Systems modeling in practice usually involves six broad steps, within each of which there may be many subsidiary steps and some checking and revision. There is also likely to be iteration back to the earlier steps, as issues which call for changes in earlier decisions are uncovered.
Nevertheless, in my experience, the following six steps are likely to cover the basics.
1. Identify the system of interest, in particular specify the system boundary and specify the level of detail in which you (and other participants or stakeholders) are interested. This usually involves specifying what are to be considered sub-systems or elements within the overall system. Another way of expressing this is the level of aggregation of the system. For example, is it relevant to describe what happens to each person in a particular system, or would some average (an aggregate measure) be more appropriate?
2. Recognize the purpose of the systems study, and identify the purpose of the modeling activity within it. The most common purposes of systems studies are:
• Improving understanding of a situation.
• Identifying problems or formulating opportunities.
• Supporting decision making.
Modeling can be used to support all of these - by predicting system behaviour, by predicting the outcome of an intervention or by providing a basis for discussion or dialogue. This should lead to increased understanding.
3. From items 1 and 2 above, identify the main features or behaviours of the system of interest. These will then become the state variables in the model. By implication this step involves further simplification by specifying areas of the system that can be aggregated together or omitted from the modeling activity.
This is a critical step in the process, since omitting an important feature at this stage can decrease, or even destroy, the value of the modeling activity (Box 5 gives an example).
4. Select a modeling technique that will address the features/behaviour of the specified system in a way that matches the specified purpose. After working through this pack, you will begin to see how different techniques are suited to different purposes.
5. Modeling technique, develop an outline of a suitable model. Use this outline to check compliance with items 1, 2 and 3 above - or modify the model or adjust the specifications in items 1, 2 or 3.
6. Develop a full version of the model by a process of iteration, expansion and inclusion of detailed data as required.
You should now read the document; "Box 5- Omissions from the model", in the section titled 'Extra reading materials'.
Look at each of the stages of the process listed as 1-6 above, and explain how each relates to the specified activities (verbs) of the conceptual model set out at the beginning of unit 2- part 2.
My mapping of the stages of the actual mathematical modeling process against the conceptual model is given below:
A key feature both of the conceptual model and the practical sequence is that of choosing a method of modeling. This step is crucial, for several reasons..
As you will see as you work through the rest of this unit, each of the different modeling techniques can be more or less appropriate for different situations, and for different types of system which have been identified. In the succeeding material, we will return regularly to this question of choosing an appropriate model from among a range of quantitative techniques. But first, we need to consider when it is even appropriate to think about using any form of quantity.
The stage of choosing a model could include consideration of diagrams or conceptual models as well as quantitative models. So when should you consider a quantitative model as the appropriate next step? There are four main conditions that are necessary for a quantitative model to be an appropriate choice.
1. At the chosen level of aggregation, all the significant features or behaviours of the system must be adequately quantified, i.e. measured. If this condition is not satisfied then any model will have to impute numerical values for the unqualified features or behaviours, which can lead to distortions in any conclusions derived from the model. Even where all the important issues are quantified, there are other issues associated with data that may preclude the use of a quantitative model. In particular, if the data are unreliable, or are extremely expensive in time or money to collect, then quantitative modeling may not be feasible.
2. The purpose should involve a level of discrimination or differentiation that can only be achieved by quantitative comparisons.
There are many of these, for example:
• Which is the most effective intervention?
• When will this behaviour become manifest?
• How many cases of each illness should we expect next month?
If the main purpose can be accomplished without a quantitative model then seek the answer non-quantitatively. The reason for this is that the sheer complexity and data gathering required for most quantitative models can only be justified if it is essential. Also the process of converting the problem into mathematical form and then interpreting the answers back from a numerical output may obscure the core systems issues.
3. Where the system of interest involves a significant number of interacting feedback loops at the level of aggregation required. That is, a situation where the behaviour of X affects the behaviour of Y, and the behaviour of Y also affects the behaviour of X.
Almost by definition all systems involve interacting feedback loops, but in most cases they do not need to be explicitly modeled if they are not essential in determining the behaviour of interest.
However if the behaviour of interest is directly governed by the interaction of more than three feedback loops you are likely to be forced to use a quantitative model to understand what is going on.
4. Where the behaviour or features of the system of interest are governed by stochastic processes. Stochastic, or random processes are those like the toss of a coin or selection of a card from a pack. Here a range of results is possible, but you cannot know in advance exactly which result will occur although you may know the chance (formally, the probability) of a particular result occurring.
In such a situation you will usually need a model to arrive at a thorough understanding, since it is only by using a model that you can explore the behaviour over and over again with randomly chosen sets of values. Human beings are notoriously bad at predicting the outcomes of systems governed by such stochastic processes. The popularity of gambling, and the interpretations placed on predictions of the weather are examples of this.
In which of the following situations do you think it would be appropriate to use a quantitative model, and why?
• Devising a policy to conserve stocks of fish in the North Sea.
• Determining the best approach to negotiating a merger between two competing companies, from the point of view of one of the companies.
• Choosing between two different routes for a new road development.
1. The size of fish stocks is governed by a complex series of feedback loops, including the relationship between fishing activities and fish stock. It would be essential to carry out sufficient quantitative modeling to establish the range of activity that could be sustained, given the available information on the fish and the sea. However this is usually the easiest part of devising a policy that will work!
2. Here quantitative modeling cannot assist in devising the approach to negotiations. There may need to be some calculation of the potential savings and benefits associated with the merger, but these will not be reliable because of the lack of data on the competitor company or on the merged company.
3. This is an area where quantitative modeling, known as cost-benefit analysis, has been widely used to try to establish the relative merits of alternatives. However many of the sensitive factors, such as conserving wildlife, avoiding traffic congestion, reducing accidents and noise, reducing amenity of countryside and so on are not readily quantified in financial terms.
The use of cost-benefit models therefore reduces to interminable arguments regarding the imputation of values to these factors. So this is a case where quantitative modeling is used, but probably should not be.
There is a wide range of quantitative models, of varying degrees of sophistication and complication. In this section of the unit, we will only cover those that I think you are likely to encounter in systems studies or could use to good effect. The techniques available subdivide broadly into two major classes, static models and dynamic models. The distinction between these will become clearer as you look at some detailed examples. Essentially, dynamic models are those where the set of calculations comprising the model is repeated a number of times.
The initial values of the variables in the current set of calculations are taken from the results of the previous set of calculations, and this process is repeated time and time again.
In static models, the calculations are executed once to obtain a result (or set of results). Even where the calculations are repeated, as with stochastic models, the values in each set of calculations is not determined by the previous calculation.