# Traffic intersection

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### Introduction

The reason for the participation and taking up this area for this project is to provide a tool for the analysis of traffic intersection performance. The various topics included in the study of fuzzy logic are what does fuzzy basically mean, basic notion and concepts of fuzzy sets, fuzzy set operations such as union, intersection, complementation, triangular norms. A detailed case study is carried out on traffic intersection control and distributed traffic control. Factors considered in the study include detailed look into fuzzy logics and fuzzy sets, traffic intersection control, signal timing algorithm, size and shape of various intersections (junctions), as well as the traffic. With a discrete-event simulation, the effects of changing or varying any of one of these factors can be monitored easily with performance measures such as the average delay time at the intersection, the time taken to change various colors in the traffic signals, average waiting time in a queue.

The span of this project is restricted to four-way signal-controlled intersections, because it is most widely found in all the major countries in the world. The effect of a network of multiple intersections linked together is considered in this study later on. Initially the various intersections studied are assumed to be isolated from any neighboring intersections but in the later studies looks into Distributed Traffic Control. Reliable with this postulate that a car that reaches the front of its lane of traffic and has a green signal is understood to be able to exit the intersection with no problem. Exit traffic from the intersection is not modeled. Various problems in exiting of traffic like accident at the junction, traffic controlling policemen present, traffic conjunction due to festivals or important days of the year, etc, is not taken in consideration. At present the model considers that there is at the most one lane from which the vehicles can turn left and one lane from which the vehicles can turn right for each direction of traffic. Lanes from which vehicles can go straight ahead are assumed to be infinite in length. The numbers of cars that can fit in straight or right turn lanes are not limited by their size i.e. lanes from which cars can turn right are also assumed to be infinite in length. The model can be expanded to include more specialized intersections by common logic, but this is the current state of the simulation program. Also, the simulation code only incorporates constant signal timing plans. However, the code has been written in such a way that an actuated signal timing plan, for any specific intersection can be easily interpreted and implemented. Each year a large amount of money is spent in studying and trying to improve traffic intersections. There are various ways and methods to improve traffic on the roads which indirectly helps in building the country's economy.

Originally, traffic intersection research paid attention on analytically describing vehicles' delay in terms of the intersection characteristics. One of the most prominent early works is Webster. For more recent analytical delay models and queuing theory approaches see Hurdle and Hagen and Courage. A discussion of more complex intersection models can be found in Meneguzzer. For a detailed study of intersection characteristics and performance, the flexibility of computer simulation is preferable to analytical approaches. Many privately and publicly funded simulation models exist for the purpose of studying traffic networks. A few examples are UTCS, TRANSYT, SCOOT, DITCS, RT-TRACS, and RHODES. Most of these programs are intended as a tool to aid in setting traffic signal timing algorithms for a network of intersections. One program developed exclusively for the purpose of evaluating traffic network management systems is MITSIM, described in Yang and Koutsopoulos.

The focus of this work differs from others in that this simulation model offers the user the chance for more detailed intersection analysis. Performance measures of an intersection's performance can be split between individual lanes of traffic, distinct turn patterns, or both. Additionally, the advantages and disadvantages of a number of intersection characteristics can be easily measured, including, size, number, and type of lanes, as well as the signal timing algorithm.

### 2.1. History

Fuzzy sets and fuzzy logic is one of the most up-and-coming areas in the field of modern-day technologies of information and data processing. Fuzzy sets have a rather brief history. This is because it has come into existence only in 1965 by Prof. Lotfi A. Zadeh of University of California at Berkeley [1]. Fuzzy set theory involves capturing, operating and representing with linguistic notion-objects with unclear or vague boundaries. Borel and Lukasiewicz , two brief experts shed light on the essence of the difficulties and problems involving these eventual solutions with vague boundaries.

Modern studies spread across various areas, from pattern recognition, control, and knowledge based systems to computer vision and artificial intelligence. There are a significant number of direct real world implementations ranging from house hold appliances to industrial installations. All of these involve fuzzy logic at some level or the other. It may be at the most primary level or at the most important level of the system but it is used at some point or the other. Fuzzy set theory has innumerous applications in various fields- automata theory, artificial intelligence, control theory, computer science, decision making, medical diagnosis, neural networks, expert systems, robotics, pattern recognition, social sciences are a few of them. Apart from this, it is being applied on a majorly in industries for building machine (engines , cars, ships, turbines, etc.), controls ( Sendai subway in Japan, stc.) and for military purposes.

Fuzzy set theory is a generalizations and also an extension of crisp set theory (CST). Thus, the basic ideas and the theme of CST will be reflected in FST also.

### 2.2 Concept of Fuzzy Set

As mentioned previously fuzzy set is an extension of the crisp set theory. Just as in a crisp set on a universal set U which is defined by its characteristic function from U to {0,1}, on the other hand in a fuzzy set the universal set U is defined by its membership function from U to [0,1]. The main difference in the above two sentences is in the brackets. In the former one the only values that are permissible are 0 and 1 and nothing else, whereas in the latter one all the values between 0 and 1 are allowed. The values can be anything including 0 and 1. Therefore there are infinite number of values that come into the picture. This is one of the major difference between crisp set theory and fuzzy set theory. Due to the easiness of fuzzy sets there has been a fundamental change in the approach of a particular problem. Consider the following example,

What would you do in such a case? This is the beauty of fuzzy logic. This illustration shows us how we can utilize fuzzy logic. Fuzzy logic means that the input that are given to a system are vague or unclear. They need not be precise as in the case of this illustration.

Let us consider another example. If we measure the height of the students in a particular class, the input in this case is the height of the students. Using the classical method we assign a particular benchmark to say whether a student is tall or not. Say we consider height greater than or equal to 180cm as tall then a student who is 179cm tall is also considered short. So when we take it in a fuzzy sense we mark students greater than 180 as tall and lesser than 160 as short. The students whose height lies between this range of 160cm and 180cm are neither tall nor short.

### • Conventional Method ( Crisp )

- Complex system - difficulty in modeling/solving

- Precision is difficult to obtain

- Does not utilize the human reasoning which don't have sharp boundaries.

### • Fuzzy Logic

- Complex system - easy to represent/solve

- Approximate solution : but as good

- Allows inputs with imprecise nature to be specified

- Cost-effective way to model complex systems, giving qualitative description
Here are certain reasons why we prefer Fuzzy Logic over Crisp Logic.

* Fuzzy logic is basically understood with ease.

The mathematical concepts behind fuzzy analysis are very straightforward. Fuzzy logic is a more instinctive advance without the far-reaching difficulty.

* Fuzzy logic is very flexible.

With any known system, it is easier to layer on further functionality devoid of starting again from the entire scratch.

* Fuzzy logic is liberal of data which is imprecise.

Everything is imprecise if you look closely enough, but more than that, most things are imprecise even on careful inspection

* Fuzzy logic can form nonlinear functions of random difficulty.

We can generate a fuzzy system to match any set of input-output data. This procedure is made mainly easy by adaptive techniques like “Adaptive Neuro-Fuzzy Inference Systems”(ANFIS), which is available in Fuzzy Logic Toolbox.

* Fuzzy logic can be build on zenith of the knowledge of experts.

In straight distinction to neural networks, which take training data and produce opaque, dense models, fuzzy logic lets you rely on the knowledge of populace who already know and understand your system.

* Fuzzy logic can be easily blended with usual control techniques.

Fuzzy systems don't essentially replace old conventional control methods. In many cases fuzzy systems add to them and abridge their execution.

* Fuzzy logic is based on ordinary verbal communication.

The basis for fuzzy logic is the foundation for human communication. This examination underpins many of the other statements about fuzzy logic. Because fuzzy logic is built on the structures of qualitative explanation used in day to day language, fuzzy logic is much simpler to use.

The last statement is possibly the most significant one and deserves additional debate. Natural language, which is used by normal people on a daily basis, has been produced by thousands of years of human history to be suitable and efficient. Sentences written in regular language represent a success of efficient communication.

### When Not to Use Fuzzy Logic

Fuzzy logic is not a cure-all. When should you not use fuzzy logic? The safest declaration is the one made in the foreword: fuzzy logic is a suitable method to plot an i/p space to an o/p space. If there is a more convenient method to a given problem we better use that rather than going into for this fuzzy logic aaproach. Fuzzy logic is the codification of universal common intelligence — employ common sense when you put into practice and you will probably make the correct choice. Many controllers, for example, do a great work without the use of fuzzy logic. However, if you take the time to become familiar with fuzzy logic, you'll see it can be a very commanding tool for dealing swiftly and resourcefully with vagueness and nonlinearity.

### 2.4 Common Control Application

One of the most basic and simple way to understand what fuzzy logic means is to use the example of cart-pole problem. This is also called the inverted pendulum problem due to the shape. Sometimes we see how a juggler balances a pole in the palm of his hand. This balancing act involves the movement of the palm in forward and backward direction and even left and right. But here we just consider forward and backward movement. This act of controlling the pole can be converted into a laboratory experiment usually called the cart-pole or inverted pendulum problem. The cart is a wooden block and a pole is attached in the middle of the top surface of the cart. This arrangement in the below:

The main objective of the task is to keep the pole in the vertical position or at least near to it. Now if we consider the conventional method it is really tedious to solve this problems because there are various equations governing this situation:

I (d2 θ/dt2) = VLsin θ - HLcos θ

V - mg = -mL[(d2 θ/dt2)sin θ+(d θ/dt)2cos θ]

These are obviously differential equations and will be simulating our system. This will be really tedious, difficult, error prone, as well as time consuming.

Now looking into fuzzy logic approach.

### The inputs are:

θ : +ve(P) right of the vertical line & -ve (N) left of the vertical line

x=dθ/dt : +ve(P) pole is falling to the right & -ve (N) pole is falling to the left

u: +ve(P) direction is right & -ve (N) direction is to the left.

INPUTS θ: N Z P

x: N Z P

OUTPUT u: NB N Z P PB

Where P: +ve, N: -ve, Z: Zero, NB: -ve Big, PB: +ve Big

Now consider the FUZZY RULE BASE as given below

X

When θ = N and x = N then u = NB

Therefore we don't have a particular fixed value for θ and x to gt the required answer. So the problem now becomes pretty simple. When θ is negative and x is also negative then the u has to be a big negative number.

### 5.1 Basics

MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation.

### Typical uses include the following:

* Math and computation

* Algorithm development

* Data acquisition

* Modeling, simulation, and prototyping

* Data analysis, exploration, and visualization

* Scientific and engineering graphics

* Application development, including building graphical user interfaces.

MATLAB is an interactive system whose basic data element is a matrix. This allows formulating solutions to many technical computing problems, especially those involving matrix representations, in a fraction of the time it would take to write a program in a scalar non-interactive language such as C.

The name MATLAB stands for Matrix Laboratory. MATLAB was written originally to provide easy access to matrix and linear algebra software that previously required writing FORTRAN programs to use. Today, MATLAB incorporates state of the art numerical computation software that is highly optimized for modern processors and memory architectures.

MATLAB has various functions to work with images. One of the most powerful tools in MATLAB is M- Function Programming. It is flexible and allows image manipulations.

### 5.2 Some Function References (Taken From MATLAB 7.7.0)

GUI Tools and Plotting

anfisedit

Open ANFIS Editor GUI

findcluster

Interactive clustering GUI for fuzzy c-means and subclustering

fuzzy

Open basic Fuzzy Inference System editor

mfedit

Membership function editor

plotfis

Plot Fuzzy Inference System

plotmf

Plot all membership functions for given variable

ruleedit

Rule editor and parser

ruleview

Rule viewer and fuzzy inference diagram

surfview

Open Output Surface Viewer

Membership Functions

dsigmf

Built-in membership function composed of difference between two sigmoidal membership functions

gauss2mf

Gaussian combination membership function

gaussmf

Gaussian curve built-in membership function

gbellmf

Generalized bell-shaped built-in membership function

pimf

Π-shaped built-in membership function

psigmf

Built-in membership function composed of product of two sigmoidally shaped membership functions

sigmf

Sigmoidally shaped built-in membership function

smf

S-shaped built-in membership function

trapmf

Trapezoidal-shaped built-in membership function

trimf

Triangular-shaped built-in membership function

zmf

Z-shaped built-in membership function

FIS Data Structure

Add membership function to Fuzzy Inference System

Add rule to Fuzzy Inference System

Add variable to Fuzzy Inference System

defuzz

Defuzzify membership function

evalfis

Perform fuzzy inference calculations

evalmf

Generic membership function evaluation

gensurf

Generate Fuzzy Inference System output surface

getfis

Fuzzy system properties

mf2mf

Translate parameters between membership functions

newfis

Create new Fuzzy Inference System

parsrule

Parse fuzzy rules

Load Fuzzy Inference System from file

rmmf

Remove membership function from Fuzzy Inference System

rmvar

Remove variables from Fuzzy Inference System

setfis

Set fuzzy system properties

showfis

Display annotated Fuzzy Inference System

showrule

Display Fuzzy Inference System rules

writefis

Save Fuzzy Inference System to file

### 3.0 GENERATING MEMBERSHIP FUNCTIONS

The method proposed by Hong, et al. [3] will automatically generate a membership functions. This process partitions a set of information into classes that can be used to obtain membership functions. The process of the algorithm has a number of chief stepladders and consists of clustering the facts and information into classes. The membership functions are then generated from the classes obtained. The algorithm is described for one parameter, and is detailed below.

### Step 1.

Given a information set, there are n exercise samples. The values for the parameter in query,, are sorted into increasing order, denoted as . The values are sorted in order to determine an connection amid neighboring or adjoining values.

### Step 2.

The divergence amid adjoining values in the sorted data is determined. The difference obtained will supply a method to compute the connection between adjoining values. The disparity for a set of training set data is given by:

, for i=(1,2,3,…n-1),

where yi and yi+1 are adjoining values in the data that is sorted.

### Step 3.

Find the similarities among adjacent values. The formula given below determines the similarities flanked by bordering values and maps them into real numbers in the range 0 and 1.

where

diffi is the distinction between bordering information,

ss is the standard deviation of diffi, and

C is the parameter of control.

The control parameter is used to decide the profile of the membership function.

### Step 4.

The statistics is grouped on the basis of their similarities. A threshold value, a, divides adjoining values into classes. The quantity of classes influenzes the number of membership functions. Determining the number of classes can be put together by a rule: If the similarity is superior or larger than the determined threshold value α, then the two adjoining data fit in to the similar class, otherwise the values are separated into dissimilar classes. That is, a fresh class is produced. Expressed as a formula,

where Ci and Ci+1 denote two different classes for the identical input or output constraint.

### Step 5.

The membership function for each and every class is definite. There are many different types of membership functions such as triangular, trapezoidal, and Gaussian, to name a few. These are the most commonly used membership functions. One of the most simplest membership functions is the triangular membership function, and will be used for the remaining equations. The triangular membrship function for class j consists of three different points: the central vertex point, bj, this is the maximum value of the membership function and the two endpoints, aj and cj. The central vertex point is determined for every class and is determined by the below given expression:

where

j represents the jth class,

k represents the ending data index for this class,

i.e., data yi through yk fall into class j, and

si is the similarity between yi and yi+1.

The endpoints of the membership function, aj and cj, are determined by the use of interpolation. The following equations determine the right and left endpoints.

Where aj is the left endpoint and cj is the right endpoint. mj(yi) and mj(yk) is the membership determined by the formula:

(10)where k represents the maximum data index value within the class.

### Types of Membership Functions

The fuzzy logic toolbox includes 11 in-built membership function types. These 11 functions are, in turn, build from a number of essential functions: piecewise linear functions, the Gaussian distribution function, the sigmoid curve, and quadratic and cubic polynomial curves. For comprehensive information on any of the membership functions mentioned, there are several information given in the “Function Reference” of Fuzzy Logic. By principle, all membership functions have the letter mf at the conclusion of their names.

The most basic and simple membership functions are shaped by means of straight lines. Of these, the simplest being the triangular membership function, and it has the function name “TRIMF”. It is nothing more than a compilation of three points forming the shape of a triangle. One point representing the apex or the maximum value of the function and other two points representing the end points. The trapezoidal membership function, “TRAPMF”, has a level top and actually is just a abridged or truncated triangle curve. These straight line membership functions have the benefit of straightforwardness.

The generalized bell membership function is precised by three parameters and has the function name “GBELLMF”. The bell membership function has an extra parameter when compared to the Gaussian membership function, so it can move toward a non-fuzzy set if the liberated parameter is tuned properly. Because of their effortlessness and concise notation, Gaussian and bell membership functions are accepted methods for defining fuzzy sets. Both of these curves have the lead of being smooth and non-zero at all the possible points.

Even though the Gaussian membership functions and bell membership functions accomplish smoothness, they are not capable to identify asymmetric membership functions, which are significant in certain applications. Next we define the sigmoidal membership function, which is either open on the left or right. Asymmetric and closed i.e. not open to the left or right membership functions can be generated using two sigmoidal functions, so in addition to the basic “SIGMF”, we also have the divergence between two sigmoidal functions, “DSIGMF”, as well as the product of two sigmoidal functions “PSIGMF”.

Polynomial based curves report for more than a few of the membership functions in the toolbox. Three related membership functions are the Z, S, and Pi curves. These functions are named on the basis of their shapes. The function “ZMF” is the asymmetrical polynomial curve which is open to the left, “SMF” is the spitting image function that opens to the right hand side, and “PIMF” is zero on both of the extremes with an elevation in the centre.

### SUGENO

The fuzzy inference process discussed so far is Mamdani's fuzzy inference method, the most common line of attack. This division discusses the so called Sugeno, or Takagi Sugeno-Kang, technique of fuzzy inference. Introduced in 1985, it is comparable to the Mamdani manner in many respects. The first two parts of the Sugeno's fuzzy inference process, i.e. fuzzifying the inputs and applying the fuzzy operator, are accurately the same. The main dissimilarity between Mamdani and Sugeno is that the Sugeno yield membership functions are moreover linear or constant.

A most common rule in a Sugeno fuzzy model has the expression:

IfInput1=xandInput2=y,thenOutputisz=ax+by+c

For a zero-order Sugeno model, the output level z is fixed (a=b =0).

The output level zi of each rule is prejudiced by the firing strength wi of the rule. For example, for an AND rule with Input 1 = x and Input 2 = y, the firing strength is

where F1,2 (.) are the membership functions for Inputs 1 and 2.

The concluding output of the system is the biased standard of all rule outputs, calculated as

where N represents the number of rules.

The first shows the fuzzy tipping model developed, which a very common example adapted for use as a Sugeno system. It is frequently the case that singleton output functions are totally enough for the wants of a given problem.

gensurf(a)

The best way to view first-order Sugeno systems is to think of each rule as defining the location of a moving singleton. That is, the singleton output spikes can shift around in a linear manner in the output space, depending on what the input is. This also tends to make the system information very packed together, resourceful and proficient. Higher-order Sugeno fuzzy models are probable, but they bring in notable complication with little obvious advantage. Sugeno fuzzy models whose yield membership functions are greater than first order are not supported by Fuzzy Logic Toolbox software.

Because of the linear reliance of every rule on the input variables, the Sugeno method is perfect for performing as an interpolating supervisor of many linear controllers that are to be applied, respectively, to different operating circumstances of a dynamic nonlinear structure. For example, the functioning of an aircraft may change spectacularly with elevation and Mach number. Linear controllers, though straightforward to compute and well suited to any specified flight condition, must be restructured frequently and easily to keep up with the varying state of the flight vehicle. A Sugeno fuzzy conclusion system is tremendously well suited to the mission of smoothly interpolating the linear gains that would be functional across the input space; it is a expected and efficient gain scheduler. Correspondingly, a Sugeno system is suitable for modeling nonlinear systems by interpolating among numerous linear models.

### Traffic Intersection Control

Most urban traffic network links crisscross recurrently, leading to a variety of conflicts between the flows in the traffic. This function of intersection is often a significant factor in shaping the overall competence and performance of a network, therefore traffic engineers continuously face the problem of controlling and checking flow at intersections to improve the performance.

### 3.1 Three Phases of Traffic Lights

Traffic lights are used to control car flowing through most of the cities intersections. The cycle length of a signal is the time period required for one complete sequence of signals at a given intersection. The signal light is basically divided into three different part:

1) Red Phase

2) Amber Phase

3) Green Phase

The cycle length is normally divided into a number of phases, each phase being a part of the time cycle allocated to one or more traffic and pedestrian movements. The green phase is a particular phase provides a green light ( right of way ) for a given particular direction. Green time represents the time period or the amount of tie for which the green phase is operative. Similarly we have for the other two phases as well.

There are various things that have to be kept in mind while designing these phases for a particular traffic signal. This may differ according to the location, the density of the vehicles, the density of the pedestrians, no of lanes available, reaction time for the vehicle users to react while waiting in the queue, etc. These are some points that have to be kept in mind while designing the time period for the three phases. In order for proper control and free flow of the traffic.

### 3.2 Planning and Strategy

Often there are many plans and strategies that are employed by the traffic engineers in order to keep the traffic flow under check. These consist of changing the green time ( and consequently changing the cycle length ) as a function of the incoming traffic so that the cars share the intersection more effectively and efficiently. But there is a problem that arises; each intersection has its own specific characteristic features ad physical layout, rate at which traffic flows in, turning movements, density of the pedestrians, and so on. There are mathematical models describing the traffic flow though an intersection for a given flow density, but it is really difficult to take into account the fluctuations of the traffic that flows towards a junction from different directions. As the flow of the traffic increases in a particular direction the vehicles are forced to wait in the queue for a longer time and this increases the load on the traffic that is going to arrive at the junction after some time.

Clearly, the state of an intersection may be clearly characterized by the number of vehicles arrivals, length of the queue and the control decision is the green phase or the green time. There are other parameters like the physical layout of the intersection, number of lanes per approach and the dimensions of the lane.

### 3.3 Policies in traffic control systems

There are mainly two policies under which traffic control is classified, these are:

1) Fixed Time Systems

2) On line Systems

### 3.3.1 Fixed Time Systems

In this type of policy or plan the various traffic plans are applied on-line but they are generated off-line.it consists of a control plan which is computed from average measured traffic flows. The controller that is used in this type of policy can store a number of such plans and then they can be implemented during different hours of the day as per the use. This particular policy requires periodic check on the traffic at each and every signal separately. Therefore surveys have to be conducted to keep a record of the average traffic flow at different junctions.

### 3.3.2 On-line Systems

In this policy the various plans are generated on-line and are then implemented directly for the traffic control. For example, during office hours like around 9 a.m. the green phase will be on for a longer period of time when compared to the time its on for at around 12 noon. Also when during late night when the number of pedestrians are very few compared to the number of car, the green phase will be extremely long. In such cases we also use certain type of prompters that are used by the pedestrians and the signal turns red for the vehicles only when the traffic controller is prompted to do so. Otherwise it remains in the green mode.

Both these policies have their own advantages as well as disadvantages but their common aim is to minimize the average vehicle delay intersections cause and decreases the length and waiting time of the vehicles in the queue.

### Fuzzy Traffic Controller

The ground-breaking work in using these kinds of fuzzy set in the field of traffic control, by Pappis and Mamdani (197), considers a solitary junction only of two one-way streets. The outcome found by these by realization of fuzzy logic controller were compared to those obtained using the conservative, effective vehicle actuated controllers. Pappis and Mamdani considered the typical delay of the vehicles as the performance factor or in other words taking the delay of the vehicles as the output found out that the results obtained using fuzzy logic controller are better than those attained using the conventional actuated controllers.

### ­How does a sensor work?

There is something exotic about the traffic lights that "know" you are there -- the instant you come and stop at a signal, they change! How do they detect the presence of your car?

Some lights do not have any kind of detectors. For instance, in a large city, the traffic lights may simply function on timers -- no matter what time of day, there is always going to be traffic. In the suburbs and on country roads, however, detectors are more common. They detect when a car arrives at an intersection of roads, when too many vehicles are stacked up in queue at an intersection. This helps to control the length of the green phase, or when cars have entered a turn lane in order to activate the arrow light.

There are a number of technologies that are used for detecting cars, everything from lasers to rubber hoses which are filled with air. By far the most common technique is the inductive loop. An inductive loop is a simple coil of wire embedded in the surface of the roads. To install these inductive loops, they lay asphalt and then cut a groove in the asphalt with heavy machines. The inductive wire is then placed in the groove and sealed with a rubbery compound. You can often see these big square or rectangular shaped loops cut in the pavement because the compound is obvious.

If we take the inductor i.e. the piece of iron, out of the given circuit, then what we have here is a normal flashlight and a normal bulb which glows as long as the battery is connected to it and the switch is closed. You close the switch and the bulb lights up. With the inductor in the circuit as shown, the behavior is astonishingly different. The light bulb acts as a resistor (the resistance within creates heat to make the filament in the bulb glow). The wire in the coil has much lower resistance because it is just a normal wire wound, so what we expect when we close the switch, bulb glows very dimly. This is because most of the current flows through the low-resistance path present in the loop. What happens instead is that when you close the switch, the bulb burns brightly and then gets dimmer. When you open the switch, the bulb burns very brightly and then dies out quickly.

The reason for this different behavior is due to the presence of the inductor in the circuit. When current first begins to flow in the coil, the coil wants to build up a magnetic field. While the field is building, the coil counters or inhibits the flow of current. Once the field is built, then current can flow normally through the wire. When the switch gets opened, the magnetic field around the coil keeps current flowing in the coil until the field collapses. The presence of this current keeps the bulb lit for short period of time even though the switch is not closed.

The capacity of an inductor is mainly controlled by two important factors:

1) Number of coils.

2) Material that the coils are wrapped around. This is also known as the core of the inductor.

Putting iron in the core of an inductor gives it much more inductance than air or any other non-magnetic core would. Each and every core has a different inductance. The inductance of a magnetic material is more than that of a non-magnetic material. There are also devices that can measure the inductance of a coil. The standard unit of measure is the Henry.

So let us say we take a coil of wire perhaps 4 feet in diameter, containing four or five loops of wire. We cut some grooves in the asphalt and place these coil in the grooves. We attach an inductance meter (an instrument that measures the inductance) to the coil and see what the inductance of the coil is. Now when we park a car over this coil and check the inductance again the inductance shown in the inductance meter will be much higher than shown before in the presence of no car. This increase in the inductance is due to the presence of a magnetic material (steel body of the car) in between the coils. The car parked over the coil is acting like the core of the inductor, and its presence changes the inductance of the coil.

A traffic light sensor uses the loop in that same way. It constantly checks the inductance of the loop in the road, and when the inductance rises, it knows there is a car waiting. This is how a sensor works. There are several other methods to detect the presence of a car which are not discussed in this project.

### Passive control

When the volume of traffic is less, no explicit control is required. Here the road users are required to obeythe basic rules of the road. Passive control like traffic signs, road markings etc. are used to complement the intersection control. Some of the intersection control that are classiffied under passive control are as follows:

1. No control If the traffic coming to an intersection is low, then by applying the basic rules of the road like driver on the left side of the road must yield and that through movements will have priority than turning movements. The driver is expected to obey these basic rules of the road.

2. Traffic signs: With the help of warning signs, guide signs etc. it is able to provide some level of control at an intersection. Give way control, two-way stop control, and all-way stop control are some examples.

The GIVE WAY control requires the driver in the minor road to slow down to a minimum speed and allow the vehicle on the major road to proceed. Two way stop control requires the vehicle drivers on the minor streets should see that the conicts are avoided. Finally an all-way stop control is usually used when it is difficult to diffierentiate between the major and minor roads in an intersection. In such a case, STOP sign is placed on all the approaches to the intersection and the driver on all the approaches are required to stop the vehicle. The vehicle at the right side will get priority over the left approach. The traffic control at 'at-grade' intersection may be uncontrolled in cases of low traffic. Here the road users are required to obey the basic rules of the road. Passive control like traffic signs, road markings etc. are used to complement the intersection control.

3. Traffic signs plus marking: In addition to the traffic signs, road markings also complement the traffic control at intersections. Some of the examples include stop line marking, yield lines, arrow marking etc.

### 39.3.2 Semi control

In semi control or partial control, the drivers are gently guided to avoid conicts. Channelization and traffic rotaries are two examples of this.

Introduction to Transportation Engineering 39.2 Tom V. Mathew and K V Krishna Rao

### 1. Channelization:

The traffic is separated to ow through deffinite paths by raising a portion of the road in the middle usually called as islands distinguished by road markings. The conicts in traffic movements are reduced to a great extent in such a case. In channelized intersections, as the name suggests, the traffic is directed to ow through diffierent channels and this physical separation is made possible with the help of some barriers in the road like traffic islands, road markings etc.

### 2. Traffic rotaries:

It is a form of intersection control in which the traffic is made to ow along one direction around a traffic island. The essential principle of this control is to convert all the severe conicts like through and right turn conicts into milder conicts like merging, weaving and diverging. It is a form of `at-grade' intersection laid out for the movement of traffic such that no through conicts are there. Free-left turn is permitted where as through traffic and right-turn traffic is forced to move around the central island in a clock-wise direction in an orderly manner. Merging, weaving and diverging perations reduces the conicting movements at the rotary.

### 39.3.3 Active control

Active control implies that the road user will be forced to follow the path suggested by the traffic control agencies. He cannot maneuver according to his wish. Traffic signals and grade separated intersections come under this classiffication.

### 1. Traffic signals:

Control using traffic signal is based on time sharing approach. At a given time, with the help of appropriate signals, certain traffic movements are restricted where as certain other movements are permitted to pass through the intersection. Two or more phases may be provided depending upon the traffic conditions of the intersection. When the vehicles traversing the intersection is very large, then the control is done with the help of signals. The phases provided for the signal may be two or more. If more than two phases are provided, then it is called multiphase signal.

The signals can operate in several modes. Most common are ffixed time signals and vehicle actuated signals. In ffixed time signals, the cycle time, phases and interval of each signal is ffixed. Each cycle of the signal will be exactly like another. But they cannot cater to the needs of the uctuating traffic. On the other hand, vehicle actuated signals can respond to dynamic traffic situations. Vehicle detectors will be placed on the streets approaching the intersection and the detector will sense the presence of the vehicle and pass the information to a controller. The controller then sets the cycle time and adjusts the phase lengths according to the prevailing traffic conditions.

The intersections are of two types. They are at-grade intersections and grade-separated intersections. In at-grade intersections, all roadways join or cross at the same vertical level. Grade separated intersections allows the traffic to cross at diffierent vertical levels. Sometimes the topography itself may be helpful in constructing such intersections. Otherwise, the initial construction cost required will be very high. Therefore, they are usually constructed on high speed facilities like expressways, freeways etc. These type of intersection increases the road capacity because vehicles can ow with high speed and accident potential is also reduced due to vertical separation of traffic.

### conclusion

In this mid-semester report the topics that are covered are firstly what exactly is a fuzzy setwhat do you mean by fuzzy, what is the difference between the conventional method and the fuzzy method. It highlights its uses and applications in other fields like automata theory, robotics, neural networks, medical diagnosis and in military uses. The report looks into the problem that most of the over populated cities is currently facing that is of traffic conjunction and how can fuzzy logic be used to solve this problem. It contains an in-depth study of traffic intersection control, fuzzy traffic control and its various components in the form of a block diagram.

In my final report I will do a detailed study on distribution of this traffic and simulation using MATLAB, various graphs by changing different factors that affect traffic control like queue, arraival, extension, etc.

### REFERENCES

1. C. Pappis and Mamdani, “A Fuzzy Logic controller for a Traffic Control System,for Traffic Junction” , IEEE Trans. On systems, Man, and cybernetics, vol. SMC-7. Oct 1977.

2. N. Findler and J. Stapp, “Distributed Approach to Optimized Control of Street Traffic Signals,” Jour. Of transportation Engineering, Vol 118, Jan/Feb 1992.

3. W.Pedrycz and F. Gomide, “An Introduction to Fuzzy Sets Analysis and Design”, Prentice Hall of India Private Ltd.

4. M. Ganesh, “Introduction to Fuzzy Sets and Fuzzy Logic”, Jay Print Pack Private Ltd, New Delhi

5. http://www.mathworks.co.uk/matlabcentral/fileexchange/11078