Systems-Dynamics Diagrams

http://growingwingsontheway.blogspot.com

Using systems-dynamics diagrams

Rosalind Armson

[This guide was originally intended as a chapter in Growing Wings on the

Way, but was excluded to avoid the book becoming unduly long. Many of

the terms used and a number of references are explained in the book itself.

See http://growingwingsontheway.blogspot.com for details.]

I refer in the book to the useful vagueness of the word influences. Systems-

dynamics diagrams relate closely to influence diagrams and specify the

effect of the influence. An influence diagram can often provide the starting

point for a systems-dynamics diagram. A systems-dynamics diagram

makes sense of how key variables influence each other in a messy situation.

Systems-dynamics diagrams make sense of change, specifically change

recognisable in terms of more or less; bigger or smaller; higher or lower;

better or worse; expensive or cheap.

Choosing a systems-dynamics diagram

Choose a systems-dynamics diagram if you find yourself thinking about a

messy situation in terms of more or less; bigger or smaller; higher or lower;

better or worse; expensive or cheap; wherever an underlying variable

influences other variables in the situation. A systems-dynamics diagram

will not map all of the mess but it may make sense of parts of it. Systems-


dynamics diagrams help identify why things seem to get worse (and may

suggest ways in which they could get better) and why some phenomena

stay the same, despite efforts to disrupt them. They will also help identify

why initial success has not been sustained.

Systems-dynamics diagrams draw attention to the subtle effects of interacting

influences but they can also form a brief for a computerised model.

Working with systems-dynamics diagrams

The grammar of a systems-dynamics diagram conveys meaning very

efficiently. As with influence diagrams, the key interconnection is

‘influences’ but the words represent variables rather than things.

Systems-dynamics diagrams1 have words, arrows labelled ‘s’ or ‘o’, and a

title. Figure 1 shows the two key elements of a systems-dynamics diagram.

Each set of words indicates a variable – something that can increase or

decrease in value – such as room temperature, interest rate, number of

people employed, annual tonnage shipped and so on. It is not necessary for

the variable to be measurable: any phenomenon that increases or decreases

can appear in a system-dynamics diagram – customer satisfaction, volcanic

activity, disappointment, comfort, reputation, pain, and so on. Arrows

connect the variables. An arrow labelled ‘s’ indicates that the two variables

it connects will vary in the same direction, in the absence of other

influencing variables. The ‘s’ stands for ‘same’. Thus, in Figure 1, the larger

the value of A the larger will be the value of B and the smaller the value of

A, the smaller will be the value of B. You can picture this sort of influence

as the same-direction movements in Figure 2. An arrow labelled ‘o’

indicates that the bigger the value of C, the smaller will be the value of D

and the smaller the value of C, the larger will be the value of D. The ‘o’

stands for opposite. In Figure 2 this is pictured as a see-sawing motion.


Figure 1: The meaning of signs in systems-dynamics diagrams

Figure 2: Men demonstrating meaning


It is important to notice that each arrow has two simultaneous meanings. In

Figure 3, the two meanings are:

as the tonnes of ash in the airspace increases, it influences the number

of flights cancelled to increase

as the tonnes of ash in the airspace decrease, it influences the number

of flights cancelled to decrease.

Figure 3: The s (same) effect of volcanic ash on airlines

Systems-dynamics diagrams with o-arrows (for example, in Figure 4), also

carry two simultaneous meanings:

as the number of flights cancelled increases, it influences airline

revenue to increase.

as the number of flights cancelled decreases, it influences airline

revenue to decrease.


Figure 4: The o (opposite) effect of volcanic ash on airlines

Making sense with a systems-dynamics diagram

As I engaged with the long-term issues in managing Mum’s finances, it

was not clear what the issues were or how Mum’s future care could be

funded. [Working out how to help my Mum in her old age is the subject of an

ongoing case study in the book.]

I drew Figure 5 over several weeks as the issues became clearer. (It took a

while before I realised that separating ‘erosion of Mum’s savings from

‘Mum’s savings’ made it much easier to understand what was going on. It

became obvious that Mum’s income would not cover care-home fees, if

they became necessary. She would have to draw on her savings, which

would last only a few months unless we sold her house, even though its

market value was rising. I now knew what questions to ask about savings,

interest rates and annuities.

This was, in fact, the most useful outcome of this diagram. I could ask

questions knowing that the key issues were for bolstering Mum’s income

as much as possible and reducing the erosion of her savings. The

relationship was a vicious spiral2 (two o’s). Once Mum’s savings started

eroding, her income too would decrease and she would need to draw on

more and more of her savings to pay her care-home fees. (We were unclear

what we would do if her money ran out. We decided Mum’s circumstances

would be very different by then and would need discussions we could not

anticipate.)


Figure 5


Rules and guidelines for drawing systems-dynamics diagrams

Systems-dynamics diagrams only work when you obey the rules (unlike

systems diagrams with a less-formal ‘grammar’.)

1. Phrases refer to variables.

2. Phrases should not themselves refer to variations, so do not use

‘more/less’ or ‘increase/decrease’ in the phrases.

3. Use an s-arrow where a change in the influencing variable (at the

tail of the arrow) would, on its own, influence a same-direction

change in the influenced variable (at the head of the arrow).

4. Use an o-arrow where a change in the influencing variable (at

the tail of the arrow) would, on its own, influence an opposite-

direction change in the influenced variable (at the head of the

arrow).

5. A system boundary is optional but not usually included.

6. A title defining the diagram is essential.

Understanding a systems-dynamics diagram: sequences of arrows

Systems-dynamics diagrams carry many subtle meanings so interpreting

them requires thought and patience. Indeed, there are rules for tracking the

effects of chains and loops of influence. The following rules concern

interpreting systems-dynamics diagrams:

7. A sequence of s-arrows, an even number of o-arrows or a

mixture of s-arrows and an even number of o-arrows are the


equivalent of an s-arrow connecting the first variable and the last

variable in the sequence.

8. A sequence of arrows containing an odd number of o-arrows is

the equivalent of an o-arrow.

9. Rewording and changing the arrows may make a sequence

easier to understand.

Each of these rules is easier to understand with the aid of a diagram and an

example. Figure 6 captures Rule 7. The rule does not mean that the

intervening variables can, or should, be left out of the diagram but it allows

us to determine the effect of variables further back in a sequence.

Figure 6: Equivalences

Figure 8 shows an example of changing the words, as allowed in Rule 9.

This is useful for eliminating paired o-arrows in favour of easier-to-

understand s-arrows.

Figure 9 shows the effect of an odd number of o-arrows in a chain. You can

check the effect of Rule 8 by working through each interaction.


Figure 8: Changing the words

Figure 9: Reworking the arrows

Understanding a systems-dynamics diagram: parallel arrows

It is impossible to tell the effect of two arrows on one variable from the

diagram alone. In Figure 10, for example, B and C will ‘compete’ to push


variable D up or down. The diagram does not say which variable’s effect is

stronger so D may go in the same direction as A or in the opposite

direction.

Figure 10: Parallel arrows

Understanding a systems-dynamics diagram: balancing and

reinforcing loops

Systems-dynamics diagrams can give rise to loops of variables. Such loops

may be either balancing loops or reinforcing loops. Balancing loops balance

themselves so that changes in any one of the variables balance out,

resulting in little change. Reinforcing loops reinforce changes in any of the

variables in the loop. This leads to two more rules:

10. A sequence of arrows forming a loop with an odd number of o-

arrows is a balancing loop whose effect is to stabilise the

variables in the loop. This is shown in Figure 11a. An increase in

A will decrease B. The decrease in B will decrease A, thus

neutralising the increase in A.


11. A sequence of arrows that forms a loop containing an even

number of o-arrows (Figure 11b) or no o-arrows (Figure 11c) is a

reinforcing loop whose effect is to reinforce changes in the

variables in the loop.

Figure 11: Loop labels

The idea of balancing and reinforcing loops is an important one and

underlies many complex phenomena. Figure 12 shows a phenomenon I

observe at a local coffee house. As the length of the queue increases,

customers arriving at the shop notice the queue and often leave again,

presumably to go to the coffee house up the road. As the length of the

queue gets shorter, the number of people joining it increases again. This is a

balancing loop and, in this particular example, tends to stabilise the queue

length at around five customers, on a busy day.

Figure 12: Queues


If I broaden my observations at the coffee house, I see that, as the queue

lengthens, the general level of organisation behind the bar deteriorates and

the time it takes to slice cakes, gather clean crockery and grind new bags of

coffee increases. This slows the service down and increases the time it takes

to serve each customer. Figure 13 shows my extended systems-dynamics

diagram. It now includes a reinforcing cycle with two o-arrows. It shows

the increasing queue length decreasing the level of organisation, increasing

the time taken to complete each order, and lengthening of the queue still

further. But any pair of connected variables in a systems-dynamics diagram

has two meanings. The reinforcing cycle also shows that if the level of

organisation behind the bar increases, perhaps by more tidying and

preparation during slack times, then the time it takes to serve customers

and their wait time will decrease. This allows the number of customers

served each hour to increase. Notice, however that the length of the queue

may not decrease significantly: it is stabilised by the balancing loop.


Figure 13: Service

Notice that the wait time for each customer decreases with more baristas

available to serve them. But the diagram contains a warning. The

reinforcing loop remains in place, even with additional baristas. The

diagram suggests that additional baristas might usefully organise and

prepare, as soon as the need arises.

Delay

Systems dynamics studies the effect of variables upon each other. It attends

particularly to loops of interactions and delays occur between changes.

Systems-dynamics diagrams represent time delay by a double slash in the

arrow, as shown in Figure 14.

Figure 14: Representing a time delay.

Systems dynamics is a huge subject and I cannot do it justice here3. I can

however, use a systems-dynamics diagram with loops and a delay to show

one of the characteristic phenomena generated by attempts to deal with a

messy situation as if it were a difficulty (see Chapter 1 in the book). In

Figure 15, attempts to ‘fix’ problematic symptoms in a messy situation

work at first. Because the messy situation has multiple interconnections,

the unintended consequences of the quick fix take some time to emerge.


Figure 15: Treating a problem as a difficulty

Drawing a systems-dynamics diagram

Systems-dynamics diagrams have many associated rules but they are fun

to draw and make sense of interacting phenomena in very satisfying ways.

You may want to draw something from a messy situation of your own but,

if not, there are suggestions at the end of the chapter for practising4. As

with other diagrams, start with a simple relationship and build backwards

and forwards.

Do not force loops in a systems-dynamics diagram if there are none. You

can check you have the right directions by looking at sequences of arrows,


and how changes at one end influence change at the other. As with

influence diagrams, keep asking: What else influences this? and What else does

this influence? and asking, of each arrow, whether it is an s-arrow or an o-

arrow. Sense making is often a case of identifying where there are

uncertainties: locating an uncertain relationship is as much an output as a

completed diagram.

Using a systems-dynamics diagram with others

Using systems-dynamics diagrams with other people is less easy than other

diagrams in this book. The relative subtlety of the rules and their

interpretations mean that systems-dynamics diagrams work best with

people who understand the rules, rather than novices. The diagrams have a

significant appeal to ‘techies’, who may be relatively quicker at picking up

the subtleties and may even develop an addiction to drawing them.

1 Naming systems-dynamics diagrams

Diagrams with s-arrows and o-arrows have a bewildering variety of names.

In the systems-dynamics community, these diagrams are variously known as

systems diagrams or causal-loop diagrams. The latter name comes about

because systems-dynamics is fundamentally about exploring the effects of

loops of elements that lead to change (wanted or unwanted) or to stability

(wanted or unwanted.) In the book, I use systems diagrams to mean the whole

suite of systemic diagrams. I do not use the term causal-loop diagram because

it risks confusion with multiple-cause diagrams, discussed in Chapter 11 of

the book.

I first encountered systems-dynamics diagrams as sign graphs. Sign graphs

have exactly the same intention as the diagrams I describe here but have plus

signs instead of ‘s’ on arrows indicating same-direction change and minus

signs instead of ‘o’ in opposite-direction arrows. This sign convention can be

immensely confusing so I now use the s-arrow and o-arrow notation

systems-dynamicists use.


2 Loops and feedback

Balancing loops and reinforcing loops are examples of feedback. A balancing

loop is a manifestation of negative feedback. Negative feedback has the effect of

stabilising variables and acting against change. In engineering contexts,

negative feedback keeps conditions constant. A reinforcing loop is a

manifestation of positive feedback. Positive feedback promotes and reinforces

change. The designations positive and negative are often mistaken as ‘good’

or ‘bad’ respectively. This is not the case. Positive feedback, for example,

shows up as a ‘vicious spiral’ or as a ‘virtuous circle’. Similarly, negative

feedback is not necessarily critical. It may come in the form of ‘Don’t ever

change. You’re wonderful as you are.’

In the UK, the Munro Review (2010) includes some interesting examples of

balancing and reinforcing loops in the context of child protection policy.

Munro, E. (2010). The Munro Review of Child Protection, Part 1: A Systems

Analysis. London: Department for Education.

3 Books on systems dynamics

Peter Senge’s book is a classic and discusses systems-dynamics in terms of

the phenomena loops and delays can generate. He identifies some archetypes

– loops present in many intractable problems – and discusses how they might

be tackled.

For a more technical discussion of systems dynamics, and some free software

for exploring complex interactions between variables, I recommend Maani.

and Cavana’s book. It is full of systems-dynamics diagrams drawn from their

own and others’ work.

Maani, K. E., & Cavana, R. Y. (2007). Systems Thinking, Systems Dynamics:

Managing Change and Complexity. North Shore: Pearson Education New

Zealand.

Senge, P. M. (1992). The Fifth Discipline: The Art and Practice of The Learning

Organization. London: Century Business.


4 Practising drawing systems-dynamics diagrams

Use any of the subjects suggested for influence diagrams for practising

systems-dynamics diagrams. Here are some additional suggestions,

particularly suited to systems-dynamics diagrams:

• Value-for-money vacations

• Waiting to be seen at the hospital Accident and Emergency Department

• The length of a queue (at the supermarket, train station, telephone

helpline, etc.)

• Stock control (ordering enough to meet demand but not spending

money on unnecessary stocks)

• Driving to the supermarket for lower prices, versus shopping locally on

foot

• Taking public transport versus driving the car

Similarly, systems-dynamics diagrams allow rigorous exploration of complex

relationships without specifying the variable’s influence beyond same or

opposite direction.

Documents

Systems-Dynamics Diagrams