# Traffic Light Sequences

Essay by Daniel Baird, A+, January 1996

MEI Mechanics-1 Maths course-work

An investigation into automatic Traffic Lights

Introduction         3

Question         3

Aims         3

Simplifications and Assumptions         4

Traffic Lights         4

Vehicles         4

General assumptions.         4

SEQUENCE OF THE TRAFFIC LIGHT         5

MODEL 1         5

Maximum distance travelled in order for a vehicle to clear the system         5

Period of one cycle         6

Period of green light         6

Period of red light         7

MODEL 2         8

Data collection         9

Real Situation         9

List of other factors         9

CONCLUSION         10

Introduction

In this brief report, my aim is to attempt to determine the factors that affect the pattern of operation of temporary traffic lights in operation while roadworks or another obstruction is blocking one lane of a two-way, single carriageway road. Once this has been accomplished, I shall attempt to create a simple mathematical model and attempt to apply it to real life.

Question

When major roadworks take place on a two-way single carriageway road, contractors frequently regulate a one-way flow of traffic in alternating directions by use of automatically controlled traffic lights. What considerations affect the timings of such lights?

Aims

1. Analyse problem.

2. Propose a formula.

3. suggest errors involved.

4. look into ways where timings from formulae could be modified other than 'simplest case'.

Simplifications and Assumptions

n The road is two-way, single carriageway.

n The road is straight, there are no obstructions.

n Road surface is constant, friction is constant.

· Traffic Lights

n Drivers have 'infinite' patience and always obey traffic lights perfectly.

n All sets of lights are perfectly co-ordinated, and their pattern constant.

· Vehicles

n Vehicle size is constant.

n Vehicle acceleration/deceleration is constant.

n Distance between vehicles is constant.

n All vehicles are 'perfect'.

n Distance travelled by...