TRAFFIC CONTROL

Intro

A lot of people around us use roadways to make sure their essentials are met on daily basis. It is always a happy moment when these sort of things are done within no time. But, there are many others like us who continuously work. Sometimes they may obstruct us in our path which is very common. The most common example are our traffic signals.

These become very annoying when there’s a long que of vehicles and you need to do something urgent. These are basically the effects of lack of proper traffic management and yes this needs to be sorted out. The most annoying thing in the junctions is the RED signal. It is the most hated colour when it comes to traffic signals. We always look out to make sure somehow the red light time is reduced either by choosing another way or getting up early or moving out of our house early. These are ways to avoid this situation, but sometimes it seems as if it is unavoidable where the role of traffic management comes into action.

So here we bring you our project’s main motive that is to reduce the red light time of vehicles in traffic use concepts of mathematics as key.

Problem Statement

Evolve a method to minimize the red light time of all vehicular streams coming to a junction at a traffic signal by implicitly reducing the red light time using suitable mathematical theories.

The inclusion of volume of roads and size of the road in the problem may be neglected. It may be solved by keeping ideal conditions in mind.

Approach to the problem

1.Problem can be solved by a particular method which is applicable to all such sort of problems.

2. We look at the vehicles streams first, then make a compatibility graph out of it.

3. Then we have to divide the graph into cliques which would be calledas phases.

4. Each phase will be having a particular amount of time for green light.

5. The phase consists of certain streams.

6. We set some constraints like total time of 1 cycle and minimum amount of time of green light for each phase according to us.

7. Then giving variable names for phases, we follow the mathematics which gives us the least red light time of all streams.

Files

LATEX FILE

YOUTUBE VIDEO

IMAGES

Conclusion

Finally we are here with all of the explanation and to sum up all of this in three lines. We would say that this problem is a real world problem yet it needs to be developed with some more inevitable constraints to give it full-fledged life. Traffic jams being a real headache for people who use roadways daily is an evident problem to solve and yes we can say that we have provided a less lively but a wonderful solution to this problem.

Distribution of work regarding Project

ROHIT RAO - Research and Solution of Problem

RONIT JAIN - LATEX DOCUMENT

KULDEEP PRAJAPATI - PPT

KARTIK SINGHVI - WEBSITE

Commercialization

If this was to be commercialized someday. We would add the volume of traffic and size of the roads into consideration and yes it will become slightly complex to solve but yes it will be an exact lively solution which we can directly put into a working software which will use this method to solve out any type of constraints in a particular traffic signal. The values which we will get will be definitely tone with the practical requirement but it will need more information and constraints as said above.

Bibliography

DISCRETE MATHEMATICS AND ITS APPLICATIONS, SEVENTH EDITION by Kenneth H. Rosen

Application of graph theory concept for traffic light control at cross-road https://aip.scitation.org/doi/abs/10.1063/1.4994457

Clique (graph theory) https://en.wikipedia.org/wiki/Clique(graphtheory)

Complete graph https://en.wikipedia.org/wiki/Completegraph

Images are taken from different sites using Google

Contact

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Elements

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