Introduction to System Dynamics

Home , Computer simulation, Phyllis Fox, System dynamics

系统动力学入门教程

U.S. Department of Energy's

A Systems Approach to Understanding Complex Policy Issues

Version 1.0

Prepared for: U.S. Department of Energy, Office of Policy and International Affairs, Office of Science & Technology Policy and Cooperation

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Index

Overview ...... 4 Chapter 1 Introduction ...... 6 Origin of System Dynamics ...... 6 System Dynamics and Energy Modeling ...... 11 Chapter 2 Why Model? ...... 25 Why Build Models in the First Place? ...... 25 Formal Models ...... 25 Mental Models ...... 26 Combining Mental Models with System Dynamics ...... 27 Chapter 3 The Building Blocks ...... 29 Taking A Dynamic Perspective...... 29 Time Paths ...... 29 Actual Data ...... 33 Seeing System Structure ...... 39 Stocks and Flows ...... 39 Identifying Stocks and Flows ...... 40 Four Characteristics of Stocks ...... 40 Feedback ...... 47 Implicit and Explicit Goals ...... 55 Archetypes ...... 58 Nonlinearity ...... 59 Implications of System Structure ...... 60 A System Problem and Its Symptoms are Separated By Time and Space ...... 60 Counterintuitive Behavior ...... 62 Better Before Worse or Worse Before Better...... 63 Policy Resistance ...... 64 Unpredictability ...... 65 Disequilibrium ...... 68 Chapter 4 Simple Structures ...... 69 Exponential Growth, Exponential Decay, and Goal Seeking Behavior ...... 69 Analytical Versus Simulated Solutions ...... 70 Exponential Growth ...... 76 Goal Seeking Behavior ...... 90 Exponential Decay ...... 93 System Oscillation ...... 97 S-Shaped Growth ...... 102 Chapter 5 The Modeling Process ...... 107 The Modeling Process ...... 107 Management Flight Simulators ...... 110 Chapter 6 Natural Gas Discovery Model ...... 114 Natural Gas Discovery Model: Reference Modes ...... 114

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Step-By-Step Re-Creation of the Natural Gas Discovery and Production Model ...... 116 Natural Gas Discovery and Production Model: First Cut ...... 116 Natural Gas Discovery and Production Model: Second Cut ...... 119 Natural Gas Discovery and Production Model: Third Cut ...... 124 Natural Gas Discovery and Production Model: Fourth Cut ...... 129 Natural Gas Discovery and Production Model: Fifth Cut ...... 133 Natural Gas Discovery and Production Model: Sixth Cut ...... 137 Policy Explorations with Natural Gas Model...... 142 Chapter 7 Next Steps ...... 148 System Dynamics Resources ...... 148

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Overview

The success or failure of a particular policy initiative or strategic plan is largely dependent on whether the decision maker truly understands the interaction and complexity of the system he or she is trying to influence. Considering the size and complexity of systems that public and private sector decision makers must manage, it is not surprising that the "intuitive" or "common sense" approach to policy design often falls short, or is counter-productive, to desired outcomes. This online book was written to introduce the concepts and "language" that make a systems-based study of such complex problems possible. Our intent is to provide the reader with a broad overview of the field of system dynamics, acquaint him or her with the fundamental stock-flow-feedback structures that determine the dynamic behavior in systems, and motivate the reader to begin analyzing problems dynamically and holistically. Knowing how to speak and think in terms of systems and interconnections is a critical step in effective policy design, policy implementation, and consensus building.

 In Chapter 1, Introduction, we provide some context for system dynamics by presenting a brief history of the field, beginning with Professor Jay W. Forrester's work at the Massachusetts Institute of Technology in the 1950's, through the present day. In addition, work related to energy policy is presented in some detail to provide the reader with examples of the type of issues that can be studied using system dynamics principles. In Chapter 2, Why Model?, we continue this discussion by exploring the question: "Why model at all?"  Chapter 3, Building Blocks, presents the basic concepts behind the study of complex systems by first examining the patterns of behavior that real-world systems exhibit, and then discussing the structure that causes such patterns to emerge. This chapter can be thought of as the "language chapter" because it is here that the reader learns the concepts and terms required to construct the "theories" or "models" of their particular issues.  With the concepts and language of system dynamics in hand, Chapter 4, Simple Structures, examines system behavioral types such as exponential growth or oscillation in greater detail. In this chapter, the reader is introduced to the concept of computer simulation. Current computer simulation technology allows decision-makers to easily construct models of a system's structure (including mathematical equations) to use in conducting policy experiments.  In chapter 5, Basic Modeling Process, we share some thoughts and ideas about the process of constructing system dynamics models, from conceptual causal diagrams through detailed computer simulation models.  Chapter 6, Natural Gas Discovery, reinforces the concepts introduced in the first five chapters by presenting a case-study based on a well-known system dynamics model of the U.S. natural gas industry. For this discussion, we recreate the model's structure incrementally by presenting a series of model versions - each version increasing in complexity as additional structure is added. Throughout the chapter,

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the reader is invited to "run" a computer simulation of the particular structure being discussed to observe the dynamic behavior first hand.  Finally in Chapter 7, Next Steps, we conclude with a brief discussion of the resources available to the reader interested in further study of system dynamics.

Layout of Introduction to System Dynamics

The figure below shows the basic layout of Introduction to System Dynamics. Although we present the material in what we feel is the most logical learning progression, you are free to move to any section that interests you by using the chapter and section menus along the top and left-hand side of the screen, respectively.

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Chapter 1 Introduction

System dynamics is a powerful methodology and computer simulation modeling technique for framing, understanding, and discussing complex issues and problems. Originally developed in the 1950s to help corporate managers improve their understanding of industrial processes, system dynamics is currently being used throughout the public and private sector for policy analysis and design. In this chapter, we provide some context for this book by presenting a general history of the field. The land-mark models presented in this chapter will give the reader an idea of the types of issues/problems that can be explored using system dynamics.

Origin of System Dynamics

Jay W. Forrester and the History of System Dynamics

System dynamics was created during the mid-1950s by Professor Jay W. Forrester of the Massachusetts Institute of Technology. Forrester arrived at MIT in 1939 for graduate study in electrical engineering. His first research assistantship put him under the tutelage of Professor Gordon Brown, the founder of MIT's Servomechanism Laboratory. Members of the MIT Servomechanism Laboratory, at the time, conducted pioneering research in feedback control mechanisms for military equipment. Forrester's work for the Laboratory included traveling to the Pacific Theater during World War II to repair a hydraulically controlled radar system installed aboard the aircraft carrier Lexington.The Lexington was torpedoed while Forrester was on board, but not sunk .

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WHIRLWIND I and SAGE

At the end of World War II, Jay Forrester turned his attention to the creation of an aircraft flight simulator for the U.S. Navy. The design of the simulator was cast around the idea, untested at the time, of a digital computer. As the brainstorming surrounding the digital aircraft simulator proceeded, however, it became apparent that a better application of the emerging technology was the testing of computerized combat information systems. In 1947, the MIT Digital Computer Laboratory was founded and placed under the direction of Jay Forrester. The Laboratory's first task was the creation of WHIRLWIND I, MIT's first general-purpose digital computer, and an environment for testing whether digital computers could be effectively used for the control of combat information systems. As part of the WHIRLWIND I project, Forrester invented and patented coincident-current random-access magnetic computer memory. This became the industry standard for computer memory for approximately twenty years. The WHIRLWIND I project also motivated Forrester to create the technology that first facilitated the practical digital control of machine tools.

After the WHIRLWIND I project, Forrester agreed to lead a division of MIT's Lincoln Laboratory in its efforts to create computers for the North American SAGE (Semi-Automatic Ground Environment) air defense system. The computers created by Forrester's team during the SAGE project were installed in the late 1950s, remained in service for approximately twenty-five years, and had a remarkable "up time" of 99.8%.

System Dynamics

Another outcome of the WHIRLWIND I and SAGE projects that is perhaps, for the purposes of this online book, most noteworthy, was the appreciation Jay Forrester developed for the difficulties faced by corporate managers. Forrester's experiences as a manager led him to conclude that the biggest impediment to progress comes, not from the engineering side of industrial problems, but from the management side. This is because, he reasoned, social systems are much harder to understand and control than are physical systems. In 1956, Forrester accepted a professorship in the newly-formed MIT School of Management. His initial goal was to determine how his background in science and engineering could be brought to bear, in some useful way, on the core issues that determine the success or failure of corporations.

Forrester's insights into the common foundations that underlie engineering and management, which led to the creation of system dynamics, were triggered, to a large degree, by his involvement with managers at General Electric during the mid-1950s. At that

学习型组织研修中心·中国学习型组织网 http://www.cko.com.cn 编辑发布，2007 7 系统动力学入门教程 time, the managers at GE were perplexed because employment at their appliance plants in Kentucky exhibited a significant three-year cycle. The business cycle was judged to be an insufficient explanation for the employment instability.

From hand simulations (or calculations) of the stock-flow-feedback structure of the GE plants, which included the existing corporate decision-making structure for hiring and layoffs, Forrester was able to show how the instability in GE employment was due to the internal structure of the firm and not to an external force such as the business cycle. These hand simulations were the beginning of the field of system dynamics.

During the late 1950s and early 1960s, Forrester and a team of graduate students moved the emerging field of system dynamics, in rapid fashion, from the hand-simulation stage to the formal computer modeling stage. Richard Bennett created the first system dynamics computer modeling language called SIMPLE (Simulation of Industrial Management Problems with Lots of Equations) in the spring of 1958. In 1959, Phyllis Fox and Alexander Pugh wrote the first version of DYNAMO (DYNAmic MOdels), an improved version of SIMPLE, and the system dynamics language that became the industry standard for over thirty years . Forrester published the first, and still classic, book in the field titled Industrial Dynamics in 1961.

Urban Dynamics

From the late 1950s to the late 1960s, system dynamics was applied almost exclusively to corporate/managerial problems. In 1968, however, an unexpected occurrence caused the field to broaden beyond corporate modeling. John Collins, the former mayor of Boston, was appointed a visiting professor of Urban Affairs at MIT. Collins had been stricken with polio during the 1950s and, as a result, required an office in a building with automobile access to the elevator level. By chance, Jay Forrester's office was located in such a building and the office next to his was vacant. Collins thus became Forrester's work-day neighbor, and the two began to engage in regular conversations about the problems of cities and how system dynamics might be used to address the problems.

The result of the Collins-Forrester collaboration was a book titled Urban Dynamics . The Urban Dynamics model presented in the book was the first major non-corporate application of system dynamics . The model was, and is, very controversial, because it illustrates why many well-known urban policies are either ineffective or make urban problems worse. Further, the model shows that counter-intuitive policies -- i.e., policies that appear at first glance to be incorrect, often yield startlingly effective results. As an example, in the Urban Dynamics model, a policy of building low income housing creates a

学习型组织研修中心·中国学习型组织网 http://www.cko.com.cn 编辑发布，2007 8 系统动力学入门教程 poverty trap that helps to stagnate a city, while a policy of tearing down low income housing creates jobs and a rising standard of living for all of the city's inhabitants.

World Dynamics

The second major noncorporate application of system dynamics came shortly after the first. In 1970, Jay Forrester was invited by the Club of Rome to a meeting in Bern, Switzerland. The Club of Rome is an organization devoted to solving what its members describe as the "predicament of mankind" -- that is, the global crisis that may appear sometime in the future, due to the demands being placed on the earth's carrying capacity (its sources of renewable and nonrenewable resources and its sinks for the disposal of pollutants) by the world's exponentially growing population. At the Bern meeting, Forrester was asked if system dynamics could be used to address the predicament of mankind. His answer, of course, was that it could.

On the plane back from the Bern meeting, Forrester created the first draft of a system dynamics model of the world's socioeconomic system. He called this model WORLD1. Upon his return to the United States, Forrester refined WORLD1 in preparation for a visit to MIT by members of the Club of Rome. Forrester called the refined version of the model WORLD2. Forrester published WORLD2 in a book titled World Dynamics .

From the outset, World Dynamics drew an enormous amount of attention. The WORLD2 model mapped important interrelationships between world population, industrial production, pollution, resources, and food. The model showed a collapse of the world socioeconomic system sometime during the twenty-first century, if steps were not taken to lessen the demands on the earth's carrying capacity. The model was also used to identify policy changes capable of moving the global system to a fairly high-quality state that is sustainable far into the future.

In response to the notoriety of World Dynamics, the Club of Rome offered to fund an extended study of the predicament of mankind via system dynamics. As Forrester was committed to extending his Urban Dynamics project at the time, he declined to participate. He did, however, suggest that one of his former Ph.D. students -- Dennis Meadows -- conduct the study. The model that was created by Meadows and his associates was called WORLD3 and published in a book titled The Limits to Growth . Although the WORLD3 model was more elaborate than WORLD2, it generated the same fundamental behavior modes and conveyed the same fundamental messages as its predecessor. Despite the similarities, The Limits to Growth received even more world-wide attention than World Dynamics. Some authors have speculated that this was due to the "friendly" style of writing that made the book accessible to nontechnical readers .

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In 1991, three of the original authors of The Limits to Growth redid the study in preparation for the twentieth anniversary of the book's publication. The results were published in a book titled Beyond the Limits . The revised system dynamics model created for the study was called WORLD3-91. Once again, the results presented in Beyond the Limits were consistent with the results presented in World Dynamics and The Limits to Growth, although Beyond the Limits included a significant amount of numerical data that did not exist when the original studies were undertaken. Beyond the Limits also contained a careful presentation of arguments aimed at counteracting the criticisms that were directed at the earlier world modeling books.

The System Dynamics National Model and K-12 Education

During the last twenty years, Jay Forrester's attention has been focused primarily in two areas: 1) the creation of a system dynamics model of the United States economy, and 2) the extension of system dynamics training to kindergarten through high school education. Forrester sees the former project as leading to a new approach to economic science and a fundamental understanding of the way macroeconomic systems work. He views the latter project as crucial, not only for the future health of the field of system dynamics, but also for the future health of human society.

Although Forrester's national economic model remains unfinished, early and intermediate results have been published . The most noteworthy of the results is that the model generates a forty- to sixty-year economic cycle or "long wave" that not only explains the Great Depression of the 1930s, but also shows that deep economic slumps are a repetitive feature of capitalist economies. At the time of this writing, Forrester's model shows that the United States economy is just beginning to rise out of the trough of the latest long wave downturn.

Forrester's efforts to extend system dynamics to K-12 education have, in a sense, taken him full circle, as the story begins with his original MIT mentor Gordon Brown. Brown retired from MIT in 1973 and began wintering in Tucson, Arizona. During the late 1980s, Brown introduced system dynamics to teachers in the Tucson school system. The results were remarkable. System dynamics spread, not only through the original junior high in which it was introduced, but through the entire school district. Subjects as diverse as Shakespeare, economics, and physics are today taught in the school district, wholly or in part, via system dynamics. Moreover, the district itself is using system dynamics in an effort to become a learning organization .

The future of system dynamics in K-12 education appears promising. Today, an international clearinghouse for K-12 system dynamics materials exists and Internet and World Wide Web sites have been created to disseminate information . Numerous K-12

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System Dynamics and Energy Modeling

The World Models

System dynamics modeling has been used for strategic energy planning and policy analysis for more than twenty-five years. The story begins with the world modeling projects conducted in the early 1970s by the System Dynamics Group at the Massachusetts Institute of Technology. During these projects the WORLD2 and WORLD3 models were created to examine the "predicament of mankind" -- that is, the long term socioeconomic interactions that cause, and ultimately limit, the exponential growth of the world’s population and industrial output .

One of the central assumptions underlying the world models is that the earth’s natural resources are, at some level, finite and that the exponential growth in their use could ultimately lead to their depletion and hence, to the overshoot and collapse of the world socioeconomic system. Due to the decision to explain the "predicament of mankind" with fairly small system dynamics models, the resource depletion dynamics were represented in the world models with structures that aggregated all of the earth’s natural resources into a single variable.

The decision to represent the earth’s natural resources in aggregate form did not take place in a vacuum. As part of the WORLD3 modeling project, several disaggregated, resource-specific/issue-specific, models were created . The conclusion drawn from these models was that it was appropriate to lump all natural resources into a single variable in the WORLD3 model .

The Life Cycle Theory of M. King Hubbert

One of the disaggregated, resource-specific, system dynamics analyses that was conducted in support of the world modeling efforts was a natural gas discovery and production model created by MIT Master’s student Roger Naill . Naill based his model on the life cycle theory of oil and gas discovery and production put forth by petroleum geologist M. King Hubbert .

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In formulating his theory, Hubbert took the physical structure of the fossil fuel system into account and assumed that the total amount of oil and gas in the United States (i.e., the amount of oil and gas "in place"), and hence the "ultimately recoverable" amount of oil and gas in the United States, is finite . As a result, according to Hubbert, the cumulative production of domestic oil and gas must be less than or equal to the ultimately recoverable amount of oil and gas in the United States .

Figure 1 is a system dynamics stock-flow structure that represents Hubbert’s theory. The most important features of the structure are that (1) there is no inflow to the Ultimately_Recoverable stock (i.e., there is a fixed stock of oil and gas), and (2) the resource is being produced and consumed at an exponential rate.

Figure 1: Stock-Flow Structure Representing Hubbert’s View of Oil and Gas Discovery and Production

A direct implication of Hubbert’s theory is that a time series graph of either oil or gas production (at either the world-wide or domestic levels) must, at a minimum, be "hump" shaped. That is, the area beneath the production curve for oil or gas is the cumulative production of the resource, and the cumulative production of the resource must be a finite number. In fact, Hubbert argued that the life cycle of oil and gas discovery and production yields a bell-shaped production curve, which describes a period of low resource price and exponential growth in production, a peaking of production as the effects of resource depletion cause discoveries per foot of exploratory drilling to drop and resource price to rise, and a long period of rising costs and declining production as the substitution to alternative resources proceeds. Figure 2 shows a graphical representation of Hubbert’s life cycle theory of oil and gas discovery and production.

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Figure 2: M. King Hubbert’s Life Cycle Theory of Oil and Gas Discovery and Production

Before proceeding, it is important to note that Hubbert’s view of natural resource discovery and production is not shared by all energy analysts. For example, Morris Adelman, a world-renowned resource economist (emeritus) at the Massachusetts Institute of Technology, believes that there is no fixed stock of oil. Indeed, Adelman’s views vis-à-vis oil price and depletion were summarized in a 1991 column by Boston Globe reporter David Warsh:

The price of oil is a study in monopoly, nothing more. The question of mineral depletion doesn’t really enter into it...[I]n fact, there is no ‘fixed stock’ of oil, says Adelman; there is only an inventory we call ‘reserves,’ which we replenish with new prospecting and lifting techniques. What we don’t choose to find or lift remains a secret of the earth, ‘unknown, probably unknowable, surely unimportant; a geological fact of no economic interest.’ In the endless tug of war between diminishing returns and increasing knowledge,’ he says, technology wins out...[The] worldwide stability of the development cost of new oil since 1955 shows that oil is no more scarce today than it was then. ‘The great shortage is like the horizon, always receding as you go toward it,’ says Adelman. What’s left are the monopolistic political high-jinks .

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Figure 3: Stock-Flow Structure Representing Adelman’s View of Oil and Gas Discovery and Production

Figure 3 is a system dynamics stock-flow structure representing Adelman’s view of oil and gas discovery and production. It is directly comparable to Figure 1. Two things about the figure are important to note. First, the cloud-like icon on the left side of the figure indicates that there is no limit to oil or gas discovery (i.e., there is no fixed stock of oil or gas). Second, two influences are battling each other for control of the Discovery_Rate: technological change and diminishing returns. Historically, technology has always defeated diminishing returns and Adelman, as well as many energy analysts, feels it will continue to do so.

Naill's Master's Thesis

The results of Roger Naill’s Master’s thesis study confirmed Hubbert’s life cycle hypothesis. Indeed, Naill concluded that the production of US domestic natural gas, which peaked in 1973, will continue to decline well below the US natural gas discovery rate until depletion halts all domestic production sometime in the late twentieth or early twenty-first century.

The results of Naill’s work brought to the forefront the following question among the system dynamicists who were working on energy modeling problems under the umbrella of the world modeling programs: Will US economic growth be impeded by an energy limit similar to those suggested in the Limits to Growth? To begin answering this question, in 1972 the Resource Policy Group at Dartmouth College received a three year contract from the National Science Foundation to study the United States’ "energy transition problem."

The US Energy Transition Problem

The "energy transition problem" refers to the set of disruptions that the US economy must go through as it reduces its dependence on domestic gas and oil (due to depletion) and increases its reliance on new sources of energy. Historically, the US economy has gone through two energy transitions: (1) from wood to coal during the late 1800s, and (2) from coal to oil and gas during the early 1900s. But, these transitions were motivated by the availability of abundant new energy sources that were cheaper and more productive than

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The implications of the energy transition problem for the United States are quite significant. The continued growth in US energy demand, coupled with the depletion of domestic oil and gas resources and long delays in the development of alternative domestic energy sources is causing a widening domestic energy gap (domestic energy demand - domestic energy supply). This gap can only be filled, in the near term at least, through increased dependence on foreign imports of natural gas and oil. In addition, as long as abundant oil and gas imports are available at prices that are low relative to the marginal cost of developing new domestic supplies (i.e., as long as it’s easier to import oil and gas than it is to develop new domestic energy sources), US oil and gas depletion will continue, if not accelerate .

The COAL1, COAL2 and FOSSIL1 Models

Roger Naill’s natural gas model represented the US gas system at a very aggregate level. The model was not broken down by region, technology, or type of gas. It did not allow for the substitution of fuels nor for endogenous technological change. Thus, although it helped to motivate the study of the US energy transition problem, it was inadequate for the study itself. A new, expanded, model was required.

For his Ph.D. dissertation at Dartmouth, again under the supervision of Dennis Meadows, Naill expanded the boundary of his natural gas model to include all major US energy sources (energy supply), as well as US energy consumption (energy demand) . He called his dissertation model COAL1, because his analysis showed that the best fuel for the US to rely on during the energy transition was coal .

After he had completed his Ph.D., Naill worked with the Dartmouth Resource Policy Group to improve and extend COAL1 as part of the Group’s National Science Foundation grant activities. The improved and extended version of the model was called COAL2 . In 1975, the Energy Research and Development Administration (which later became the US Department of Energy) provided support to further improve and extend COAL2 for use in government energy planning. This improved and extended model was called FOSSIL1, since it looked at the transition of an economy that is powered by fossil fuels (i.e., by oil, gas, and coal) to one that is powered by alternative energy sources.

The FOSSIL1 model (as were its predecessors) was thus based on Hubbert’s theory of resource abundance, depletion, and substitution, and used to analyze and design new legislation that would enable the US economy to pass through the energy transition smoothly. It consisted of four main sectors: (1) energy demand, (2) oil and gas, (3) coal, and (4) electricity, and addressed, among others things, the following questions:

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 Is energy independence for the US feasible and, if so, when?  Should a national energy strategy emphasize conservation or increased supply?  Which transition energy source should be accelerated?

The results from using FOSSIL1 to analyze the energy transition questions were that:

 Due to the momentum of past energy policies and the inherent delays before new policies become effective, in the short term the US energy problem cannot be solved.  Neither supply side nor demand side policies alone will ameliorate the transition problem sufficiently.  Smoothly passing through the energy transition requires policies that both stabilize energy demand and increase alternative energy supplies.

The FOSSIL2 and IDEAS Models

In response to the United States’ first energy crisis in 1977, the Carter Administration created the first National Energy Plan. Shortly thereafter, the US House of Representatives asked the Dartmouth Resource Policy Group to evaluate the Plan using the FOSSIL1 model. After the evaluation of the Plan was completed, Roger Naill left the Resource Policy Group to head the Office of Analytical Services at the Department of Energy and, among other things, prepare energy projections in support of future National Energy Plans.

To prepare the energy projections for future National Energy Plans, Naill implemented FOSSIL1 in-house at the Department of Energy and supervised a team that extensively modified it so that national energy policy issues could be analyzed. The modified version of FOSSIL1 was called FOSSIL2 .

From the late 1970s to the early 1990s, the FOSSIL2 model was used at the Department of Energy to analyze, among other things:

 the net effect of supply side initiatives (including price deregulation) on US oil imports.  the US vulnerability to oil supply disruptions due to political unrest in the Middle East or the doubling of oil prices.  policies aimed at stimulating US synfuel production.  the effects of tax initiatives (carbon, BTU, gasoline, oil import fees) on the US energy system.  the effects of the Cooper-Synar CO2 Offsets Bill on the US energy system.

In 1989, the Congress directed DOE to conduct a study of energy technology and policy options aimed at mitigating greenhouse gas emissions. FOSSIL2 was used for this purpose. Some preliminary conclusions from the study were that:

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 Reforestation is a promising alternative to taxes or standards.  Effectively promoting cost-effective conservation measures would be worthwhile.  There needs to be a significant long-term switch from coal to advanced nuclear power and renewables (environmentally benign) in the US electric power sector.  Due to compensating feedbacks in the US energy system, a combination of policies, rather than any single policy, is going to be necessary to successfully combat the global warming problem.  Policy makers should not aim policy changes at a single sector of the US energy system because this approach ignores the ramifications of the policy changes in other sectors of the US energy system .

In recent years, extensive improvements have been made to FOSSIL2’s transportation and electric utilities sectors . The improved version of FOSSIL2 has been renamed IDEAS, which stands for Integrated Dynamic Energy Analysis Simulation. The IDEAS model is now maintained for the DOE by Applied Energy Services of Arlington, Virginia .

Sterman's Model of Energy-Economy Interactions

During the late 1970s John Sterman, an MIT Ph.D. student and former Dartmouth College undergraduate, was hired by Roger Naill to work with a team to modify and extend the FOSSIL1 model into the FOSSIL2 model. During this work, Sterman came to realize that the FOSSIL2 model ignored important feedbacks and interactions between the energy sector of the economy and the economy itself. For his Ph.D. dissertation, Sterman built a system dynamics energy model that captured, for the first time, significant energy-economy interactions .

To be more precise, Sterman noticed that in the COAL-FOSSIL-IDEAS family of models, the energy sector is modeled in isolation from the rest of the economy. That is:

 GDP is exogenous to the model. It is not affected by the price or availability of energy.  Costs of unconventional energy technologies are exogenous to the model.  Investment in energy is unconstrained by the investment needs of other sectors of the economy.  Interest rates are exogenous to the model.  Inflation is unaffected by domestic energy prices, production, or policies.  World oil prices are unaffected by domestic energy prices, production, or policies .

Sterman addressed these deficiencies through his modeling and found that:

 The economic consequences of depletion are much more severe during the transition period (extending to approximately 2030) than during the long run or equilibrium state.

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 The magnitude of the economic effects are substantial in absolute terms and include reductions in economic growth; increased unemployment;inflationary stress; higher real interest rates;reduced consumption per capita.  Energy price increases (sudden or gradual) alone cannot produce sustained inflation. An accompanying increase in the money supply, relative to real economic activity, is also required (or an increase in the velocity of money).  The model’s major behavior modes are remarkably robust -- i.e., insensitive to parameter variations (uncertainties).  In the model, a large exise tax on energy coupled with offsetting income tax reductions caused economic performance to improve; energy prices to fall; OPEC revenues to fall; short term inflationary pressures to worsen; income taxes to be reduced only during the transition .

Fiddaman's Model of Economy-Climate Interactions

Building on the work of his teachers, in 1997 Tom Fiddaman submitted his Ph.D. dissertation on economy-climate interactions to the Sloan School of Management at MIT . The dissertation included a critique of existing (non system dynamics) climate-economy models and a new climate-economy system dynamics model called FREE (Feedback-Rich Energy Economy model). The FREE model explicitly incorporates the dynamics of oil and gas depletion as a "source constraint" on the energy-economy system (as do all of its system dynamics predecessors), as well as the dynamics of a "sink constraint" (i.e., climate change) on the energy-economy system. The FREE model is the first energy-economy model of any kind to explicitly examine the impact of a source constraint on energy-economy interactions.

The FREE model also explores a number of feedback processes (e.g., endogenous technological change and bounded rational decision making with perception delays and biases) that have not been previously explored in a climate change context. In addition, it is constructed so that a particular parameterization will yield the results found in neoclassical (traditional) climate-economy models.

Estimating the Amount of Oil In-Place

In the early 1980s, system dynamicist George Richardson met a British petroleum analyst who claimed that the "amount of oil in the world is increasing." Richardson replied that, although world oil reserves may be increasing, or that the estimate of the amount of oil in the world may be increasing, the actual amount of oil in the world (the amount of oil in-place) is decreasing.

Richardson was unable to persuade the British petroleum analyst to change his mind, so he decided to build a system dynamics model that could demonstrate his point. He enlisted the assistance of John Sterman, who had recently finished his dissertation on

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Richardson and Sterman produced an oil exploration, discovery, and production model that was similar in spirit to Naill’s natural gas model, but that also had important extensions and improvements. More precisely, their model allowed for endogenous technological change and the substitution of synfuels for oil .

Richardson and Sterman first used their model to run a synthetic data experiment that addressed the following question: Which method of forecasting the world’s ultimately recoverable supply of oil is more accurate, M. King Hubbert’s life cycle method or the geological analogy method? Since the world’s ultimately recoverable supply of oil is currently not known, and cannot be known until all of the world’s oil has been depleted, a synthetic data experiment was required to answer the question.

The logic of Richardson and Sterman’s synthetic data experiment was quite simple. First build a system dynamics model that accurately replicates the exploration, discovery, and production behavior of the world oil system and assume that it is the "real world." Second, formally code and add the Hubbert and geologic analogy methods to the model so that they "watch" the "real world oil system" and create forecasts of the ultimately recoverable amount of oil in the "world." The results of the synthetic data experiment were that:

 The model replicated the behavior of the actual world oil system very well.  The model replicated the actual forecasts produced by the Hubbert and geologic analogy methods very well.  Hubbert’s method was clearly the most accurate.  over simulated time, the geologic analogy method rose to, and then overestimated, the ultimately recoverable amount of oil in the world .

The implications of the geologic analogy method significantly overestimating the ultimately recoverable amount of oil in the world include:

 a possible reduction in oil conservation efforts.  the probable overestimation of the amount of time available to develop substitutes for oil and the technologies, institutions and values needed to create a sustainable energy system.

Sterman and Richardson, with the assistance of system dynamicist Pål Davidsen, went on to apply their model and synthetic data technique to the question of the amount of ultimately recoverable oil in the United States . As in the case of world oil, Hubbert’s method was judged to be clearly superior and the model was able to replicate US oil discovery and production data extremely well. Of course, unlike the case of world oil production which has not yet peaked, US domestic oil production (in the lower 48 states) peaked in 1970. Since Hubbert had forecast in 1956 that US oil production (in the lower 48 states) would peak between the years 1966 and 1971, his forecast is one of the most accurate

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Other System Dynamics Modeling in the Oil and Gas Industry

System dynamics modeling has been used by numerous researchers, outside of the Naill-to-IDEAS lineage, to examine firm-level and industry-level issues in the oil and gas industry. Table 1 lists some of the work that has been done. Inspection of the table reveals that topics such as the behavior of OPEC and world oil markets, business process re-engineering in an oil and gas producing firm, international relations stemming from world oil supply and demand relationships, and oil firms as learning organizations, have been addressed with system dynamics. The Energy 2020 model was developed by George Backus and Jeff Amlin to provide individual energy firms and state agencies with a multi-fuel energy model. It is similar in design to the DOE’s IDEAS model.

Topic Area Authors

Hubbert’s method versus the Sterman and Richardson (1985); Sterman, geologic analogy method Richardson and Davidsen (1988); Davidsen, Sterman and Richardson (1990)

Hubbert’s Method applied to Mexico Duncan (1996a, 1996b)

The behavior of OPEC and world oil Powell (1990a, 1990b); Morecroft (1992); markets Morecroft and van der Heijden (1992)

Business process re-engineering in a Genta and Sokol (1993) gas and oil producing firm

Shell Oil as a learning organization De Geus (1988)

Learning about the oil industry from Kreutzer, Kreutzer and Gould (1992); a management flight simulator Morecroft (1992); Morecroft and van der Heijden (1992); Genta and Sokol (1993)

International relations stemming Choucri (1981) from world oil supply and demand relationships

Multi-fuel energy model for use by Ford (1997, pp. 58-59) individual firms and state agencies

Table 1: Some Well-Known System Dynamics Studies in the Oil and Gas Industry

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The efforts of oil companies to become "learning organizations" through the use of "management flight simulators" is a particularly noteworthy use of system dynamics in energy modeling. In 1990, system dynamicist Peter Senge wrote a book that outlined a way for organizations to become "learning organizations" through the use of system dynamics and other tools . A learning organization is composed of employees who possess a shared, holistic, and systemic vision, and have the commitment and capacity to continually learn, rather than simply executing a "plan" put forth by the "grand strategist" at the top of the organization.

One of the principal tools used by learning organizations is the "management flight simulator." Management flight simulators are computerized learning environments that invite decision makers to train in a simulator just like a pilot does. The flight simulator runs an underlying system dynamics model for a number of periods, pauses, and waits for the decision maker to make a policy change. After the policy change has been entered, the flight simulator again simulates the model forward in time, pauses, and waits for the next policy change. After a decision maker has finished a session in the simulator, he or she is invited to determine why the system behaved as it did. Once the decision maker ascertains this, he or she is invited to play again. Of course, after a number of plays the decision maker’s understanding of the system should improve and, hopefully, he or she will apply the lessons learned to an actual organization.

System Dynamics Modeling in the Coal Industry

Applications of system dynamics outside of the Naill-to-IDEAS lineage also exist in the coal industry. As shown in Table 2, system dynamics has been used to study industry-level problems, mining systems, the dynamics of small surface coal operations, international mining ownership, and the representation of discrete events in system dynamics models.

Topic Area Authors

The dynamics of small surface Kinek and Jambekar (1984a, 1984b, 1983) coal operations

Industry-level studies Zahn (1981); Mendis, Rosenburg and Medville (1979)

Mining systems Wolstenholme and Holmes (1985); Wolstenholme (1983, 1982b, 1981); Schwarz (1978)

International mining ownership Wolstenholme (1984)

Representing discrete events in Coyle (1985) system dynamics models

Table 2: Some Well-Known System Dynamics Studies in the Coal Industry

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System Dynamics Modeling in the Electric Power Industry

One of the studies that followed the world modeling projects, was conducted by the Dartmouth Resource Policy Group and undertaken in a fashion parallel to Roger Naill’s COAL1 study, was Andrew Ford’s system dynamics analysis of the future of the US electric power industry . For his Ph.D. dissertation, Ford produced the ELECTRIC1 model, which was the first in a series of system dynamics electric utility models known as the EPPAM models . Modified versions of Ford’s model and its descendants were also used to build the electricity sectors of the COAL2, FOSSIL1 and FOSSIL2 models .

Since Ford’s pathbreaking work, system dynamics has been used extensively by utility managers for strategic planning . Table 1 lists some well-known system dynamics studies that have addressed problems in the electric power industry, including: the effects of regulatory policy on utility performance, the "spiral of impossibility," the effects of external agents on utility performance, the financial performance of utilities, the effects of energy conservation practices on utility performance, regional strategic electricity/energy planning, national strategic electricity/energy planning, electric vehicles, deregulation in the UK electric power industry, deregulation in the US electric power industry, and river use and its impact on hydroelectric power.

The system dynamics work on river use and its impact on hydroelectric power is particularly noteworthy as it involves the use of a management flight simulator in a public policy context. More precisely, the management flight simulator is designed to allow ordinary citizens, as well as utility managers and other stakeholders, to test policies aimed at moving hydroelectric systems in desired directions, while taking multiple criteria into account.

Topic Area Authors

Effects of regulatory policy on utility Geraghty and Lyneis (1983) performance

The "spiral of impossibility" Ford and Youngblood (1983).

Effects of external agents on utility Geraghty and Lyneis (1985) performance

Financial performance of utilities Lyneis (1985)

Effects of energy conservation practices on Ford, Bull and Naill (1989); Ford and utility performance Bull (1989); Aslam and Saeed (1995)

Regional strategic electricity/energy Dyner et al. (1990) planning

National strategic electricity/energy Coyle and Rego (1983); Naill (1977,

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planning 1992); Sterman (1981)

Electric vehicles Khalil and Radzicki (1996); Ford (1996b); Ford (1995a); Ford (1994)

Deregulation in the UK electric power Bunn and Larsen (1992, 1994, 1995); industry Bunn, Larsen and Vlahos (1993); Larsen and Bunn (1994)

Deregulation in the US electric power Lyneis, Bespolka and Tucker (1994) industry

River use and its impact on hydroelectric Ford (1996a) power

Table 3: Some Well-Known System Dynamics Studies in the Electric Power Industry

Summary: Intellectual Lineage of System Dynamics Energy

Modeling

Figure 4 presents a diagram of the intellectual lineage of system dynamics energy modeling. The lineage begins with the first book on system dynamics modeling -- Industrial Dynamics by Jay W. Forrester . Forrester’s original work spawned various firm and industry-level system dynamics energy models and inspired Peter Senge to write the Fifth Discipline. Senge’s book has led to the creation of energy-related management flight simulators and several attempts at turning energy companies into learning organizations.

Forrester was also responsible for creating the WORLD2 model and initiating the world modeling projects at MIT. The world models, along with M. King Hubbert’s work on oil and gas discovery and production, stimulated the creation of Roger Naill’s natural gas model, his COAL1 model, and the improvements to COAL1 that have culminated in the IDEAS model and its offshoots (FOSSIL79 and DEMAND81). Naill and Hubbert’s work formed the basis for Sterman, Richardson and Davidsen’s synthetic data experiments on analyzing techniques for forecasting the ultimately recoverable amount of oil in the world and in the United States, while knowledge of the weaknesses in the FOSSIL2 model caused Sterman to investigate the dynamics of energy-economy interactions during the energy transition. Fiddaman’s recognition that, although the source constraints on the energy-economy system had been investigated by energy modelers, sink constraints had not, lead to the creation of the FREE model. The world modeling projects also stimulated the study of the US electric power industry by Andrew Ford and the subsequent EPPAM models and their offshoots.

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Chapter 2 Why Model?

As we see from the brief history of system dynamics presented in Chapter 1, much of the emphasis of system dynamics centers around the use of models and modeling techniques to study complex policy issues. As we proceed to outline system dynamics concepts, it is important that we step back briefly to consider the question, Why model at all? From observation, we know that modeling is something that all human beings do, and for a variety of reasons. However, the importance of understanding the distinction and application of models is less obvious. In this chapter, we continue to outline the basic premise and philosophy of system dynamics by addressing this fundamental question.

Why Build Models in the First Place?

Given that the stated goal of this online book is to teach basic system dynamics concepts and modeling techniques, it is legitimate to step back and ask: Why build models in the first place? Are there some advantages to be gained from the creation of system dynamics models? In general what, if anything, is to be gained from the creation of models?

Formal Models

Modeling is something that all human beings do. Children create models out of playdough, tinker toys, legos, blocks, cards, sand, and the like. Engineers create clay models of automobiles, metal models of aircraft, wooden models of bridges, plastic models of cities, hand-drawn models of buildings, and computer models of most of the things they create. Natural scientists create physical models of molecules, the human body, and the solar system, and mathematical and/or written models of the evolution of the universe. Social scientists create computer and written models of the mind, mathematical and computer models of the economy, and physical models of ancient civilizations. Managers build

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Humans create models for a variety of reasons. Models are simplifications of reality and (usually) help people to clarify their thinking and improve their understanding of the world. Models can be used for experimentation. A computer model, for instance, can compress time and space and allow many system changes to be tested in a fraction of the time it would take to test them in the real world. Further, testing changes on a model, rather than on an actual system, is a good way to avoid "shooting yourself in the foot." That is, if a change does not perform well in a model of a system, it is questionable as to whether it will perform well in the actual system itself. In addition, experimenting on a model can avoid causing harm to an actual system, even when the change being tested is successful. For example, testing a more effective sprinkler system design does not require setting an actual building on fire, if the testing is done on a model of the building.

Mental Models

Although it is perhaps self-evident that humans regularly create and use formal models, it is less obvious that they regularly create and use informal models, or mental models. More precisely, human beings do not have actual families, clubs, churches, universities, corporations, cities, states, national socioeconomic systems, and the like, inside of their heads, but rather mental representations of these systems. Thus, in the field of system dynamics it is argued that policy makers should not worry about whether or not to use a model, but rather which model to use . In other words, system dynamicists believe that policy makers should decide whether they wish to make decisions based on results obtained from their unaided mental models, or from results obtained from some combination of formal and mental models.

Both formal models and mental models have many strengths and weaknesses . Mental models are flexible, rich in detail, and constructed from the most abundant and valuable source of information in the world - experience "data" collected in your brain. John Sterman, a prominent system dynamics professor at Massachusetts Institute of Technology, points out that the "great systems of philosophy, politics, and literature are, in a sense, mental models" .

To illustrate the importance of mental models, it is useful to consider the following thought experiment . Imagine that spacemen land in Detroit, remove every worker from one of the city's automobile plants, and replace them with workers who are identical in every way to the removed workers, except that they have no mental information to guide them in making automobiles. Could the new workers build automobiles by using the available written and numerical information? The answer is "no," and the reason is that an overwhelming majority of the information that is crucial for automobile manufacturing is contained in the minds of the removed workers.

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Although mental models have many strengths, they also have many weaknesses. Mental models are often fuzzy, incomplete, imprecise, and filled with unstated assumptions and goals. During conversation and debate, different people use different mental models, and these models can and do change -- even during the course of a single conversation or debate . Further, the human mind is a poor dynamic simulator. Cognitive limitations prevent humans from accurately thinking through the dynamic behavior inherent in all but the simplest of their mental models .

To illustrate the richness and complexity of human mental models and the difficulty of thinking through their dynamic consequences, it is useful to examine Douglas Hofstadter's book Gödel, Escher, Bach: An Eternal Golden Braid . In his book, Hofstadter integrates Gödel's Incompleteness Theorem, the music of Johann Sebastian Bach, and the art of Maurits Cornelis Escher, to address the issue of whether machine reasoning and artificial intelligence are truly possible. Hofstadter's self-made sketch of a portion of his mental model that underlies his book is presented in Figure 1.

(click on image to see detailed view)

Figure 1: Hofstadter's self-made sketch of a portion of his mental model

After examining Hofstadter's sketch, it is perhaps easier to accept the argument that trying to accurately think through the dynamic behavior inherent in mental models is a difficult task indeed!

Combining Mental Models with System Dynamics

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The solution to the "mental model problem," according to system dynamicists, is to have decision makers map-out their mental models on the computer via system dynamics, and let the machine trace through the inherent dynamics. Then, through interaction with the computer, decision makers can improve their mental models and learn about the system they are trying to understand and control. Indeed, in system dynamics modeling, the process of modeling is seen as being more valuable than the model itself .

In system dynamics modeling it is also typical to take a model that is insightful and turn it into a game or management flight simulator. The argument for doing this is that a decision maker should train in a simulator just like a pilot does and, in doing so, greatly improve his or her mental model of the system he or she is trying to understand and control. Creating an effective system dynamics game from an insightful system dynamics model is a nontrivial task and a research area in and of itself.

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Chapter 3 The Building Blocks

System dynamics provides the basic building blocks necessary to construct models that teach us how and why complex real-world systems behave the way they do over time. For us, the goal is to leverage this added understanding to design and implement more efficient and effective policies. This chapter introduces the concept of time paths and how to begin looking at the world in terms of changing patterns over time rather than as static snap-shot events. This chapter also introduces the concept of system stocks, system flows, and system feedback. To understand the dynamic behavior of a system, its key physical and information stocks, flows and feedback structures must be identified.

Taking A Dynamic Perspective

System dynamics is concerned with the behavior of a system over time. A critical step in examining a system or issue is to identify its key patterns of behavior - what we often refer to as "time paths." In this section, we examine the meaning of a time path and consider the general types commonly found in dynamic systems. To provide a "real life" grounding to this discussion, several time path examples reproduced from books, newspapers, and magazines are presented.

Time Paths

System dynamics modeling is concerned with the dynamic behavior of systems - that is, the behavior of systems over time. In system dynamics modeling, the modeler attempts to identify the patterns of behavior being exhibited by important system variables, and then build a model that can mimic the patterns. Once a model has this capability, it can be used as a laboratory for testing policies aimed at altering a system's behavior in desired ways.

Figure 1 is a straight line with a positive slope and an example of a dynamic time path. Although actual systems can exhibit a variety of time paths (often simultaneously), the good news is that the number of distinct time path "families" that exists is relatively small.

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Figure 1: Example of time path

Figures 2 through 5 present a collection of fifteen distinct time paths which occur frequently in the real world. These paths have been grouped into five distinct families, one of which is shown in each of the figures. Other, more complicated, time paths are observable, but they are almost always combinations of the paths presented here.

Linear Family

The first identifiable family of time paths is the linear family, which is presented in Figure 2. The linear family of paths includes equilibrium, linear growth, and linear decline. Given the simplicity and intuitive appeal of these paths, it is important to point out some facts which can place them in the proper perspective, vis-à-vis system dynamics modeling.

Figure 2: Linear Family of Time Paths

The first thing to note is that the average person, not trained in dynamic modeling, tends to think that actual systems grow or decline in a linear fashion - that is, as shown in second and third time paths of Figure 2.The truth, however, is that most systems do not grow and decline along linear time paths, but rather along exponential time paths (as shown in Figure 3) . Pure linear time paths are usually generated by systems devoid of feedback - a crucial building block of both actual systems and system dynamics models.

A second thing to note is that the equilibrium time path presented in Figure 2 is a dynamic behavior that few actual systems exhibit. It is a state of perfect balance in which there are no pressures for change. In fact, from a system dynamics point of view, equilibrium implies that all of a system's state variables reach their desired values simultaneously - a very

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Exponential Family

The second distinct family of time paths is the exponential family, shown in Figure 3. The exponential family consists of exponential growth and exponential decay. As previously mentioned, real systems tend to grow and decline along exponential time paths, as opposed to linear time paths.

Figure 3: Exponential Family of Time Paths

Goal-seeking Family

The third distinct family of time paths is the goal-seeking family as shown in Figure 4. All living systems (and many nonliving systems) exhibit goal-seeking behavior. Goal-seeking behavior is related to exponential decay. This can be seen by comparing the second time path in Figure 3 with the second time path in Figure 4. The only difference between the two is that in Figure 3, the time path is seeking a goal of zero, whereas in Figure 4, the time path is seeking a nonzero goal.

Figure 4: Goal Seeking Family of Time Paths

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Oscillation Family

The fourth distinct family of time paths is the oscillation family. Oscillation is one of the most common dynamic behaviors in the world and is characterized by many distinct patterns. Four of these distinct patterns are shown in Figure 5: sustained, damped, exploding, and chaos.

Figure 5: Oscillating Family of Time Paths

Oscillations that are sustained can have periodicities (the number of peaks that occur before the cycle repeats) of any number. Sustained oscillations are characterized by a periodicity of one. Damped oscillations are exhibited by systems that utilize dissipation or relaxation processes. Examples of dissipation or relaxation processes include friction in physical systems and information smoothing in social systems. Exploding oscillations either grow until they settle down into a sustained pattern or grow until the system is torn apart. . As a result, exploding oscillations usually do not occur very frequently in the real world, nor last very long when they do. Chaotic behavior is an oscillatory time path that unfolds irregularly and never repeats (i.e., its period is essentially infinite). Chaos is a unique type of time path because it is an essentially random pattern that is generated by a system devoid of randomness .

S-shaped Family

The fifth distinct family of time paths is the s-shaped family, shown in Figure 6. Close inspection of the s-shaped growth time path pattern reveals that it is really a combination of two time paths - exponential growth and goal-seeking behavior. More precisely, in the case of s-shaped growth, exponential growth gives way to goal-seeking behavior as the system approaches its limit or carrying capacity (indicated by the green line).

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Figure 6: S-Shaped Family of Time Paths

Sometimes, however, a system can overshoot its carrying capacity. If this occurs and the system's carrying capacity is not completely destroyed, the system tends to oscillate around its carrying capacity. On the other hand, if the system overshoots and its carrying capacity is damaged, the system will eventually collapse. This is referred to as an "overshoot and collapse" system response. A third possible outcome from an overshoot event is that a system will simply reverse direction and approach the system capacity in a reverse s-shaped pattern. As with a "normal" s-shaped pattern, a reverse s-shaped pattern is a combination of two time paths -- exponential decay and a self-reinforcing spiral of decline.

Actual Data

A story that is frequently recounted by Jay Forrester is that a student once told him that he "learned to read the newspaper differently," after taking a class in system dynamics. Although it is possible to interpret the student's comment in a number of ways, one can speculate that, among other things, he began to see the graphs of actual time series data, presented in the media, in a different light after studying system dynamics.

Figures 1 through 10 present graphs of a variety of actual time series data reproduced from books, newspapers, and magazines, which appeared during the last few years. An examination of the figures reveals that it is possible to identify, in actual data, many of the time paths shown in the previous section.

Figure 1, for example, is a graph of actual Medicare costs from 1967 to 1994 and Medicare costs from 1967 to 1994 as projected in 1965. Two things about this graph are noteworthy. The first is that Medicare costs were projected to grow linearly from 1967 to 1994 -- a common mistake among persons not familiar with the dynamics of systems. The second is that actual Medicare costs grew exponentially from 1967 to 1994. This time path is clearly a member of the exponential family of time paths.

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Figure 1: Actual and Projected Medicare costs from 1967 to 1994

Figure 2 is a graph of the number of cases of the measles reported in the United States from 1960 to 1993. The time shape exhibited by these data is clearly exponential decay.

Figure 2: Measle cases from 1960 through 1993

Figure 3 below is a graph of National Basketball Association attendance during the years 1988 to 1993 and Figure 4 is a graph of the average U.S. selling price of a 486 desktop computer. These data are clearly following non-zero goal-seeking time paths.

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Figure 3: National Basketball Association attendance from 19988 through 1993

Figure 4: Average U.S. selling price of a 486 desktop computer.

Figure 5 is a graph of the number of lynx trapped in Canada (in log form) from 1821 to 1933. Although slightly "noisy" or choppy, the time path can certainly be classified as a sustained oscillation.

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Figure 5: Lynx trapped in Canada (in log form) from 1821 to 1933.

Figure 6 is a graph of Norwegian pulp inventory, production, and sales, for the years 1957 to 1978. Clearly, the time path of pulp inventory is an exploding oscillation .

Figure 6: Norwegian pulp inventory, production, and sales, for the years 1957 to 1978.

Figure 7 is a time series graph of the number of third class mail pieces (in billions) delivered by the United States Postal Service, during the years 1981 to 1991. The path is clearly s-shaped.

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Figure 7: Number of third class mail pieces (in billions) delivered by US Postal Service, 1981 to 1991.

Figure 8 is a time series graph of materials consumption in the United States for the years 1900 to 1992. Although a bit noisy, the data exhibit an overshoot and oscillate time path.

Figure 8: Materials consumption in the US from 1900 to 1992.

Figure 9 presents a time series graph of United States bank, savings and loan, and total financial institution, failures, during the years 1980 to 1992. All three series exhibit an overshoot and collapse time path.

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Figure 9: United States bank, saving and loan, and total financial institution failures, 1980 to 1992.

Figure 10 is a graph of grainland in Japan for the years 1950 to 1994. The time path exhibited by this data is clearly a reverse s-shape.

Figure 10: Grainland in Japan, 1950 to 1994.

The general conclusion that the reader should draw from these graphs is that real systems often generate clearly identifiable time patterns and that system dynamic models can be built to mimic the patterns.

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Seeing System Structure

In the previous section, we defined the concept of time paths and considered how these system behavioral patterns can be placed into one or a combination of five distinct categories. Now, we consider the source of these characteristic patterns. Specifically, we discuss the concept of cumulative (stock) and rate-of-change (flow) system variables. As the elemental building blocks of system feedback networks, "stocks" and "flows" virtually ensure that a dynamic system will behave in a difficult-to-understand or counterintuitive way. In addition, the role of nonlinear relationships in determining a system's limits, the strength or dominance of its feedback loops, and the complexity of its behavior,will be discussed.

Stocks and Flows

In system dynamics modeling, dynamic behavior is thought to arise due to the Principle of Accumulation. More precisely, this principle states that all dynamic behavior in the world occurs when flows accumulate in stocks.

Figure 1: Example of a simple stock and flow structure

In terms of a metaphor, a stock can be thought of as a bathtub and a flow can be thought of as a faucet and pipe assembly that fills or drains the stock as shown in Figure 1. The stock-flow structure is the simplest dynamical system in the world. According to the principle of accumulation, dynamic behavior arises when something flows through the pipe and faucet assembly and collects or accumulates in the stock. In system dynamics modeling,both informational and noninformational entities can move through flows and accumulate in stocks.

Figure 2 is an example of a system dynamics stock and flow structure that has two flows -- an inflow and an outflow. In this case, the dynamic behavior of the system arises due to the flows into, and out of, the stock (the inflow minus the outflow). Clearly, if the inflow exceeds the outflow the number of entities in the stock will increase. If the outflow exceeds the inflow, on the other hand, the number of entities in the stock will decrease. Finally, if the outflow equals the inflow, the number of entities in the stock will remain the same. This last possibility describes a state of dynamic equilibrium in a system dynamics model.

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Figure 2: Example stock and flow structure with an inflow and outflow

In principle, a stock can have any number of inflows and outflows. In practice, however, a system dynamics model usually contains stocks with no more than four-to-six inflows and/or outflows. The principle of accumulation holds regardless of the number of inflows and outflows that work to change the number of entities accumulating in a stock.

Identifying Stocks and Flows

One of the fundamental skills a system dynamics modeler must learn is how to identify the stocks and flows in the system experiencing the problem that he or she is trying to model. This is a nontrivial task and one that people often find difficult. For example, it is not at all unusual for people, not trained in system dynamics modeling, to confuse stocks and flows. They'll say "deficit" (a flow) when they mean "debt" (a stock), or they'll say that "inflation (a flow into a stock) is lower so therefore the general level of prices (a stock) is falling" In fact, decreasing inflation to a lower value means that prices are rising but at a slower rate.

In order to identify stocks and flows, a system dynamics modeler must determine which variables in the system experiencing the problem define its state (its stocks), and which variables define the changes in its state (its flows). That said, the following guidelines can be used to help identify stocks and flows:

 Stocks usually represent nouns and flows usually represent verbs.  Stocks do not disappear if time is (hypothetically) stopped (i.e., if a snapshot were taken of the system); Flows do disappear if time is (hypothetically) stopped.  Stocks send out signals (information about the state of the system) to the rest of the system.

Four Characteristics of Stocks

Stocks possess four characteristics that are crucial in determining the dynamic behavior of systems. More specifically, stocks:

 Have memory,  Change the time shape of flows,  Decouple flows,  Create delays.

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Each of these characteristics will be discussed in turn.

Stocks have memory

The first key characteristic of stocks is that they have memory (i.e., persistence or inertia). An easy way to see this is to recall the simple stock-flow structure presented in Figure 1. If the inflow to the stock is shut-off, the number of entities in the stock will not decrease, but rather stay at the level it is at when the inflow stops. An outflow in excess of the inflow is required to decrease the number of entities in the stock. The importance of this characteristic should not be underestimated. This is because people often believe that shutting-off an inflow to a stock will cure a problem being created by the number of entities in the stock. Regrettably, nothing could be further from the truth.

Figure 3: US federal budget deficit, 1930 - 1993.

Consider the problem that the United States is currently having with its federal deficit and debt. Figure 3 presents a time series graph of the U.S. federal deficit and Figure 4 presents a time series graph of the U.S. federal debt. The deficit is the yearly amount that the U.S. federal government spends in excess of its revenues, while the debt is the accumulation of all the previous deficits (less the debt that has been retired). From an inspection of these figures, it is clear that both the U.S. federal deficit and the U.S. federal debt are growing exponentially.

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Figure 4: US Federal Debt from 1930 - 1993.

In terms of a simple system dynamics model, the deficit is a flow and the debt is a stock, as shown in Figure 5 . Therefore, if the U.S. federal government were to balance its budget (i.e., make the deficit inflow zero), the debt would not decrease at all. This fact is surprising to many people!

Figure 5: Structure of US Debt/Deficit problem.

A similar case involves the depletion of the earth's ozone layer. In 1990 the nations of the world agreed to a ban on the production (and hence on the eventual release into the atmosphere) of ozone-killing chlorofluorocarbons (CFC's).

Figure 6: System dynamics structure of CFC accumulation in atmosphere.

From a system dynamics point of view, this agreement caused the flow of chlorofluorocarbons into the atmosphere to stop, but did nothing to remove any of the chlorofluorocarbons already in the atmosphere and destroying ozone (a stock -- see Figure 6). The removal of these pollutants can only be accomplished via the earth's natural cleansing processes .

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Stocks Change the Time Shape of Flows

A second important characteristic of stocks is that they (i.e., the accumulation process) usually change the time shape of flows . This can be seen by simulating the simple stock-flow structure shown in Figure 1, with different time shapes for the flow. Figure 7 for example, presents the time shape of the stock when the flow is at a constant level of 5 units/time. An examination of the figure reveals that the accumulation process changes the horizontal time shape of the flow into a linear growth shape for the stock .