Chapter 15: System Dynamics
Prepared by Prof. Michael J. Radzicki
What is System Dynamics
System dynamics is a computer modeling technique that has its origins in control theory, cybernetics, organizational theory, behavioral psychology, economics, and digital computer simulation. It is used to build models of systems that are experiencing problems and/or exhibiting behaviors that are not well understood. The completed models are used as "laboratories" for testing policy changes aimed at improving system behavior.
One of the great strengths of the system dynamics method is its ability to span disciplinary boundaries. System dynamics modeling is problem-oriented. That is, problems are modeled, not systems. Any information that is thought to be relevant to the modeling problem at hand, therefore, regardless of academic discipline, can be (and is encouraged to be) formally incorporated into a system dynamics model. Technically speaking, the non-discipline-constrained nature of the mathematics of dynamics enables any relationship -- biological, physical, or social -- to be represented formally in a system dynamics model. It is not unusual, therefore, for system dynamics models to embody knowledge from both the natural and social sciences.
A system dynamics model can be thought of as a "computerized case study." Unlike a traditional case study, however, "what-if" scenarios can be tested on the model. The structure of a system dynamics model consists of an extremely "rich" collection of stock and flow structures embedded in an interacting web of feedback relationships. These stocks, flows, and feedback relationships map-out the actual structure of a system -- including any physical and biological flows, nonmeasured or nonmeasurable variables that are important to the problem being addressed, and actual (as opposed to idealized) human decision making structures.
Stock and Flows and Dynamic Behavior
A fundamental idea in system dynamics modeling is the "principle of accumulation." This principle says that all dynamic behavior in the world occurs when flows are accumulated (integrated) in stocks. A stock can be thought of as a bathtub. A flow can be thought of as a pipe and faucet assembly (a time derivative) that either fills-up or drains the tub. Figure 15.1 below shows some examples of stock and flow structures.
Feedback
In a system dynamics model, stock and flow structures are embedded in feedback loops. There are two kinds of feedback loops -- positive loops and negative loops. Positive loops generate self-reinforcing behavior and negative loops generate goal seeking behavior. An example of a positive loop is presented in Figure 15.2. Inspection of the figure reveals that as VHS VCRs become more prevalent, there is more demand for VHS format tapes, which feeds back to generate more demand for VHS VCRs.
An example of a negative feedback loop is presented in Figure 15.3. Inspection of the figure reveals that if the actual temperature in a room drops below the desired temperature, the operation of the furnace increases (i.e., the furnace turns on), and the actual temperature is brought back into line with its desired value (goal).
Reference Modes
As mentioned above, system dynamics modeling is problem-based. Thus, a system dynamics model cannot be built until a definition of the problem to which it will be addressed is arrived at.
System dynamicists define their dynamical problems with "reference modes." Reference modes are time series graphs of important system variables that are behaving problematically or in a perplexing way. In additional to helping the modeler identify important variables, the specification of a system's reference modes helps the modeler identify the time scope of the study (e.g., years, months, weeks, minutes; beginning in 1900, 1980, the first month of 1992, etc.), and the relevant behavior the model is supposed to mimic (e.g., oscillation, overshoot and collapse, sigmoidal growth.) Replication of a system's reference modes is one way that a system dynamicist builds confidence in a model. Finding policies that alter a system's problematic reference modes is the usual goal of a system dynamics study.
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