mathematics in traffic

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MATHEMATICS IN TRAFFIC

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ABSTRACT
Traffic and transport have always been key industries in the history of
mankind. Progress often came from revolutionary innovations in vehicles
technologies such as domesticated animals, the wheel, sailing ships,
railways, subways, cars, and aircraft, as well as from the build-up of
corresponding infrastructure networks and suitable organizational
structures with which the transportation problems of their time could be
solved.

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INTRODUCTION
Traffic behaves in a complex and nonlinear way, depending on the
interactions of a large number of vehicles. Due to the individual reactions
of human drivers, vehicles do not interact simply following the laws of
mechanics, but rather display cluster formation and shock
wave propagation, both forward and backward, depending on
vehicle density. Some mathematical models of traffic flow use a vertical
queue assumption, in which the vehicles along a congested link do not
spill back along the length of the link.
In a free-flowing network, traffic flow theory refers to the traffic stream
variables of speed, flow, and concentration. These relationships are
mainly concerned with uninterrupted traffic flow, primarily found on
freeways or expressways. Flow conditions are considered "free" when
less than 12 vehicles per mile are on a road. "Stable" is sometimes
described as 12–30 vehicles per mile per lane. As the density reaches the
maximum mass flow rate (or flux) and exceeds the optimum density
(above 30 vehicles per mile), traffic flow becomes unstable, and even a
minor incident can result in persistent stop-and-go driving conditions. A
“breakdown" condition occurs when traffic becomes unstable and
exceeds 67 vehicles per mile."Jam density" refers to extreme traffic

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density when traffic flow stops completely, usually in the range of 185–
250 vehicles per mile per lane.
However, calculations about congested networks are more complex and
rely more on empirical studies and extrapolations from actual road
counts. Because these are often urban or suburban in nature, other factors
(such as road-user safety and environmental considerations) also
influence the optimum conditions.
And also mathematics plays an important role controlling traffic lights by
helping traffic controllers optimizing the signal changes of traffic light
NEED AND SIGNIFICANCE
 The roadways leading into and out of most major cities can become
gridlocked due to an accident, road construction or simply a high
number of cars on the road. Traffic congestion can have a number
of effects on drivers, the environment, health and the economy.
Fortunately, not all of the effects are negative.
 The truth is the traffic congestion is caused by multiple causes and
here they are not in the order of importance. 1-too many cars for
the roadway due to inadequate mass transit options or other
reasons. Road work, Lane closure due to utility work

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OBJECTIVES
The aim of this study is to identify the relationship between mathematics
and traffic, and rove that they are more linked than they seem. The
project is trying to investigate the relation between mathematics and
traffic and these concept in detail .That means this project aim to study
application of mathematics in traffic control.
The basic objective of this study is to
 Make the students understand the application of mathematics in
real life
 Improve the students mathematics knowledge
 to help the students to develop critical thinking skills
DATA ANALYSIS AND STUDY
From this study we can analysis that there is obviously a strong link
between mathematics and traffic. Mathematics has just started to unveil
its enormous potentials in traffic. These are needed in order to solve the
gigantic transportation problems of the present and future. Mathematics
currently contributes most to operational planning problems to allocate
and schedule vehicles and crews. This is important, but has a much
smaller leverage than the big decisions of system design. Also this study
analysis how various mathematical concepts used in the development of
traffic control and how it provide solution to them .The mathematical idea
like graph theory, permutation etc. has role in this field

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Different areas in traffic Mathematical concepts/terms used
Railway
Airway
Motorway
Parameters
Partial Differential equations
Graph Theory
Mathematical optimization
Permutation
MAJOR FINDINGS
 Their is a strong relationship between mathematics and traffic
 Mathematics has vital role in optimizing of traffic lights in road
 Mathematics play great role in railway optimization and air traffic
different types of mathematical concepts have a great application
on traffic field

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SUGGESTION
1. Metro operations are to be hastened
2. There is need to inter-connect inner ring roads, outer ring roads
radially
3. All parking of vehicles along public transport routes be banned,
in order to create more moving space even for private vehicles.
4. With provision of slabs on storm water drains on both sides of
the roads there is no need for pavements at all. All such
pavements be removed making way for parking, pedestrian
movement etc.
5. In each ward 1-2 percentage road space be converted by
marking for pedestrian use only, senior citizens cannot move on
pavements, they are comfortable to move along border of the
roads.

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CONCLUSION
It’s pretty amazing to know how math can be involved with the biggest
Things. Especially, how it’s involved with traffic .What I found very
interesting is that, as sample as the traffic network might seem, the
technology is still old fashioned .It’s interesting how they collect data on
traffic flow and calculate timing for lights. Maths really is everywhere
The above explanations ,examples and proofs show that mathematics has
great application in traffic .Mathematics is an abstract science ,but its
effects can be seen everywhere and in every organism .All the
explanation given above study clearly indicate that traffic field have used
mathematics to solve the problems