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MODELLING SYSTEM DYNAMICS

 

Lorika Hisari, UCL Deep Cities researcher, shows a simulation on the Beresford Square Model on Vensim


In order to model the dynamic hypothesis as this is manifested in the causal-loop diagram we need to translate the variables of the causal-loop diagram into ‘stocks’ and ‘flows’ assigning the respective equations that depict the relationships between the ‘stocks’ and ‘flows’. The ‘stock’ refers to what is accumulated over time and the ‘flow’ to what drives this accumulation. Before drawing the ‘stock’ and ‘flow’ diagram we will launch a new file on Vensim and set the model parameters in terms of time as below. By clicking on Model we can set the time parameters that the model will operate its simulations. We have opted for the following options but any decision will very much depend on the time horizon under exploration and the available data. For our model we have specified the following parameters:

1. Unit of time: Month

2. Initial time: 0 (this is usually be default)

3. Final time (100 or can be less if the intention is to look at the simulation of variables over a shorter period of time)

4. Time step (it is important for the simulation to discretize the time into time intervals): 0.01

 

 

The next step is to convert our ‘causal-loop’ diagram above into a ‘stock’ and ‘flow’ diagram. If we look first at the variable ‘market growth’ which indicates ‘something that grows’, we will need to be a bit more specific and refine where this growth refers. We can do this first on a causal-loop diagram before moving to ‘stock’ and ‘flow’ diagram. Now for the purposes of this exercise, let’s move straight to designing the ‘stock’. Market growth is a rather generic term. It can indicate growing number of stalls, increasing diversity of food or increasing diversity of products as demonstrated by the interviews. Here, let’s focus on the ‘market stalls’ as a stock. In order to draw the stock we click on the relevant ‘icon’ which in some versions of Vensim is displayed as ‘Level’ or as ‘S’.

 

The next step is to draw the ‘flows’, in other words, what contributes to the increase and decrease of the ‘market stalls’, what is the rate of change. In the case of the ‘market stalls’ the rate of change relates to the number of stalls being installed and the number of stalls being removed or relocated. The flows can be drawn by clicking on the black arrow icon.

 

Having identified the ‘stock’ and ‘flows’, the next step is to map the ‘auxiliary’ variables, that is the variables that contribute to the ‘identified flows. In other words, what drives the installation of market stalls and what drives the removal of market stalls. In our causal loop diagram we identified a few forces. One force that we identified as contributing to the growth of market stalls was the fact that the Beresford square functioned as a connection point of bus/tram commuters and pedestrians. On the contrary, the re-routing of the buses and pedestrianization of the square led to the removal of stalls. These ‘cause’ variables can be depicted using the ‘variable tool’ as with the causal-loop diagram above.

 

Now that we have created the first ‘stock’ and ‘flow’ diagram we will try to simulate the relationship. Our dynamic hypothesis as has emerged from interviews and historic research is that the decline of the market in terms of numbers of market stalls is due to the change of the nature of the square as a connecting point which resulted due to the re-routing of the buses. This implies that if we simulate the relationships we should be able to create a visual graph that illustrates the gradual decline of the market as the pedestrianization increases and vice versa. To do so, we will need to translate the relationships into simple mathematic equations. We click on the ‘equations’ button. As we click, all variables are shown in black.

 

This is because certain variables are missing equations. We will need to click on each variable and insert the relevant equation. If we click on ‘buses going through the square’ we will get the following image.

 

As indicated in the image, the type of variable we clicked is a ‘constant’ variable which requires a number indicating the variable. For the ‘buses coming through’ we can define the number that used to pass by the square prior to the re-routing. In the case of pedestrianization of square, which is non-quantifiable variable, we can use a scale from 1 to 10.

When we click on the ‘flows’ we get a window identifying the relationship of the variables contributing to this flow as below. The ‘equations’ box is empty. We can draw the equation by clicking on the variable ‘market stalls’ and divide it with the ‘buses going through the square’ which gives us the rate of change. We proceed following the same with the other ‘flow’ (pedestrianization of square).