The model: a simple bank account

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We will make a model for a simple bank account, with interest paid annually at a rate of 10%, and $10 taken out every year. The account initially contains $300. This is what we expect to happen:

Year 1

Year 2

Year 3

And so on. Note that the increments are getting bigger each year because each time the balance goes up, so the interest paid increases. The balance of the bank account is increasing at a faster and faster rate.

Having understood the calculations that we are going to perform, we now turn to the concepts needed to express these ideas in Simile.

We use a compartment to represent the amount of money held in the bank account, since this a quantity that changes incrementally over time. We use two flows, one to represent the gain of money from interest and the other to represent the loss of money by withdrawal. One flow (interest) will go into the compartment, while the other flow (withdrawal) will come out of the compartment. We will also use a variable to represent the interest rate (10%, or 0.1). This variable will be linked to the flow representing the payment of interest by an influence arrow, indicating that the amount of interest paid depends on the interest rate. Since the amount of interest paid also depends on the amount in the bank account, there we will also use an influence arrow from the compartment representing the bank account to this flow.

In this tutorial we want to introduce you mainly to the mechanics of working with Simile, and these are explained in detail in the following steps. The concepts involved in representing even a simple system like this one in a modelling language can be quite complex.

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Step 1: Starting Simile: what's on the screen

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Starting Simile

You start Simile by double-clicking on the desktop icon created during installation, or by clicking on the Simile icon in the Start Menu.

These are both shortcuts to the file <Simile Program Files>\System\bin\Simile.exe, where <Simile Program Files> is the directory you chose to install the program. By default, this is commonly "C:\Program Files\Simile50", though if you are using a network, it may be on a remote hard drive. If you would like to be able to start Simile from a different location, create a shortcut to this file.

Linux users can start Simile by typing the command 'simile' in a terminal. Also, a shortcut is added to the Science/Education submenu of the Applications menu, which can be dragged to the desktop or taskbar, depending on your desktop environment.

On a Mac, Simile will be added to the Applications folder, from which it can be dragged to the desktop or task bar.

Within a few seconds, the main window will be displayed.

The Main Window

When Simile starts, you see a single window. This contains:
 

• a menu bar (at the top of the screen on a Mac), containing a standard File menu, some menus specific to Simile, and a Help menu. Hold the mouse over the title for each menu to see the options it contains.
   
• a toolbar, extending over two rows. The top row has standard tools (e.g. for opening and closing files), plus some specific to Simile.

• a component bar, containing buttons corresponding to each type of model-diagram element: you will use these for building up your model diagram. The right-hand part contains buttons for editing the model diagram. Hold the mouse over each button to get a brief description of its function.

• an equation bar, for entering equations into the model. At the right-hand end of the equation bar are the tools to accept or reject changes to equations, and to help build equations.
   
• a big blank area (the "desktop canvas") with faint lines. This is where you will draw your model diagram. The grid can help you arrange your diagram neatly.

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Step 2: Making the model diagram

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We begin by drawing the model diagram for the bank account model. A note on colours used in the following description: when you add a component to the model diagram, it is initially drawn in blue. This means that the component is selected. You will see the ways in which this is useful later on. When the component is not selected, it will turn red. This is its usual colour, and means that the component needs some extra information (like a value or equation) before the model can be built.

1. Add a compartment to the model diagram.

• Click on the compartment symbol in the toolbar.
• Move the mouse to the middle of the desktop window, and click again.

You should see a box labelled comp1.

2. Rename the compartment "account".

3. Add an interest flow and a withdrawal flow.

• Click on the flow symbol in the toolbar.
• Move the mouse into some space to the left of the compartment labelled account, hold the mouse button down, and drag the mouse into the centre of the compartment. Release the mouse button.
• Type in the label interest.
• Move the mouse into the centre of the compartment, and drag to the blank area to its right. Release the mouse button.
• Type in the label withdrawal.

As an alternative to dragging out the flow, you can just click on its start and finish positions.

4. Add a variable for the interest rate

• Click on the variable symbol in the toolbar.
• Move the mouse to the blank area above the interest flow, and click once.
• Type in the label interest rate.

7. Draw the influences

• Click on the influence arrow button in the toolbar.
• Move the mouse to the middle of the compartment labelled account, and drag an influence arrow to the flow labelled interest.
• Release the mouse button when the flow has turned green.
• Move the mouse to the middle of the variable labelled interest rate, and again drag an influence arrow to the flow labelled interest.

8. Re-arrange the model diagram

• Click on the pointer button in the toolbar.
• Move the mouse to the middle of the compartment labelled account.
• Drag the mouse, and watch the compartment and its associated arrows re-arrange themselves.
• You can also move the following components:
• the cloud symbol at the end of each flow arrow;
• the variable;
• the valve symbols on the flows;
• the middle of an influence arrow;
• the position of the "kink" that appears in a flow arrow when it goes between two components that are not exactly above, below or to the left or right of one another; and
• the labels. (A note on moving captions: if a component is selected, and is coloured blue, then the caption can be edited. To edit a caption, click on the label and type. You can drag the mouse to select a range of characters. To move the label relative to its component, make sure the component is not selected. You can then drag the label into its new position.)

This completes the drawing of the model diagram. In the next step, you will provide the numeric values and equations you need for simulating the behaviour of the bank account. Note, however, that this sequence (complete the model diagram before providing any quantitative information) is followed here for convenience: in general, you are free to provide the quantitative information at any stage in the diagramming process.

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Step 3: Adding initial values, parameter values and equations

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1. Prepare to set component properties

Click on the pointer button in the toolbar.

2. Assign the initial value for the compartment

• Click on the compartment labelled account.
• Enter the value 300 into the equation bar.
• Click on the green tick mark or press the Return key.

3. Add the interest rate equation

• Click on the flow labelled interest.
• Variables account and interest_rate are now listed as influences upon interest. These influences are visible by clicking on the x_s button. Selecting an influence from the drop-down list, places the text in the equation bar.­

• Enter the expression account*interest_rate into the equation bar, either by selecting each variable in turn or by typing. Be sure to use an underscore rather than a space in interest_rate.
• Click on the green tick mark.

4. Assign the value for the withdrawal flow

• Click on the withdrawal flow.
• Enter the value 10 in the equation bar.
• Click on the green tick mark.

5. Assign the value for interest rate

• Click on the variable labelled interest rate.
• Enter the value 0.1 in the equation bar.
• Click on the green tick mark.

Notice that every component of the model diagram is now black, rather than red as it was before. This indicates that every component has been mathematically specified, and so the model is ready for running: Simile has enough information to work out the flows, and thus to update the amount of money in your bank account forward through time.

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