Practice with More Extensive Computer Modeling
-Study Notes in System Dynamics, Section 3.10-3.12 by Michael R. Goodman
This section introduces more advanced models than you have seen before. It demonstrates how more complicated models are built on positive and negative feedback loops. You will not have to derive the models yourself because the flow diagrams, DYNAMO equations, and run outputs are provided with each example. You will have to convert the DYNAMO equations to STELLA and then run the model for each example.
Please read and do Section 3.10-3.12 now. The following tip may help you. A tip for STELLA: Table Graphs
One new DYNAMO equation, a table equation, is introduced.
The DYNAMO equations, 5 and 5.1 from page 63 are: PAT.K = TABLE(PATT,POLR,0,80,10) PATT =.6 / 2.5 / 5 / 8 / 11.5 / 15.5 / 20 / 31 / 50 PAT - POLLUTION ABSORPTION TIME (YEARS) POLR - POLLUTION RATIO (DIMENSIONLESS)
PAT.K — This is the variable in the model that will represent the table. In the STELLA model the name will be POLLUTION ABSORPTION TIME.
-Open the dialog box for POLLUTION ABSORPTION TIME.
TABLE(.....) — This defines the variable, PAT.K as a table.
In STELLA, the equivalent is to open the dialog box of POLLUTION
ABSORPTION TIME and to define it as "A graph of ..." POLLUTION
RATIO.
-Select POLLUTION RATIO from the Required inputs box.
-
Click once on the Become Graph button on the bottom of the dialog box. A new dialog box will appear, to define the table.
-
Click once on the To Equation button on the bottom of the dialog box to view the equation. You will see POLLUTION ABSORPTION TIME = "graph of..." POLLUTION RATIO.
-
Click once on the To Graph button.
PATT — In STELLA, this name is the same as PAT.
DYNAMO requires two different names for a table, whereas STELLA
requires only one.
POLR — This is the variable of which POLLUTION ABSORPTION TIME
is a function. In STELLA this means that one value for POLLUTION
ABSORPTION TIME corresponds to one value for POLLUTION RATIO.
0 — This value represents the minimum value that POLLUTION RATIO can
have.
80 — This value represents the maximum value that POLLUTION RATIO
can have.
-Return to the graph dialog box. Notice that the horizontal and vertical side of the graph ranges from 0 to 100 (100 is the default number in STELLA). But, POLLUTION RATIO on the horizontal axis ranges from 0 to 80, as the equation tells us.
-Notice that "100," the maximum range, is highlighted on the horizontal axis for POLLUTION RATIO. To enter the correct number for POLLUTION RATIO, type "80."
10 — This value is only necessary in DYNAMO. It is the length of
incrementations on the graph between 0 and 80.
PATT = .6 / 2.5 / 5 / 8 / 11.5 / 15.5 / 20 / 31 / 50 — These nine values represent the values that the table will have. Thus the range for POLLUTION ABSORPTION TIME for the vertical axis is 0.6 to 50.
-Press tab on your keyboard to highlight the maximum value for POLLUTION ABSORPTION TIME and type "50." Press tab on your keyboard again to highlight the minimum value for POLLUTION ABSORPTION TIME and type "0.6."
-Notice that there are eleven points to be defined on the output table in STELLA, but only 9 points given in Study Notes for POLLUTION ABSORPTION TIME.
-
Highlight the number 11 in the Data Points box. Type "9."
-
Highlight the first number, 0.000 under Output, by clicking once on it. Type "0.6." Press return on your keyboard. Type "2.5." Press return on your keyboard, and type "5." Press return.... Continue until you have filled in all of the points under Output.
-The graph should resemble as much as possible the table in Figure 3-20 on page 61 in Study Notes in System Dynamics.
-If it does, click once on OK.
-See page 26 in Getting Started with STELLA II: A Hands-on Experience for more information on table functions in STELLA.
After finishing Section 3.10-3.12...
Working with the models in Sections 3.10-3.12 gave you more a sense of the system dynamics approach. We now introduce another important system principle.
Development and Modeling of S-shaped Growth
The next two sections of Road Maps Three build on your knowledge of positive and negative feedback loops and guide the development of a model of an S-shaped growth system.
-Study Notes in System Dynamics, Chapter 5 by Michael R. Goodman
Chapter 5 helps you develop a STELLA model of a system generating S-shaped growth. When you are finished, compare the output of your STELLA model to the answer in DYNAMO. The output of your model should match the answer given.
Please read and do the exercise in Chapter 5 now. After finishing Chapter 5...
Chapter 5 developed the concepts of positive and negative feedback loops, and introduced the basic ideas behind S-shaped growth. It also reviewed the use of table functions in STELLA.
The following principle is another recurrent principle. We are restating System Principle #3 in order to emphasize its importance.
-Study Notes in System Dynamics, Chapter 4 by Michael R. Goodman
Chapter 4 focuses on the structure and behavior of the different variables in an S-shaped growth system. The chapter explores two systems which exhibit S-shaped growth. One is an epidemic and the second is a pendulum. Although the pendulum example may seem confusing without prior knowledge of the equations that govern a pendulum’s movements, work through the model along with the book, and focus on understanding the system through your knowledge of system dynamics.
Please read and do Chapter 4 now.
After finishing Chapter 4...
Chapter 4 described the key characteristics behind S-shaped growth. Because systems producing this behavior are very common, you will be modeling several more S-shaped growth systems in later Road Maps. Some key characteristics are:
-exponential growth
-goal-seeking behavior
-loop dominance
-dynamic equilibrium
Real-life Applications of System Dynamics
Revised by Lei Lei
-Urban Dynamics 6
Road Maps 3 concludes with the reading of one of Professor Jay Forrester’s classic system dynamics books. It is not necessary to complete the book before continuing on to the next chapter of Road Maps. However, reading Urban Dynamics will aid the reader in giving real world relevance to system dynamics. Urban Dynamics is an introduction to complex urban systems and their characteristics. The reader should not be discouraged if s/he cannot fully understand the models introduced in the book. The reading is assigned as part of Road Map’s spiral-learning approach, where concepts are referred to and expanded upon continually throughout the series.
Urban Dynamics provides a glimpse of the origins of the field of system dynamics before the name “system dynamics” was coined. The book presents excellent examples of using simulation models to understand and explain the counterintuitive nature of complex social systems. Urban Dynamics is one of Professor Jay W. Forrester’s more controversial books. The publication of Urban Dynamics in 1969 marks a unique event in the analysis of social systems.
Although Urban Dynamics addresses crises that our cities faced twenty years ago, many of the same problems still exist today. The Urban Dynamics model refutes the conventional wisdom that urban problems are caused by such factors as rural-urban migration, dwindling fiscal resources, and suburbanization.
Instead, the book suggests that most urban problems arise from the interactions of processes that occur within the cities themselves. After showing what established policies have actually done to our cities and why, Forrester uses the model to test new policies and programs for the revival of urban cities. The policies presented in the book challenge the status quo. For example, Forrester suggests that demolishing, rather than constructing, low-cost housing will be a better long-term solution to the urban crises. By reading Urban Dynamics, the reader will gain a deeper understanding of how high leverage policies can be pushed in the wrong direction.
Forrester discusses how cities are nonlinear systems that contain multiple feedback loops. Thus, fully understanding and managing the complex systems defies simple human reason and intuition. Forrester suggests, however, that by examining urban problems with computer simulation, we can better understand outcomes of various policies. The book uses DYNAMO models of generic urban areas to discuss and test urban policy options presented by the author.
At the time Urban Dynamics was published, the book sparked a controversy that related to the nationwide debate over urban crises. The controversy is summarized as follows:
Business Week praised the book in 1969 and said, "Urban Dynamics is an unsettling, complex and ground-breaking new book about our cities and the decay that afflicts them."7 On the other hand, Kain says in Fortune, “such models (as used in Urban Dynamics) have a great deal of potential for the analysis of urban problems,” but also says, “before adequate models become available, many inadequate ones will be put forward. Forrester’s model is a conspicuous example.”
A study by Jerome Rothenberg published in the Journal of Urban Economics in 1974 pointed out that, "the insistence upon treating 'the city' as a self-contained system results in grave difficulties." Jantsch, in Futures, best summarizes the controversy as, "Urban Dynamics had become the subject of heated debate even prior to publication. It has captured the imagination of politicians and managers in the public domain, and it has been furiously attacked and rejected by social scientists." In 1969 Jantsch said, "It is a safe prediction to state that it [Urban Dynamics] will become one of the most provocative and stimulating books of our time." “But,” he also said, "Urban Dynamics is not the only approach to long-range planning and it is not perfect." Each article above concludes that Urban Dynamics is a notable piece of work, and highlights the controversy created by the book.
Urban Dynamics is one of the most important book