# Mathematical Modelling: Introduction

ACMNA208; ACMNA193

This unit Introduction to Mathematical Modelling is one of 5 units making up the Special Topic “Mathematical Modelling”.

It introduces students to mathematical modelling and the key processes involved. Students model two situations which involve rates: a traffic jam and  time for queueing in a theme park. They begin with simple models, and gradually include more factors. They are introduced to the diagram of the mathematical modelling cycle used in all the units.

### Lesson 1: Modelling a Traffic Jam

Students approach modelling by considering how many vehicles there might be in a 200-metre section of a blocked highway. They first identify factors that might be taken into account. They then consider how to calculate how many vehicles, making some assumptions and either researching or estimating the values. They write a description of how to tackle the problem using their approach and how to develop a more sophisticated model. Groups work out a first solution and think about the effects of the assumptions they made.

### Lesson 2: Modelling Theme Park Queues

Building on the ideas developed in Lesson 1, students consider a structurally similar problem about queueing to get on a ride at a theme park. Initially they explore how many people might be expected to be in a fixed length of queue. They develop a model for time to get onto the ride by considering the length of the line and the rate of flow of people onto the ride (i.e. combining the number of people on the ride and the time taken for the ride).

### Lesson 3: Understanding the Modelling Process

Students work through the modelling process as summarised in the modelling diagram. After reviewing their work from Lesson 2, they link their work on theme park queues to each stage to the modelling process, and reflect on how this helps them to analyse real problems and get realistic solutions.

### Lesson 4: Improved Theme Park Model

Students plan a new ride to maximise flow of people through the ride whilst maintaining excitement. They investigate how aspects of the design of a ride affect the potential queuing time. They use this in combination with consideration of patterns of people joining lines to gain understanding of the net effect of the numbers of those leaving the line to go on the ride and those joining at the other end. They can improve their models of queuing time by including additional factors.

### Lesson 5: Improved Traffic Jam Model

Students return to the traffic jam situation from Lesson 1, seeking to transfer to traffic flow the understandings gained in the theme park context. They look at what happens as the traffic jam clears, developing a more sophisticated model that considers inflow and outflow. They map their work onto the modelling diagram, reflecting on the factors involved and how they influence stages in the modelling process.

Last updated November 9 2018.