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Traffic Light Sequences Essay

1012 words - 4 pages

MEI Mechanics-1 Maths course-workAn investigation into automatic Traffic LightsTable of contents 2Introduction 3Question 3Aims 3Simplifications and Assumptions 4Road 4Traffic Lights 4Vehicles 4General assumptions. 4SEQUENCE OF THE TRAFFIC LIGHT 5MODEL 1 5Maximum distance travelled in order for a vehicle to clear the system 5Period of one cycle 6Period of green light 6Dead Time 6Period of red light 7MODEL 2 8Data collection 9Real Situation 9List of other factors 9CONCLUSION 10IntroductionIn 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.QuestionWhen 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?Aims1. 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· Roadn 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 Lightsn Drivers have 'infinite' patience and always obey traffic lights perfectly.n All sets of lights are perfectly co-ordinated, and their pattern constant.· Vehiclesn 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 LIGHT1. Red2. Red/Amber3. Green4. Amber5. RedMODEL 1Distance between traffic signals. 34mMean speed of traffic. 5ms-1Time for traffic to clear the system (34m) at 5ms-1 6.8secMean length of one vehicle. 4mMean inter-vehicle gap (dynamic). 5mMean inter-vehicle gap (static). 0.5mNumber of vehicles per flow. 8Time 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...

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