Traffic Light Sequences

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MEI Mechanics-1 Maths course-work

An investigation into automatic Traffic Lights

Table of contents 2

Introduction 3

Question 3

Aims 3

Simplifications and Assumptions 4

Road 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

Dead Time 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

· Road

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 cars between traffic lights is constant.

General assumptions.

n Weather is constant, clear and dry.

n The time that the amber light is displayed for is quasi-instantaneous and therefore can be ignored.

N.B. These assumptions have been made in order to allow my models to function properly. The theoretical values that the models formulate are to be taken with a pinch of salt and therefore to take account of other variables, error bounds should be applied to reduce these discrepancies.

SEQUENCE OF THE TRAFFIC LIGHT

1. Red

2. Red/Amber

3. Green

4. Amber

5. Red

MODEL 1

Distance between traffic signals. 34m

Mean speed of traffic. 5ms-1

Time for traffic to clear the system (34m) at 5ms-1 6.8sec

Mean length of one vehicle. 4m

Mean inter-vehicle gap (dynamic). 5m

Mean inter-vehicle gap (static). 0.5m

Number of vehicles per flow. 8

Time delay between cars starting at first set of signals. 1sec.

Duration of amber light. 3sec's.

In this model, it is assumed that every cycle of the lights, no mre or less than eight vehicles pass through the system in one direction. The minimum distance a car has to travel to clear the sytem is 34m. On the lights turning green, the first car instantly reaches a speed of 5ms-1 one second later the second car does the same and so on.

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

34+(7x0.5)+(8x4)=69.5m

The last vehicle in the flow has to travel the 34m between the traffic lights plus the distance between itself and the first set of lights. This latter distance is the length of all eight cars plus the distance of seven static inter-car gaps.

Period of one cycle

Time = Distance / speed

= 69.5m / 5ms-1

= 13.9 sec's

This is the time taken for the first vehicle to clear the system, however the last vehicle has to wait 7 seconds before it can start to move.

13.9+7=20.9 sec's

The time from the first car starting until the last car clearing the...
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