Реферат: Traffic Light Sequences Essay Research Paper MEI
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Traffic Light Sequences Essay, Research Paper
An investigation into automatic Traffic Lights
Maximum distance travelled in order for a vehicle to clear the system 5
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.
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?
4. look into ways where timings from formulae could be modified other than simplest case .
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.
n Drivers have infinite patience and always obey traffic lights perfectly.
n All sets of lights are perfectly co-ordinated, and their pattern constant.
n Vehicle acceleration/deceleration is constant.
n Distance between vehicles is constant.
n Distance travelled by cars between traffic lights is constant.
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.
Distance between traffic signals. 34m
Time for traffic to clear the system (34m) at 5ms-1 6.8sec
Mean inter-vehicle gap (dynamic). 5m
Mean inter-vehicle gap (static). 0.5m
Time delay between cars starting at first set of signals. 1sec.
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
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.
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.
The time from the first car starting until the last car clearing the last set of lights is therefore 20.9 seconds.
This is the time for the last vehicle to clear the first set of lights, however, we have to consider the time delay between cars starting.
Therefore the minimum time the green light must be illuminated is 14.1 seconds.
Time = period of one cycle – period of green light.
Therefore, the system cannot be clear until 6.8 seconds after the green light has been extinguished.
To find the duration of the red light, I shall map out the two sets of lights and fill in the blanks!
Therefore the period of the red light is (6.8+3+14.1+3+6.8)=33.7 seconds
In order to produce an equation for these traffic lights, I shall introduce some unknowns.
Distance between traffic signals. Dsig
Mean inter-vehicle gap (static). Gs
Time delay between cars starting at first set of signals. t
Tgreen = Dmaxv-1 – Dsigv-1 + tn – t
The data I have used was collected in Broughton, Edinburgh. A construction site near the road is blocking one lane of this two-way, single carriageway road. The data was collected by the students in the Mechanics A-level maths set. Stop watches were used to time the traffic signals, and a wheel ruler to measure the dimensions of the road. The weather was clear and windy.
In a real situation it is even more complicated as not only would we have to bear in mind the acceleration and deceleration of the vehicles, but even these would not be constant.
Many other factors also effect the results, such as if the traffic is already moving at the first set of signals, also factors such as weather conditions effect the style of driving.
Time when system is empty 5secx2.5sec
+ Presence of special vehicles, e.g. Articulated lorries, bicycles, horses etc.
This project has given me an interesting insight into the outwardly simple maths of everyday systems. I would consider these models to be anything but perfect as there are far to many random factors involved and this makes it too difficult to model accurately without chaos theory.
Название: Traffic Light Sequences Essay Research Paper MEI
Раздел: Топики по английскому языку
Тип: реферат
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Реферат: Traffic Light Sequences Essay Research Paper MEI
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