are stored on the server in the open-source MySQL database, while the open-source
language PHP and the open-source content management system Drupal are used to store data and implement server-side
application logic. The open-source application Lighttpd is used as the actual server software.
Fig. 3. Example of simulation output displays. Clockwise from upper left: the simulation of the spread of disease in a community, the distribution of two
attributes of individual agents in a simulation, a simulation of world population growth, the simulation of location and connections between individual
agents in a model.
Server
Client
• Stores models
• Manages user accounts
• Manages collaborative
editing
• Model construction
• Simulation
• Result display
Fig. 4. Overview of tool’s client–server architecture.
32 S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
5. Simulator architecture and capabilities
The simulator portion of Insight Maker is architected modularly in multiple layers, where the higher-level layers depend
on functionality provided by the lower levels (Fig. 5). The layers may be grouped into separate tiers that represent broad
classes of functionality. Tier 0, the lowest level tier that provides the foundation for the simulator, is the ECMAScript
programming language (colloquially referred to as ‘‘JavaScript’’). ECMAScript is a dynamic programming language with high
performance implementations available in every modern browser. The simulator uses ECMAScript 5 or higher and is
supported in all modern browsers.
5.1. Tier 1
Tier 1 provides mathematics and equation language engines to evaluate equations entered by users. The engines
themselves are generic, computational tools and do not provide simulation and modeling specific features. Such features
are provided by the higher tiers that will build on this tier.
5.1.1. Mathematics engine
The mathematics engine parses and evaluates mathematical statements. There are two distinct underlying numerical
libraries that the simulator may use. One generic calculation engine is provided by the ECMAScript environment itself. This
is a purely double precision floating-point library with no integer, fractional or decimal data types. The second library is an
arbitrary precision mathematics library implemented in ECMAScript. This second library supports precise decimal mathe-
matics and numbers of arbitrary size with no numerical errors or imprecisions. The tradeoff between the two libraries is
one of performance versus accuracy. The arbitrary precision library requires a large performance penalty over the native
ECMAScript mathematics. On the other hand, the native library will have small errors due to the inherent inaccuracies in
floating point numbers.
3
The open-source simulator can be configured to use either library. For the deployment of the Insight
Maker code base on InsightMaker.com, only the native ECMAScript numeric library is made available to users in order to max-
imize the performance of user models (at the cost of some precision).
Fig. 5. Overview of the simulator architecture.
3
An illustration of this lack of precision in double precision floating point math engines (utilizing the IEEE 754 standard [14]) is that the summation of ‘‘0.1’’
and ‘‘0.2’’ will evaluate to ‘‘0.30000000000000004’’. Many environments (such as Insight Maker) will attempt to round off the imprecisions when displaying the
results thus hiding the issue from the user. Applications that require high precision, however, render such imprecisions potentially problematic.
S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
33
Additionally, the mathematics engine supports tagging numbers with arbitrary measurement units (e.g., instead of
stating the length of an object in the model as ‘‘5’’, it can be declared as ‘‘5 meters’’). The engine enables the transparent
conversion between equivalent units and also the raising of exceptions when incompatible unit operations are attempted.
This is primarily useful for end-users in that it provides an additional check that equations are entered correctly.
5.1.2. Equation engine language
The simulator includes a general equation engine language that sits above the mathematical engine. This equation engine
language is a general-purpose programming language with domain specific features targeted toward modeling and simula-
tion utilization. Language features include: the usage and creation of block-scoped variables; the usage and creation of func-
tions; flow control, including If-Then-Else statements, While loops and For loops; and the construction of vectors (arrays).
Although the equation engine has a rich feature set, in most practical cases it serves as a thin layer over the mathematics
engine in order to allow users to enter simple mathematical expressions. The more complex features are generally only
required when constructing complicated Agent-Based Models. An example of the equation engine used for a simple recursive
calculation is shown in Table 1 and provides the reader a feel for the language characteristics. Again it is important to under-
score that the equation engine language is implemented purely in ECMAScript (including the equation engine language’s
tokenizer, parser and interpreter) and can be run in a web browser.
5.2. Tier 2
Tier 2 of the simulator is a multi-paradigm modeling environment that supports several different approaches to modeling
(Table 2). Each approach has a different tradeoff between flexibility and ease-of-use. System Dynamics is highly abstract and
aggregate. Agent-Based Modeling is often much more granular, allowing increased control over the system but at the
potential cost of decreased performance and increased modeling effort. Imperative programming, on the other hand, has
no modeling-specific constraints and can be flexible to address any modeling task but potentially at a high cost in develop-
ment time. The simulator allows for the seamless integration of the three approaches within a single model, enabling differ-
ent resolutions and methods for different portions of the model as required.
5.2.1. System Dynamics environment
System Dynamics is a modeling paradigm developed in the 1950s to study industrial systems [15]. The technique is
general and has since been applied to a range of different systems including, notably, the development of urban systems
[16] and forecasting world wide trends [17]. Mathematically, System Dynamics models are often sets of nonlinear differen-
tial equations. What sets System Dynamics apart from the standard analytical analysis of differential equations is that the
System Dynamics community focuses on easy-to-use graphical tools and numerical analysis of simulation results. System
Dynamics modelers are also primarily focused on feedback loops and the roles they play in the evolution of a system.
Table 1
Example usage of equation engine to define and utilize a custom function.
Function Fib(n)
If
n=1orn=0
Then
1
Else
Fib(n 1) + Fib(n 2)
End If
End Function
# Calculates the tenth Fibonacci number
Fib(10)
Table 2
Modeling paradigms supported by the simulator.
Basic principle Strengths Weaknesses
System Dynamics Models system on a highly aggregate
level using rates of changes and state
variables
Results are generally easy to interpret.
Models can be simulated rapidly
Not well suited to modeling heterogeneity
Agent-Based Modeling Models individuals each with their
own properties and the interactions
between individuals
Highly relatable results useful for
communication. Can model systems
in great detail
Potentially slow and can be hard to interpret
results due to stochasticity
Imperative
Programming
Develop logic using standard
programming concepts
Highly flexible. Potentially very fast
model execution
Limited abstraction. May require significant
development effort
34 S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
5.2.1.1. Primitives. System Dynamics models are built graphically out of primitives: building blocks each with a unique
function. The basic paradigm is that of a stock-and-flow model (referred to in some fields as a compartmental model), where
material is moved by flow primitives between stock primitives. This maps conceptually and directly onto standard differen-
tial equation or dynamical systems models used in many fields. In this mapping, stocks represent state variables and flows
represent the derivatives (or rates of change) of these state variables. The key primitives provided by the simulator are
described in Table 3.
5.2.1.2. Functions.
Although not strictly formalized, the System Dynamics community has evolved conventions for functions
and patterns of model construction. These numerous conventions are generally shared among different System Dynamics
simulation software tools along with System Dynamics education resources. The conventions are followed within the sim-
ulator’s System Dynamics environment by including standard System Dynamics functions, such as those for generating
canonical inputs (e.g. RAMP, STEP, and PULSE input functions) and functions for causing various forms of delays and feedback
(e.g. DELAY1 and DELAY3, being first and second order exponential delays respectively). Such conventions facilitate the
movement of models and ideas between System Dynamics software environments and they are supported in the implemen-
tation of the simulator.
5.2.1.3. Numeric differential equation solver.
The simulator includes two numerical solvers to estimate solutions to user-
defined differential equations underlying the System Dynamics models: Euler’s method and a 4th Order Runge–Kutta
method. Generally, the 4th Order Runge–Kutta method should be the preferred choice over Euler’s method due to its
increased accuracy per unit of computational effort. Nonetheless, Euler’s method may be preferred in two cases first, when
there are a number of discontinuities in the rates of change for the systems state variables. In this case, the averaging process
of the Runge–Kutta method might not be desirable. The second usage case for Euler’s method is for learning and educational
environments, as it is conceptually simpler and easier to understand as compared to the 4th Order Runge–Kutta method.
5.2.2. Agent-Based Modeling environment
Agent-Based Modeling simulates the individual actors or agents in a model [18]. Each agent has the potential ability to
independently modify its state, based on rules or algorithms. Agents may modify their state in relation to other agents, form-
ing systems and developing complex system-level behaviors [19,20]. This represents a significant difference from System
Dynamics modeling, which addresses aggregated behavior and results. Simulating individual agents allows for finer grained
models and greater flexibility, but it comes at a cost of increased computational effort and potentially leads to results that are
more difficult to interpret.
5.2.2.1. Primitives.
The simulator includes an approach to constructing Agent-Based Models that, in terms of user-interface
elements, is very similar to that used to construct System Dynamics models. As in System Dynamics models, Agent-Based
Models are built graphically using a set of primitives, each of which fulfills a specific modeling function. Whereas in the Sys-
tem Dynamics modeling paradigm the primary product was the stock and flow diagram, in Agent-Based Modeling it is a state
transition chart where an agent may occupy one or more states and transition between them as a function of mechanistic or
stochastic rules. Table 4 summarizes the primitives used to construct Agent-Based Models in the simulator.
Table 3
Overview of key System Dynamics primitives in the tool.
Primitive Use Example usages
Stock To store a material. Equivalent to a state variable in a
differential equation
A lake that stores water. A bank account that stores money. A population
that stores people
Flow To move material between stocks. Equivalent to a
derivate term in differential equations
A river into a lake. Withdrawals from a bank account. Deaths in a population
Variable To store a parameter value or dynamically calculate a
feature of the model
The flow rate for a river. The interest rate for a bank account. The death rate
for a population
Converter To load tabular data. To carry out a non-parametric
transformation function
A schedule of flow rates by time of year. A non-parametric function relating
population death rate to population size
Table 4
Overview of key Agent-Based Modeling primitives in the tool.
Primitive Use Example usages
Agent population A collection of agents of a given type A population of people. A forest of trees
State Defining the status of a given agent.
A binary attribute
a
Given a person, are they a male or female?
Given a disease simulation, is the person in the healthy
or infected state?
Transition Moves agents between states The process of infection moving a person from the healthy state to infected state
Action Executes arbitrary actions for an agent An action to move the agent away from infected agents. An action to change a
state based on a global condition
a
For continuous state variables, stocks may be used within an agent.
S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
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Although Agent-Based Modeling can be conceived as distinct from the System Dynamics paradigm, they are in fact fully
integrated in the simulator and the distinction between them is made solely to facilitate discussion in regards to existing
paradigms. System Dynamics primitives can readily be included in primarily Agent-Based Models (for instance, a stock
and flow model can be created within an individual agent) and vice versa. Thus, while states only represent binary values,
stocks can be included within agents to track continuous state variables.
5.2.2.2. Functions.
A number of functions included in the simulator are specifically targeted at building Agent-Based Models.
One category of functions deals with selecting agents matching certain criteria from a population. For instance, the FIND-
STATE function will return a vector of all the agents in a model that have activated a given state. Find statements can be
nested enabling binary AND logic, and the results from separate find-statements may be merged enabling binary OR logic.
The Agent-Based Modeling in the simulator supports two forms of geographic relationships between agents: two-
dimensional geography and network geography. Agents may be given a physical position within the plane. Their position
may be queried or used as a selector (e.g. the FINDNEAREST or FINDFURTHEST functions to select agents that are, respec-
tively, close to or far from a given target) and the position may also be modified (e.g. the MOVE or MOVETOWARDS func-
tions). With regard to network geometry, each agent may have one or more connections to other agents. Each connection
is binary and may be queried or modified as the simulation progresses (e.g. with the CONNECT or FINDCONNECTED
functions).
5.2.2.3. Imperative programming environment.
The equation engine language is an imperative programming language. This
language will generally be used to write elementary mathematical equations. It can also be used to implement algorithms
or model logic that does not fit within the System Dynamics or Agent-Based Modeling paradigms. These custom functions
and code developed using the imperative environment can augment the System Dynamics or Agent-Based Modeling
environments by providing additional functionality within them. For instance, a function could be defined in the imperative
environment to carry out some numerical algorithm and that function will automatically become available for use by equa-
tions in the other environments.
5.3. Tier 3
The third tier consists of the model itself along with tools and services that operate on a given model. Three primary tools
are offered by the simulator: an optimizer that maximizes or minimizes a goal, a sensitivity testing tool, and an API that can
be used to script model behavior or analyze model results.
5.3.1. Optimizer
The simulator includes an optimizer to determine the set of parameter values that minimize or maximize an objective
function. The user specifies the objective function, the parameters that should be adjusted, and the respective ranges of these
parameters. The optimizer then explores the specified parameter space in search of the parameter set that achieves the objec-
tive. The study of optimization methods is a wide, multi-discipline field with numerous techniques and approaches available.
Optimizations of the arbitrary user specified models in the simulator are, however, constrained by three primary features:
Non-convex objective functions: Although some models and associated optimization tasks may result in convex optimiza-
tion problems, in general it should be assumed that the parameter space for a given model has multiple local minima.
Non-smooth objective functions: Given the use of logical functions in a model (e.g. if-then-else statements), it is quite
possible for the objective function to have sharp discontinuities. Even without the usage of such functions, the numerical
limits of the floating-point mathematics engine could create discontinuities on a fine scale.
No analytic derivatives: Although the derivatives or Hessian matrix at a given point in the parameter space may be
estimated numerically, it is generally impossible to calculate them directly.
A wide class of techniques used to address such optimization problems are known as ‘‘Direct Search’’ methods [21–23].
This class includes methods which do not rely upon differentials, such as the classic Nelder-Mead Simplex search [24],
genetic algorithms [25] and simulated annealing [26]. Published comparisons between techniques exist (e.g. [27]); however,
the results can often be context-dependent and vary across applications. For the simulator, a form of direct search based on
Powell’s method [28] is implemented.
Briefly, Powell’s method takes an initial starting point and a set of search vectors that span the parameter space. The objec-
tive function is evaluated at the starting point. Then for each search vector the objective is in turn evaluated at a new position
that is a given search step size in the positive direction along that vector and, if an improved solution is not found, subse-
quently in the negative direction. As soon as an improved solution is identified, the center of the search is relocated along that
search vector to a distance twice the search step size (the optimistic assumption being that if an improvement is found in a
direction, the solution will continue to improve if the optimizer continues in that direction). After a full iteration through all
the search vectors is completed, a combined search vector is constructed as a composite from all the moves that were taken in
that iteration. This composite search vector then replaces one of the existing vectors in the set of search vectors. If no move is
made, the step size is reduced or the search can be terminated according to a stopping condition.
36 S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
Note that the search algorithm as described is purely deterministic. The algorithm will find a single minimum value that,
if multiple minima exist, may or may not be the global minimum. Many optimization techniques address this issue by intro-
ducing stochasticity into the optimization process (e.g. simulated annealing or genetic algorithms). Given convex problems,
such stochasticity may, however, reduce efficiency in finding the minimum. As such, the simulator uses the deterministic
algorithm as described, but deals with local minima by offering random starting locations for the search pattern. For
instance, given an optimization problem where local minima are known or expected to exist, the optimizer could be run
ten times, each time starting at a different random location. If all ten optimization sequences converge to the same mini-
mum, it is highly likely the global minimum has been found. If all ten optimization sequences converge to separate minima,
then little evidence is there to conclude that the global minimum has been located.
5.3.2. Sensitivity testing
The simulator’s sensitivity testing tool repeatedly runs a simulation and aggregates results. It can display the aggregated
result by plotting results for each run or by averaging the runs and calculating their distribution. The sensitivity-testing tool
has several general use cases:
Average responses and variances for stochastic models: Given a modification to a model’s parameter values, most models
will exhibit a changed trajectory of results. For stochastic models, it can be difficult to ascertain when changes in the tra-
jectory were caused by the parameter modifications and when changes were caused by the model’s inherent stochastic-
ity. The sensitivity-testing tool allows the simulation to be run many times and the results averaged to numerically
estimate a response independent of the stochastic variations.
Parameter sweeps: Parameters sweeps can determine the model’s response to a range of different parameter values. They
can be useful for exploring model behavior, and the sensitivity-testing tool can automate the process of this exploration.
Uncertainty in parameter values: Model parameter values are often known with limited certainty. The data used to estimate
them may be limited or in some cases non-existent. The simulator’s sensitivity-testing tool allows the formulation of a
probability model to define the uncertainty for one or more parameters and then obtain a numerical estimate of the result-
ing distribution of outcomes given this uncertainty. This form of analysis is recommended as part of the model validation
and verification process to determine whether model results and conclusions are robust to parametric uncertainty [29,30].
The simulator includes a set of functions to generate random numbers according to a range of common distributions (e.g.
the normal distribution, the uniform distribution, and the log-normal distribution, among others) to model the uncertainty
of knowledge about a parameter. The simulation is then repeated, each time sampling a set of a parameter values from their
distributions. This Monte Carlo method enables the propagation of the uncertainty from the parameter values to the results.
5.3.3. API/scripting
The simulator includes an API that can be used to programmatically build models and analyze their results. The API is
implemented in ECMAScript and there are several mechanisms by which it can be accessed. The most basic is through a spe-
cial primitive called a Button that can be added to the model. When a user presses a button primitive, the associated code
and API commands are executed. Another mechanism that can be used to access the API is the browser’s console that allows
users to directly enter API commands in an interactive manner.
The range of API functions includes those for model construction (e.g. CREATEPRIMITIVE or SETVALUE), those for styling
the model (e.g. SETLINECOLOR or SETSIZE), those for running the model (RUNMODEL), and those commands for input and
output (e.g. SHOWDATA or PROMPT). As the commands are implemented in ECMAScript, any standard ECMAScript data
analysis or communication functions may, of course, also be used. These capabilities allow model scripts to, for instance,
download parameter data from an external server on the fly, run the model, analyze the results, and/or upload the results
summary to another server.
6. Integration and portability
Given the usage of standard web technologies (HTML, CSS, and ECMAScript) by the simulator and model construction
interfaces, these aspects of the application are portable and may be deployed in any environment that supports rendering
and displaying web pages. The most common usage for this capability is to deploy content within other web pages. Models
built within Insight Maker can be embedded within external web pages and can retain full interactivity within these external
environments. Users embedding models can also harness the simulator’s API to develop a custom user interface for a model
and simulation. Such custom user interfaces can be used to develop ‘‘serious games’’ (e.g. [31], a game exploring the
Israel-Palestine conflict) or ‘‘flight simulators’’ (e.g. [32,33] for discussions of flight simulators in relation to management
education and training).
7. Validation and verification
Although the application’s development process does not follow testing approaches such as Test Driven Development
[34], an automated suite of internal tests has a key role in ensuring proper simulation behavior and the prevention of
S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
37
regressions. An extensive suite of over 1000 individual tests is part of the simulator that comprehensively evaluates the cor-
rectness of all aspects of the simulator’s behavior. The tests range from the trivial (does the equation engine correctly eval-
uate that 2 + 2 equals 4?) to higher-level aggregate tests (does a given model containing multiple equations and primitives
evaluate to the correct result?). Tests are written as new functionality is added to the program and also in response to reports
of issues from users. When an issue is found, the issue is first corrected and then a test for the issue is written to ensure that
it does not reappear in a later regression. The development of this test suite has proven invaluable in ensuring the proper
operation of the tool.
8. Case study
8.1. Overview
To illustrate the applied use of the tool, a case study is presented in which Insight Maker was used by a group of laypeople
as part of a collaborative modeling development process to explore the impacts of economic policies. Given Insight Maker’s
primary focus on accessibility and collaboration especially among laypeople this example is well suited for illustrating
Insight Maker’s strengths and weakness in achieving this primary goal. The case study is a review of work done by an ad-hoc
group formed under the auspices of Systems Thinking World [35], a non-profit organization focused on exploring the prac-
tical application and realization of systems thinking, a holistic approach to analysis and problem-solving that centers on
understanding the relationships and interactions between the components of a system. Out of the larger organization, fifteen
laypeople organized to better understand the 2007–2008 financial crisis and its aftermath using a modeling-based approach.
The group used Insight Maker for this modeling due to its feature set and web-based nature, allowing them to share mod-
els easily. This latter capability was critical for the group as they were geographically dispersed and all their communication
and coordination occurred over the Internet. In the following sections of the case study, we first present the group’s modeling
process, then detail their final model, and last, explore results and conclusions. While the case study only utilizes a portion of
Insight Maker’s features (it makes no use of the Agent Based Modeling features, the optimizer, or the sensitivity testing tool,
for instance), it does speak to the accessibility and collaborative potential of Insight Maker that, as underscored above, is the
tool’s primary purpose.
8.2. Modeling process
The group was organized non-hierarchically. After formation, group progress followed a ‘‘diverging/converging’’ pattern.
Group members would independently research or study a topic before returning and sharing their findings with the rest of
the group, in turn addressing what the rest of the group had produced during that period. The group found this protocol to be
highly effective; so much so that in the almost seven month period their work took, there was not a single group meeting
among the members. After having developed some dozen models, the group discovered a sector model of the economy
developed by Stephanie Kelton, chair of the Department of Economics at the University of Missouri–Kansas City [36]. This
model had a profound impact on the group’s thinking and in the remaining three months of the group’s work, they took this
base model and experimented with modifications to it.
8.3. Model details
The final version of the group’s Investment versus Austerity model is presented in Fig. 6.
4
This figure depicts a stock and
flow model combined with a number of buttons that users may use to run different scenarios or unfold the model in a struc-
tured revealing of the key components of the model. The model is a conceptual representation of a single nation’s economy.
Because most of the members of the group were located in the United States of America, the group used the term ‘‘dollars’’
to represent monetary units. However, the model was not calibrated to represent a specific economy and was instead focused
on generalized dynamics. There is not a specific currency associated with the model and therefore the term ‘‘dollars’’ as used
here means notional dollars. The rectangular primitives in the model diagram represent stocks. For instance, the firm dollars
stock represents the quantity of money currently held by firms in the economy. The solid lines are flows and in this case model
the movement of dollars between different stocks in the economy. The direction of the arrow indicates the direction of the flow.
The ovals are variables that in this model are primarily used to represent model parameters.
Table 5 shows the unfolding of the model along with descriptions of the model’s key connections and the logic behind
these connections.
Full model primitives and equations are given in Appendix A. One challenge in implementing this model in Insight Maker
was that Insight Maker does not include support for saving various combinations of parameter values. To emulate this sup-
port, the Investment versus Austerity model makes use of Insight Maker’s API/scripting capabilities to develop scenarios and
4
This model may also be accessed in runnable form at: http://insightmaker.com/insight/3023. Note that in this diagram some primitives have the same
name (e.g. there are two ftax primitives). In such cases, the two primitives refer to the same underlying object using an Insight Maker feature called ‘Ghosting’.
These duplicates are created in order to simplify the complexity of the diagram and reduce the need for connection lines that intersect other lines.
38 S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
experiments that can be switched between by end-users. For instance, the code illustrated in Table 6 is executed when a user
clicks the ‘‘Seed Economy’’ scenario button in the model. This code configures the value of the gspend variable and then runs
the model.
8.4. Simulations and results
A number of simulation experiments and scenarios were run by the group with different parameter values and configu-
rations in order to better understand the behavior of the modeled economy. Table 7 lists the primary scenarios developed by
the group. Each scenario was defined by a model parameterization that differed from the other scenarios, thereby leading to
different behaviors. The comparison of the behaviors between these scenarios increased modelers’ understanding of the sim-
ulated economy. The left column displays the scenario name and motivation, the second column indicates the equation
changes that were made to the model to implement the scenario, and the third column lists the key results from running
the scenario. The overrides in each scenario are new equations for a primitive that are used in place of the initial model equa-
tion for that primitive.
5
The overrides in each scenario in the table are cumulative with the scenarios listed above it. Thus, for
instance, the Econ Recovery scenario also includes the overrides from the Profit & Savings scenario.
Example simulation results for two of the scenarios are presented in Fig. 7. The left panel illustrates the Seed Economy
scenario, where the government undertakes deficit spending for a few years to prime the economy. The solid black line
shows additional government spending as a pulse function over three years, that results in funds circulating between firms
(dashed line) and households (dotted line) in a steady state. The accumulated government deficit spending (solid gray line)
reflects the national debt. If nothing else changed, government would not have to inject additional funds into the economy
and the dollars circulating between firms and households would keep the economy in a steady state. The right panel shows
the more realistic Econ Recovery scenario where savings are non-zero. When firms and households save a portion of their
income, they essentially subtract it from the economy. This extraction reduces the funds available for both firms and house-
holds to circulate in the economy (dashed and dotted lines). Unless the government then conducts deficit spending, the
economy will decline, by definition, into a recession and then into a depression. Economic recovery requires continued def-
icit spending on the part of the government to offset the funds extracted by firms and households, other things being equal
(for example, it is assumed no exogenous increases in factor productivity are occurring). The money put back into circulation
to ensure the recovery further adds to the national debt (solid gray line).
These findings along with the entire modeling process were met with enthusiasm among the members in the group. Gene
Bellinger, the group organizer, reports that the group members felt they now understood better how the economy works.
Fig. 6. Schematic diagram of the final version of the Investment versus Austerity model. Stocks are represented by rectangles; variables by ovals; and flows
by solid lines. The shaded rectangles on the left are interactive buttons added by the modelers.
5
These initial equations were designed such that the economy was in steady state with no money flowing.
S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
39
Table 5
Unfolding of the Investment versus Austerity model.
This first connection is based on the simplified perspective that government spending
injects money into the economy via purchases from firms. While the government injects
money into the economy via other streams such as Medicare, Medicaid, and Social
Security; purchases from firms were used as a first approximation of how money enters
the economy from the Government
This second flow represents the fact that firms employ household members to produce
the goods and services purchased from firms. Firms do not purchase services with all of
their funds as some are used to pay taxes and some are saved and distributed out to
stockholders when appropriate
This portion of the model represents the fact that households create demand on firms
though the funds they have for purchases are less than their income as some of the funds
are saved (hsave), some are used to pay taxes (htax) and some of their funds are used to
purchase imports (mpmt) which creates demand in trade dollars
These flows represent the fact that some of the household dollars are used to make
foreign purchases resulting in imports (import pmt). At the same time, foreign
governments, companies, and individuals purchase from the country’s firms, which
results in exports paid for with export payments
40 S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
One can speculate that the increase in understanding the model facilitated among the group’s participants was due directly
to the fact that they were the ones building it rather than it being a model handed down to them by the experts in the field.
9. Discussion and conclusions
This study has been a complex and long-running one that accomplished four primary goals to date:
These added flows represent firms’ tax payments (f-tax) on their profits and households’
tax payments (htax). Both of these taxes represent income to the government and are
used to support government spending (g-spending). When government income is less
than government spending, a deficit results. The accumulation of this deficit spending
over time is represented as the national debt
These flows indicate that households tend to save a portion of their income (hsave) for
future use. This reduces the funds they spend on purchases from firms. Also when firms
keep retained earnings (fsave), it reduces the funds they have available to purchase labor
from households
This final segment of the model represents the fact that if households require additional
funds, they borrow from their savings or from financial institutions (hborrow). When
firms require additional funds they borrow them from their savings or from financial
institutions (fborrow)
Table 6
Script to configure a scenario and then run the model. The findName function takes a primitive name and returns a reference to the primitive object with that
name. The setValue function takes a primitive object and sets its equation to a given value. The runModel function starts a simulation and displays the results to
the user. The equation passed to setValue results in a pulse output that is 0 until t = 1 years and then is 0.5 for the next 3 years before becoming 0 again after
t = 4 years.
setValue(findName(‘‘gspend’’), ‘‘Pulse(1, 0.5, 3)’’);
runModel();
S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
41
1. A general-purpose simulation and modeling tool was built using web-based technologies that supports multi-paradigm
modeling using a graphical model construction interface.
2. The simulation and modeling tool combined both features targeted at laypeople and individuals new to the modeling
field (e.g. a graphical interface) with those targeted at more advanced users (e.g. API and scripting, the optimization tool-
set) within a unified interface.
3. The tool was iterated based on user feedback and its direction was shaped by the needs and problems faced by its users.
This led to an evolution of the software that, though now somewhat different from the original vision, better met the
needs of the majority of users interested in using a general web-based modeling tool.
Table 7
Primary scenarios developed by the group. The overrides in the second column implement the changes needed to explore the questions in the first column.
Scenario Equation overrides Key results
Seed Economy Base Scenario gspend = Pulse(1, 0.5, 3)
Sets government deficit spending to
seed the economy with funds to
prime the simulation
Sets government spending (gspend) to a non-
zero value starting at year one and proceeding
for 3 years.
For the economy to operate, the government has to initially
conduct deficit spending which accumulates as the national
debt
Profit & Savings fsave = Step(6,0.05) Firms and households tend to save a portion of their income,
which in turn takes money out of circulation resulting in an
ongoing decline in the economy
What is the implication of firms
sitting on profits and households
saving funds?
hsave = Step(7, 0.1)
Starting at years 6 and 7, have both firms
(fsave) and households (hsave) save a fraction
of their capital
Econ Recovery gspend = Pulse(1, 0.5, 3) + Step(7, 0.15) To offset the savings by firms and households, the government
must continue deficit spending at a level equivalent to what
firms and households are taking out of the economy. The
problem is that the deficit spending also increases the national
debt
How does deficit spending offset the
savings by firms and households?
Increase government spending (gspend)
beyond the initial pulse by spending a constant
amount starting at year 7
Taxes ftax = Step(6, 0.05) The government requiring the payment of taxes reduces the
level of deficit spending, other things being equal, but also
reduces the funds in circulation thus depressing the economy
What effect does the government
levying taxes have on the
economy?
htax = Step(7, 0.1)
Add a non-zero tax burden to both firms (ftax)
and households (htax) starting in years 6 and 7
Econ Recovery 2 gspend = Pulse(1, 0.5, 3) + Step(7, 0.2)
What is the effect of increased deficit
spending given the presence of
taxes?
Increase the government spending level
(gspend) beyond that of the first Econ
Recovery scenario level
This scenario increases the long run government deficit
spending by 33% to correct the economic decline created from
the levy of taxes
Seed Economy Scenario Econ Recovery Scenario
g-spending
government dollars
household dollars firm dollars
0
-1
-2
-3
-4
1
2
0
-1
-2
-3
-4
1
2
Time (Years)Time (Years)
Monetary Units (Notional Dollars)
0 5 10 15 20
0 5 10 15 20
Fig. 7. Left-Panel, Seed Economy scenario results; Right-Panel, Econ Recovery scenario results. Notional dollars is the abstract unit of money used by the
group in their model of a general economy. In keeping with common System Dynamics modeling practice, the group focused on dynamics and trends rather
than specific quantitative magnitudes and values.
42 S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
4. Usage of the tool continues to grow, indicating the existence of a need and desire for a general web-based modeling tool
and validating the web as a platform for developing complex simulation and modeling tools. As of February 2014, the
software has some 20,000 registered users with over 12,000 models constructed and saved in its database.
Along the way, challenges and points of resistance from users were encountered in the development of the application
that stemmed from its nature utilizing web-based technologies. Four key challenges have been:
1. Security of intellectual property: Models are stored on a centralized server not controlled by the users.
6
For most users this
is acceptable (and they have the ability to back-up the model to their local machines). However, for certain users especially
those within a corporate environment lack of control over the model may be viewed as a security risk. Although Insight
Maker incorporated fine-grained settings to control model access, the fact that the model is stored on an external server
made it inappropriate for some potential users.
2. Performance: Web-based technologies are fundamentally limited in the performance they can obtain compared to their
counterparts developed in more traditional languages. That said, the performance of Insight Maker is quite good in prac-
tice and more than adequate for its main target usage cases.
3. Unfamiliarity of web-based environments: Many users at present are not comfortable using a simulation and modeling tool
within their web browser. It is expected that this will change as people become more familiar with using rich applications
within browsers. Such a trend was seen historically with email clients where once Desktop clients were the norm, but
now web-based clients are ubiquitous.
4. Perceived application quality: A final challenge centers on a perception that web-based applications are inferior to their
desktop counterparts. In the case of the modeling and simulation tool presented here, it is in some ways superior in
capabilities and features to even commercial counterparts. However, the stigma and experience of the restrictive
web applications that users may have come into contact with in the past is difficult to overcome. Again, this is a dif-
ficulty that is expected to diminish over time as users become more familiar with high-quality interactive web-based
applications.
Despite the challenges, modeling and simulation tools developed using web-based technologies have a distinctly positive
future. The application presented in this paper demonstrates the possibilities to create extensive modeling and simulation
tools in a web-based environment. Given the steady improvement in web technologies, the possibilities available to build
such applications will only grow over time. The benefits offered to developers using web-based technologies increased
accessibility, ability to push updates to users immediately, a rich toolkit of open-source libraries, etc. are starting to
outweigh the costs of web-based technologies in cases other than those where performance is the key factor. It is not hard
to imagine a future where web-based technologies are the primary platform for developing simulation and modeling tools
outside that of performance critical applications.
Acknowledgements
This work was supported by a United States National Science Foundation Grant number DGE 1106400. The two anony-
mous reviewers are thanked for their feedback and numerous suggestions that greatly improved this paper. Special acknowl-
edgement should be given to the users of Insight Maker and the invaluable feedback they have provided that has shaped its
evolution, notably, Gene Bellinger and Geoff McDonnell. Great thanks is given to the group who developed the Investment
versus Austerity model described in the case study, and to Gene Bellinger for organizing and encouraging the group.
Appendix A
This appendix presents the full set of equations used in the Investment versus Austerity model and their values given the
application of the scenarios. Primitive names may appear within multiple equations, if the same primitive is referenced
multiple times. This is seen, for instance, when applying the effect of tax. The fraction of firm capital paid in tax ftax
is used to calculate both how much is paid to the government by firms and how much is consequently available for saving
by firms. The following Insight Maker functions and notations were used in the model:
Step(Start, Height): Returns 0 until t = Start, after which it returns Height.
Pulse(Start, Height, Width): Returns 0 until t = Start and after t = Start + Width. In between these bounds, returns
Height.
INTEGRATE(Equation): Integrates the differential equation using the integration method and time step specified for the
model. This is not written within Insight Maker, however, it is included here to make clear the integration process
being carried out during simulation. Applies to stocks only.
6
When InsightMaker.com is used, all models must be saved on the centralized server. The Insight Maker software is open-source and users can download it
and set it up on their own computers. But doing so may be quite difficult for users who are not highly technically proficient.
S. Fortmann-Roe / Simulation Modelling Practice and Theory 47 (2014) 28–45
43
Full model equations:
Primitive
name
Description Initial value/equation (scenarios may change
equations)
fborrow
Fraction of f-finance dollars borrowed 0
fsave Fraction of after tax firm dollars saved Step(6,0.05)
ftax Fraction of tax paid by firm Step(6,0.05)
gspend Variable used to alter Government spending during
the simulation run
Pulse(1,0.5, 3) + Step(7,0.15)
hborrow Fraction of household finance (h-finance dollars)
borrowed
0
hsave Fraction of household income saved Step(7,0.1)
htax Fraction of household income paid in taxes Step(7,0.1)
mpmt Fraction of household dollars spent on imported goods
and services
0
xpmt Fraction of trade dollars that result in firm dollars for
exported goods and services
0
export pmt Payments for exports 0
f-finance
dollars
Balance between firm and household savings less firm
and household investments
INTEGRATE([f-save] [f-borrow])
Value t
0
=0
firm dollars Funds available from export payments, household
goods payments, and investments which are available
for input payments and savings
INTEGRATE([f-borrow] [f-input pmts] [f-
save] [f-tax] + [g-spending] + [export
pmt] + [h-goods pmts])
Value t
0
=0
government
dollars
Difference between government spending and tax
receipts
INTEGRATE([f-tax] + [h-tax] [g-spending])
Value t
0
=0
h-finance
dollars
Balance between firm and household savings less firm
and household investments
INTEGRATE([h-save] [h-borrow])
Value t
0
=0
household
dollars
Funds available for household spending INTEGRATE([f-input pmts] + [h-borrow] [h-
save] [h-tax] [h-goods pmts] [import
pmt])
Value t
0
=0
trade dollars Difference between import payments and export
payments
INTEGRATE([import pmt] [export pmt])
Value t
0
=0
f-borrow Funds borrowed as investment [f-finance dollars] [fborrow]
f-input pmts Firm input payments. This is firm inputs less savings [firm dollars] (1 [fsave])
f-save Portion of firm dollars used to pay down debt or
retained earnings
[firm dollars] [fsave] (1 [ftax])
f-tax Firm taxes paid on retained earnings [firm dollars] [fsave] [ftax]
g-spending Funds injected into the economy by the government.
This is as direct purchases, program support, and social
programs
[gspend]
h-borrow Funds borrowed to supplement household spending
dollars
[h-finance dollars] [hborrow]
h-goods
pmts
Household spending producing demand. This is
household dollars less household taxes and savings
[household
dollars] (1 [hsave] [htax] [mpmt])
h-save
Portion of household dollars used to pay down debt or
saved
[household dollars] [hsave]
h-tax Household taxes [household dollars] [htax]
import pmt Payments for imports 0
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