# Simulations

## Simulations

To simulate a system is to produce a model of it which has the same characteristics. By studying the behaviour of the model it is possible to find out how the actual system would behave in similar circumstances. Very often a simulation consists of a computer program which mimics a real-life situation. Usually the program is based on a number of formulae which form a mathematical model of the actual system.

## Example of a simulation-traffic lights

A council is considering situating traffic lights at a busy road junction. It is not clear whether this would improve the situation at the junction or not. A survey is done to find out:

1 The number of cars per hour reaching the junction from each road at different times of the day.

2 The length of queues of cars waiting at the junction.

A computer program is written giving a simulation of the cars arriving at the junction and leaving it. The simulation can include the effect of traffic lights and shows:

1 Cars arriving each minute along the roads leading to the junction. For this the computer chooses a number of cars which is random but is within the range of numbers found in the survey.

2 The traffic lights changing. The model allows the timing of the lights to be changed.

3 Queues of cars waiting at the lights. The computer shows each queue getting bigger when the lights are red. It then shows them getting smaller or disappearing when the lights are green.

First the simulation is run without any traffic lights. The queues of cars formed should be about the same as the real queues found in the survey. This shows that the model used in the simulation does work.

Then the program is run with some traffic lights included in the model. Different timings are tried in the simulation. If the council officials find that they can reduce the traffic delays, then they know it is a good idea to install the lights.

## STAGES IN PRODUCING AND USING A COMPUTER SIMULATION

1 The problem to be solved must be fully understood.

2 Data from the real-life situation is collected if possible.

3 The model is formulated. This may involve a set. of mathematical equations.

4 The computer programs are written and tested.

5 The program is run with data chosen such that the computer predictions can be compared with real-life events. This stage is called the validation of the model.

6 The computer is now ready to answer 'What if ... ?' questions. The model is used with different data to make predictions about what would happen to the real system in a new situation.

In this case there are no real-life results for comparison. It is necessary to rely on the computer and on the model which has been made.

It will not always be possible to carry out all the above steps. It may not always be possible to collect data from the real-life situation beforehand. In this case validation of the model may not take place until after the first predictions have been made.

## SITUATIONS WHERE SIMULATIONS ARE USED

1 Where conditions are too dangerous for real experiments to be carried out (e.g. studying the behaviour of a nuclear reactor if changes are made to the fuel rods).

2 Where a decision has to be reached and there are several possible courses of action (e.g. a model of the national economy). Ministers and Treasury officials can try various budget changes to see what their effect would be.

a In designing. For example extensive simulation work was carried out in the planning of the proposed new airport for London. Features incorporated into the model included:

(a) Flow of people through the airport. buildings.

(b) Flow of traffic on the proposed site and in the surrounding area.

(c) The effects of the noise of the aircraft engines.

4 Where a study being carried out is entirely theoretical and the performing of real experiments is an impossibility. A good example of this is the study into the origins of the universe. Theories such as the 'Big Bang' can be modelled and the consequences of the theory investigated.

5 In education and t.raining. By interacting with a model of a situation a student or trainee can become familiar with the situation.

## Further examples of simulations

1 Military operational research models. These are used for assessing weapons and tactics under various conditions (e.g. difficult terrain, adverse weather).

2 Economic models. These are used to analyse and predict the behaviour of firms, industries or even national economies.

3 International relations models. These simulate the state of relations between different countries of the world. They could be used, for example, to attempt to predict the outcome of certain military action by an individual country.

4 Educational simulations. These are widely available for microcomputers. One such simulation involves the user taking on the role of the owner of a small delivery service. The simulation then takes the user through the various stages in organizing deliveries efficiently. The user has to take decisions based on the information provided. The aim of the simulation is to teach the user something about vehicles and the road system as well as encouraging logical thought and good decision making.

5 Circuit testing. Computer simulation is being used to help in the design of new computers. It is no longer necessary to make an actual test circuit for any new chip which is designed. The new designs are instead tested by simulation. If the results of the simulation are satisfactory then production can be started.

## FLIGHT SIMULATION

As early as the 1940s pilots where given some training in mock ups of real aircraft. cockpits. Later, when the first multi-engined jet airliners were introduced computer-controlled flight simulators were employed. The 'cockpit' was mounted on hydraulic rams. The rams were

under the control of a computer whose program simulated various flying conditions. The crew under training had to respond by referring to their instruments and operating their controls.

In these early simulations the 'view outside' was not very realistic. Advances in computer graphics have meant that visual images are now available to improve the authenticity of the simulations.

Techniques have improved so much that it is now possible for the training of military pilots to include the experience of enemy attacks. The attacks have a random factor in them so that the pilot is forced to respond not only quickly, but in a flexible way.

Civil pilots are able to practise landing and taking off. Accurate images of real airports appear in the simulation. Again random elements are introduced into the simulation so that the pilot has to respond to, say, a burst tyre on landing.

Flight simuJation programs of a less complex nature are available for microcomputers. Some merely provide amusement, but others provide a serious exercise for would-be pilots.