## Translating Systems Thinking Diagrams to Stock & Flow Diagrams

After spending a number of hours laboring over several of the concepts put forth by David C. Lane and Chris Smart in their article on "generic structures" in the Summer 96 issue of System Dynamics Review I started toying around with some of the Archetype Stock & Flow models I had previously created. After tinkering with several of my Archetype implementations I came to the conclusion that the relation between Systems Thinking Diagrams (STDs), or Causal Loop Diagrams (CLDs), and Stock & Flow simulation models was so loose as to be almost meaningless. I found that it was very easy to make the Stock & Flow diagram look very much like one of the Archetypes, while altering the embedded equations I could make it produce behavior patterns similar to any one of about half a dozen other Archetypes. So what's the implication?

I found myself very concerned about being able to construct diagrams from which I could infer essentially very little. It seemed that if I was to make any sense out of this there would have to be a rigorous method of translating STDs/CLDs into S & F models that would provide a level of confidence I could live with. The only other alternative that came to mind was to chuck the whole mess and start over; an alternative that didn't sit well either. Therefore, after pondering the question to a point of distraction, for longer than I'd like to remember, the following is what I finally came up with as a method, or a set of conventions, for translating STDs/CLDs into S & F models.

### Systems Thinking Diagrams

Systems Thinking Diagrams are composed of only two components, elements and influences. An influence also has a direction, indicated by an arrow, and an indicator as to whether the influenced element is changed in the same (S) or opposite (O) direction as the influencing element. The simplest diagram I could come up with containing these elements is:

Figure 1

From this diagram there are only a couple things which are implied:

• E1 and E2 are elements of the model.
• E1 influences E2 in the same (S) direction as E1.

Some things that can't be inferred from the diagram, and are usually included in the associated description, are:

• Is E2 sticky? That is, as E1 increases it influenced E2 to increase. Yet, if E1 is decreasing does E2 decrease, remain the same, or continue to increase? All three are possible.
• The alternative, where the implication is that E1 decreasing influces E2 to decrease also rasises a question about what happens when E1 is increasing.
• There are no indications that E2 has any influence on E1.

### Stock & Flow Diagrams

Stock & Flow Diagrams are composed of four different components: Stocks, Flows, Converters, and Connectors. I understand the labels may vary slightly in different arenas. These labels were taken from the ithink software documentation.

As I understand it there are several conventions for Stock & Flow diagrams:

• Flows can influence Stocks
• Stocks can influence Flows or Converters
• Converters can influence Flows or other Converters
• Flows cannot influence Converters or other Flows
• Converters cannot influence Stocks
• Stocks cannot influence other Stocks

A diagram containing all of these elements is:

Figure 2

From this diagram, which just happens to be a reinforcing loop, there are several things which are implied:

• The flow influences the Stock to increase or allows it to remain the same. Because it is one directional flow I would consider it foul to create a negative flow without making the arrow bi-directional.
• An increasing Stock influences conv to increase.
• An increasing conv influences flow to increase.

Any understanding beyond this would require an understanding of the actual equations within the individual items.

### Translating STDs/CLDs to SFDs

I started out to construct a simple STD/CLD to use for this purpose, yet 15 minutes later I ended up with the following diagram. As such I would advise that you don't spend too much time worrying about its completeness; for I'm sure it's not.

Figure 3

This is a STD/CLD for some service business that bills out employee services to clients, and yes I know there's no service quality identified in the diagram.

The translation of this diagram to a SFD will be performed based on several assumptions which I'll iterate as I go.

Assumption # 1: STDs/CLDs contain no flows!

I'm still trying to figure out just why I feel this is so. Yet, from past translations I'm sure I have confused the situation by treating one or more of the influences or elements as flows. Maybe this becomes clear by the time I finish this.

Assumption # 2: If Assumption # 1 is correct then all the elements on the above diagram must be either Stocks or Converters.

Assumption # 3: Stocks represent things that accumulate and don't reflect instantaneous change.

From these assumptions it would seem to make sense that Employees, Cash, and pct Billing are Stocks.

The part that still confuses me somewhat has to do with when I have two or more influences for a single Stock as in the following diagram.

Figure 4

It would seem that this could be implemented in one of two ways:

Figure 5

or as:

Figure 6

I guess the point I really wrestle with is, "Can these be different or are are they essentially equivalent?" My conclusion is that when both the inflow and outflow originate from and terminate in clouds these two diagrams are equivalent. Yet, I can envision situations where one diagram might better portray the situation being modeled than the other. If the model is such that flows are between Stocks then there is a very substantial difference in terms of the affect there is on the model.

Based on the above assumptions the STD/CLD of Figure 3 would readily translate into the following SFD.

Figure 7

This diagram simply takes Figure 3, changes Employees, pct Billing, and Cash to Stocks, creates flows, flow1, flow2, and flow3, and moves the influences that were to the Stocks to the appropriate Flows. It is my perception that if I use this method to translate STDs/CLDs to SFDs I am less likely to repeat some of my previous errors.

And yes, there is an added influence from pct Billing to flow3 which represents the fact that pct Billing is perceived to drain over time as sort of a natural effect.

On 4/27/05 Rober Lamb commented that he didn't believe "pct Billing" was a viable stock, and I agree with him. Robert also commented that, "I think that to model this segment convincingly, the scope needs to include an inventory of work-sold-but-not-yet-carried-out (which is a stock) and a sales pipeline with conversion rates between leads, warm prospects, and firm proposals (each of which are separate stocks). Conversion rates would be driven by marketing, perceived quality, and product development..." Thanks for the feedback Robert.

Looking forward to your comments at to whether all this makes any sense. Just click on the envelope below to send me some mail....

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