TRAFFIC DENSITY

CIVIL_ENGINEERING

Traffic density

Traffic density is the number of vehicles occupying a given length of the highway in a traffic lane. 

It is expressed as vehicle/mile or vehicle/kilometer.

For example 4 vehicles are present in 500 feet. So traffic density in one mile will be 42.24 vehicles.

k = 42.24 vehicles per mile.

Density is inversely proportional to the volume of traffic. If density is less, then speed will be more and traffic volume will be more. And if the density is greater, then the speed will be low and traffic volumewill be less.

Whenever, traffic jam problem create at certain point, then by the consideration of the peak hour traffic volume, we may proceed towards widening of road, fly over or under pass.

Headway and Spacing

Consider two successive vehicles in a lane.

Spacing

Spacing is defined as the distance between successive vehicles in a traffic lane as measured from front bumper to front bumper in a traffic stream. 

It is measured in feet. It depends upon the speed.

Headway

It is the corresponding time between two successive vehicles as they pass a given point on the highway.

Clearance and Gap

The clear distance between two successive vehicles in feet is known as clearance. Time between the two successive vehicles in seconds is known as Gap.

LANE OCCUPANCY

CIVIL_ENGINEERING

Lane occupancy

Lane occupancy is the ratio of the sum of the lengths of the vehicles to the length of the road section in which those vehicles are present.

To find lane occupancy, we are concerned with the standard dimensions of the vehicles.

For example 4 vehicles of lengths 18′,20′,22′,24′ are present over a length of the road of 500′.

Lane occupancy = (18+20+22+24)/500 = 0.168

More is the lane occupancy, more will be the trafficdensity.

TRAFFIC CONTROLLING DEVICES

CIVIL_ENGINEERING

Traffic controlling devices

The devices which are used to control and regulate the flow of traffic are called traffic controlling devices.

These are of three types:

1. Pavement markings.
2. Traffic signs.
3. Traffic signals.

Pavement markings

Pavement markings are in the form of bands or strips of paints, which are physically drawn on the pavement.

Purposes

1. Pavement markings are used to mark the center lineof the road in case of 2 lane highway.
2. To make the pavement and shoulder distinct by means of shoulder lines drawn at the pavement edges.
3. To make lane boundaries for multi lane highway.
4. To make cross walks for pedestrians.
5. To make stop lines at the road surface close to signals.
6. Turning movement.
7. These are used in parking places where parking is permitted.
8. These are used in no passing zones. These are the areas where we do not over take i.e, on steep curve, on narrow bridge continuous line is drawn there.

Width of paint line = 4 inches.

Length of paint line = 10 feet dashes separated by 30 feet spaces.

Color

Yellow for distinguish one surface to other, white for controlling.

Cat’s eyes or reflectors

Sometimes we use rays reflectors or cat’s eyes instead of paint lines. These are illuminated by head lights and they are raised less than 1 inches from the surface. It warns the inattentive driver as the driver feels the jerk when passes over it.

Below is the picture of cat’s eyes along with pavement marking on the road.

Cat’s eyes along with pavement markings

TYPES OF TRAFFIC CONTROL DEVICES AND TRAFFIC SIGNS

CIVIL_ENGINEERING

Traffic Signs

Traffic signs are means of warning, regulating and informing the drivers.

Material for traffic signs

Material should be such that

1. Which does not lost its color often.
2. Rust resistant.
3. Usually a sheet metal which is protected by a coating of some rust resisting material is used.
4. Nuts, bolts are all galvanized.

Types of signs

Traffic signs are of three types.

1. Warning signs.
2. Mandatory signs.
3. Informative signs.

Warning signs

Warning signs call the attention of the driver to some approaching hazard. For example;

1. Level crossing.
2. Road functions.
3. Narrow bridges.
4. Sharp curves.
5. Bends.
6. U-turns.

Mandatory signs

These are regulatory signs or prohibitory signs enforced by the law. For example

1. Speed limit.
2. No parking.
3. No blowing horns.

Non observance of these signs constitute as penal offence, crime punishable under law. Such a sign is called mandatory sign.

Informative signs

These are the signs which convey some sort of information to the drivers. For example;

1. Sign showing the location of gasoline pump.
2. Bus stops.
3. Distance of cities.
4. Rest houses.
5. Motels etc.

They are not mandatory signs, and there is no prosecution if we ignore these signs.

Placement of traffic signs on roads

Warning and mandatory signs should be installed 5 feet above the road way and at a distance of 6′-12′ from the edge of the pavement. The distance of sign from hazard for a high speed highway is 1500 feet.

TRACK COMPONENTS AND FUNCTIONS

CAPACITY AND LEVEL OF SERVICES

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Capacity and Level of Service LOS

Lecture notes in Traffic Engineering And Management

Contents

• Introduction
• Concepts
  • Capacity
  • Level of service
  • Type of Facilities
• Illustrations
  • Capacity
  • Level of service
• Conclusion
• References
• Acknowledgments

Introduction

Often it is required to ascertain how much a transport facility can accommodate. Such information is useful in the design of traffic facility. Capacity analysis helps in answering the question. It is a quantitative assessment of the ability of a traffic facility to handle vehicles or people for which it is designed.

A related question is, what is the performance level of the system at various operating conditions. Or in other words, how good is the operation of the traffic facility. Level of Service analysis tries to answer this question which is essentially a qualitative analysis. Capacities and Level of Services are therefore closely related analysis of a traffic facility.

Concepts

Capacity

Capacity of a transport facility is defined as the maximum number of vehicles, passengers, or the like, per unit time which can be accommodated under given conditions with a reasonable expectation of occurrence. The Highway Capacity Manual(2010) defines the capacity as the maximum howdy rate at which persons or vehicles can be reasonably expected to traverse a point or a uniform segment of a lane or roadway during a given time period, under prevailing roadway, traffic and control conditions. Several observations can be made from the above definition. Although capacity is the maximum howdy rate, in many situations the break 15 minute flow rate is expressed as the capacity. The above definition also contains the term “reasonably expected” to account for the variation in traffic and driving habit at various location. However, it can be termed as a probabilistic measure. Further, analytical derivations are possible for getting the maximum flow rate, seldom it is achieved in the field. However, capacity measures are often empirically derived. Capacity is usually defined for a point or a uniform segment where operating conditions do not vary.

The capacity measure depends on these operating conditions. The first is the traffic conditions and the factors that influence the capacity includes vehicle composition, turning, movements, etc. The second factor is the roadway conditions and it includes geometrical characteristics such as lane width, shoulder width, horizontal alignment, vertical alignment. The third factor is the control conditions such as the traffic signal timings, round-about characteristics. It is also to be noted that the above capacity definition holds good for a point or at a section of the road having uniform control conditions. Another aspect of the above capacity definition is the expression that the maximum flow rate which accounts for the worst 15 minutes traffic within the peak hour traffic. Lastly the term reasonable expectancy indicates that the capacity measure is probabilistic and not an analytically derived deterministic value. The capacity measure is probabilistic, for it accounts for the unexplainable variation in traffic and diverse driving characteristics.

Level of service

Level-of-Service(LOS) of a traffic facility is a concept introduced to relate the quality of traffic service to a given flow rate. Level-of-Service is introduced by HCM to denote the level of quality one can derive from a local under different operation characteristics and traffic volume. HCM proposes LOS as a letter that designate a range of operating conditions on a particular type of facility. Six LOS letters are defined by HCM, namely A, B, C, D, E, and F, where A denote the best quality of service and F denote the worst. These definitions are based on Measures of Effectiveness(MoE) of that facility. Typical measure of effectiveness include speed, travel-time, density, delay etc. There will be an associated service volume for each of the LOS levels. A service volume or service flow rate is the maximum number of vehicles, passengers, or the like, which can be accommodated by a given facility or system under given conditions at a given LOS.

Type of Facilities

HCM has developed the capacities standard and LOS measure for various facilities. Each traffic facility has its own unit for the capacity and measure of effectiveness for each item will also vary. The traffic facilities can be divided into three, namely: the uninterrupted facilities, interrupted facilities, and others. Interrupted facilities include freeway (basic freeway, weaving sections, and ramps), multi-lane highways (unidirectional), two-lane highways(bidirectional). Freeways normally have density as the measure of effectiveness, while multi-lane and two-lane highways have delay/speed as the MoE. Interrupted facilities include un-signalized intersection, signalized intersection, and arterials or corridors. They have respectively control delay, total delay and average travel speed as the measure of effectiveness. Other facilities may include pedestrian pathways, bicycle tracks, bus-transit system, rail-transit system and air-transportation system. Each of them have facility specific measure of effectiveness.

Illustrations

For a typical freeway mid block section the capacity and LOS can be defined for an ideal section. An ideal section has uninterrupted flow from both sides and has only passenger cars and the drivers are regular travelers who are familiar with the facility. The lane width is 3.65m wide with proper shoulder and 1.8m lateral clearance is available from the edge of the pavement. The free flow speed of 115kmph is achievable on the multi-lane and 100kmph on the two-lane highway.

Capacity

Such a facility is considered as an ideal facility and for such facilities the following values can be taken as capacity.

1. A capacity of 2000 vehicle per hour per lane for a speed of 115kmph
2. A capacity of 1900 vehicles per hour per lane for a speed of 80kmph
3. A capacity of 2800 vehicle per hour for both direction at 100kmph

Note that the above values are not analytical or experimentally derived, but, statistically derived from the observed field values from large number of such sections. Needly to say that it is possible to have a flow higher than this capacity measure, but not necessary.

Level of service

The above capacity value drop due to various `non-ideal condition’ which includes changes in speed or travel time, traffic interruptions or restriction etc. Accordingly HCM has defined various levels of services for the traffic facility. Assigning quality value is based on several user surveys capturing the perception of drivers on the quality of the traffic under various operating condition. The Fig. 1illustrate the quality of services or Level-of-Services (A to F) and the various operating conditions.

Figure 1: The LOS of a Mid Block Section

The same can be shown in the form of a table .

Table 1: The LOS of a Mid Block Section

LOS	Quality	Speed	V/C	Description
		(kmph)
A	Free-flow	80	0.6	High level of physical
				and psychological comfort
B	Reasonable	70	0.7	Reasonable level of
	free-flow			physical and psychological comfort
C	Near	60	0.8	Local deterioration
	free-flow			possible with blockages
D	Medium	50	0.85	Non-recoverable
	flow			local disruptions
E	At capacity	40	0.9	Minor disturbances
	flow			resulting breakdown
F	Congested	15	1.0	Break down of flow
	flow			capacity drops

Conclusion

In this lecture the concepts of capacity and LOS is presented. Capacity is a quantitative measure, whereas LOS is a qualitative measure. Capacity defined for various traffic facilities considering the traffic, geometric and control condition and obtained from field observation. LOS on the other side is assigning quality levels of traffic based on performance measure like speed, density, etc. Together, the concepts gave planner a valuable tool in designing and evaluating various traffic facilities.

References

1. James H Banks. Introduction to transportation engineering. Tata Mc-Graw Hill, 2004.
2. W R McShane and P R Roger. Traffic Engineering. Prentice Hall Publication, 1990.
3. C. S Papacostas. Fundamentals of Transportation Engineering. Prentice-Hall, New Delhi, 1987.

Acknowledgments

I wish to thank my staff Ms. Reeba in typesetting the materials for this lecture. I also wish to thank several of my students and staff of NPTEL for their contribution in this lecture.

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TYPES OF INTERSECTION

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Grade Separated Intersection

Lecture notes in Traffic Engineering And Management

Contents

• Overview
• Classification of Intersection
  • Grade Separated Intersection
  • Classification of Grade Separated Intersection
  • Design Components
• Grade separated intersections
• Summary
• References
• Acknowledgments

Overview

An intersection is the area shared by the joining or crossing of two or more roads. Since the main function of an intersection is to enable the road user to make a route choice, it is a point of decision. Hence the problems that are encountered by the motorist while passing through an intersection must be recognized and the design should be in such a way that the driving task is as simple as possible.

Intersection is also a point of large number of major conflicts, besides a point of decision. These conflicts may be due to the crossing maneuvers of vehicles moving in different directions. Good intersection design results from a minimization of the magnitude and characteristics of the conflicts and a simplification of driver route selection process.

Classification of Intersection

Intersections are classified depending upon the treatment of crossing conflicts as follows (i) At Grade Intersection and (ii) Grade Separated Intersection.

Grade Separated Intersection

It is a bridge that eliminates crossing conflicts at intersections by vertical separation of roadways in space. Grade separated intersection are otherwise known as Interchanges. Grade separated intersections cause less hazard and delay than grade intersections. Route transfer at grade separations is accommodated by interchange facilities consisting of ramps. Interchange ramps are classified as Direct, Semi-Direct and Indirect. Interchanges are described by the patterns of the various turning roadways or ramps. The interchange configurations are designed in such a way to accommodate economically the traffic requirements of flow, operation on the crossing facilities, physical requirements of the topography, adjoining land use, type of controls, right-of-way and direction of movements.

The ultimate objective of grade separated intersections is to eliminate all grade crossing conflicts and to accommodate other intersecting maneuvers by merging, diverging and weaving at low relative speed. The relative speed of the conflicting vehicle streams is an important factor affecting the significance of a conflict. The benefit of providing for low relative speed is twofold. First, events unfold more slowly allowing more judgement time and second, in case of an impact the total relative energy to be absorbed are less and hence, the damage is less. In addition, when relative speed is low, the average motorist will accept a smaller time gap space between successive vehicles to complete his move. This condition increases roadway capacity.

Classification of Grade Separated Intersection

One of the distinctions made in type of interchange is between the directional and the non directional interchange. Directional interchanges are those having ramps that tend to follow the natural direction of movement. Non directional interchanges require a change in the natural path of traffic flow. A comprehensive classification plan for grade separated intersection design which includes all possible geometric patterns has not yet been developed. The design and operational characteristics of each of the major interchange types are mentioned as follows and are discussed in the following sections.

1. Underpass
2. Overpass
3. Trumpet Interchange
4. Diamond Interchange
5. Cloverleaf Interchange
6. Partial Cloverleaf Interchange
7. Directional Interchange
8. Bridged Rotary

Underpass

An underpass or a tunnel is an underground passageway, completely enclosed except for openings for ingress and egress, commonly at each end. A tunnel may be for foot or vehicular road traffic, for rail traffic. If an underpass is constructed for pedestrians and/or cyclists beneath a road or railway, allowing them to reach the other side in safety, then such a construction is termed as a Subway. These are constructed when it is necessary for pedestrians to cross a railroad or a limited-access highway. Subways may also be constructed for the benefit of wildlife

Overpass

An overpass also known as a flyover, is a bridge, road, railway or similar structure that crosses over another road or railway. A pedestrian overpass allows pedestrians safe crossing over busy roads without impacting traffic. And Railway overpasses are used to replace at-grade crossing as a safer alternative. Overpasses allows for unobstructed rail traffic flow from mixing with vehicular and pedestrian traffic. Stack interchanges are made up of many overpasses.

Trumpet Interchange

Trumpet interchanges have been used where one highway terminates at another highway. These involve at least one loop ramp connecting traffic either entering or leaving the terminating expressway with the far lanes of the continuous highway. These interchanges are useful for highways as well as toll roads, as they concentrate all entering and exiting traffic into a single stretch of roadway, where toll booths can be installed. Trumpets are suitable at the locations where the side road exists on only one side of the freeway, and traffic is relatively low. Each entrance and exit consists of acceleration or deceleration lanes at each end. It requires only one bridge and is the most traditional way of grade separating a three way junction. The principal advantages are low construction cost and are useful for highways as well as toll roads. But the limitations in employing trumpet interchanges are it leaves a redundant patch of the land within the loop, Disorienting to navigate for those driving in the direction that uses the loop. Moreover scaling down the interchange often results in a more dangerous suffers congestion from articulated lorries that have tipped over.

Diamond Interchange

The diamond Interchange is the simplest form of grade separated intersection between two roadways. The conflicts between through and crossing traffic are eliminated by a bridge structure. This particular intersection has four one way ramps which are essentially parallel to the major artery. The left turn crossing movement conflicts are considerably reduced by eliminating the conflict with the traffic in opposite direction. All the remaining left turn conflicts, merging and diverging maneuver conflicts take place at the terminal point of each ramp. Limitation in application of this design depends on the operations of these terminals. So, it is suitable for locations where the volume of left turn traffic is relatively low.

The diamond interchange requires a minimum amount of land and is economical to construct. Also,a diamond interchange generally requires less out-of-the-way travel and vehicle operating costs are less than those on most other types of interchanges. The single point of exit from the major roadway eases the problem of signing. This type of interchange requires the least of right-of-way. With these advantages, the diamonds appear to be the ideal solution to an intersection problem. But there might be chances of occurrence of conflicts at the locations where ramps meet the grade separated cross street are to be considered foe high ramp volumes. Improper design of signal timings at cross streets may result in the inadequacy of capacity for certain flows.

Cloverleaf Interchange

The full clover interchange eliminates all crossing movement conflicts by the use of weaving sections. This weaving section is a critical element of cloverleaf design. It replaces a crossing conflict with a merging, followed some distance farther by a diverging conflict. There are two points of entry and exit on each through roadway. The first exit is provided before the cross road structure allows right turn movements. The second exit, immediately after the cross road structure, allows for left turn movements. A weaving section is created between the exit and entry points near the structure. Sufficient length and capacity is to be provided to allow for a smooth merging and diverging operation.

Cloverleaf design requires only one bridge. In this respect, it is the cheapest form providing for elimination of all crossing maneuvers at grade. Although full cloverleaf interchanges eliminate the undesirable crossing movements of diamond interchanges, they have the disadvantages of greater travel distances, higher operating costs, difficult merging sections, circuity of travel, large areas for loops, sight distances to exits at the other side of the bridge, confusion caused by turning right to go left and large rights-of-way occasioned by the radius requirements necessary for satisfactory speeds on the ramps.

A variation of the cloverleaf configuration is the cloverleaf with collector-distributor roads. With the collector-distributor roadway, main roadway operations are much the same as in diamond interchange. For each direction of travel, there is a single point for exits and a single point for entrances. Speed change, detailed exit directional signing and the storage and weaving problems associated with a cloverleaf are transferred to the collector-distributor road, which can be designed to accommodate greater relative speed differences or encourage smaller ones. Although this configuration improves the operational characteristics of a cloverleaf interchange, the disadvantages of greater travel distances and the requirement of extra right-of-way are still present. The use of a cloverleaf with collector-distributor roads is appropriate at junctions between a freeway and an expressway where a diamond interchange would not adequately serve traffic demand.

Partial Cloverleaf Interchange

This is another variation of the cloverleaf configuration. Partial clover leaf or parclo is a modification that combines some elements of a diamond interchange with one or more loops of a cloverleaf to eliminate only the more critical turning conflicts. This is the most popular freeway -to- arterial interchange. Parclo is usually employed when crossing roads on the secondary road will not produce objectionable amounts of hazard and delay. It provides more acceleration and deceleration space on the freeway.

Directional Interchange

A Directional interchange provides direct paths for left turns. These interchanges contain ramps for one or more direct or semi direct left turning movements. Interchanges of two freeways or interchanges with one or more very heavy turning movements usually warrant direct ramps, which have higher speeds of operation and higher capacities, compared to loop ramps. Some designers do not favor entrance of merging traffic in the left lane, which is a characteristic of most direct-connection bridges. The principal limitations of this type of interchange is higher cost of construction and requirement relatively large amount of land when compared to the diamond interchanges and in some cases than cloverleaf interchange. Various combinations of directional, semi directional and loop ramps may be appropriate for certain conditions. They are the basic patterns that use the least space, have the fewest or least complex structures, minimize internal weaving and appropriate for the common terrain and traffic conditions.

Design Components

Acceleration Lane

An acceleration lane is defined as extra pavement, of constant or variable width, placed parallel or nearly so, to a merging maneuver area to encourage merging at low relative speed. The major difference in opinion concerning acceleration design stems from lack of information on driver performance. Field observations have indicated that drivers desire to follow the direct path even though extra width or tapered section is provided. The length of acceleration lanes are determined by two factors: (1) Time required for drivers to accelerate to the speed of the preferential flow from the speed of entry into the acceleration lane and (2) Maneuvering time required as a supplement to the sight distance which is provided in advance of the acceleration lane. Taper distances are based upon a lateral transition time of about 1/3 sec/ft of displacement.

Figure 1: Different forms of Acceleration lanes Figure 2: details of length of acceleration lane

Deceleration Lanes

Deceleration lanes are defined as extra pavement of constant or variable width, placed parallel or nearly so, to a diverging maneuver area to encourage diverging at low relative speed. The lengths of deceleration lanes are based on the difference in the speed of traffic of the combined flow (in advance of the collision area) and the speed at which drivers negotiate the critical diverging channel curve, as well as the deceleration practices of drivers. These deceleration lane lengths are based on the assumed performance of passenger vehicles only. Extra allowance must be made for grades and for trucks with different deceleration characteristics. In the figure below, Form A design is more economical when large speed differentials are to be overcome. Form B could be advantageous by contrasting pavement colors and Form C design is more convenient for drivers when small speed differentials are to be eliminated.

Figure 3: Different forms of Deceleration lanes Figure 4: details of length of deceleration lane

Grade separated intersections

As we discussed earlier, grade-separated intersections are provided to separate the traffic in the vertical grade. But the traffic need not be those pertaining to road only. When a railway line crosses a road, then also grade separators are used. Different types of grade-separators are flyovers and interchange. Flyovers itself are subdivided into overpass and underpass. When two roads cross at a point, if the road having major traffic is elevated to a higher grade for further movement of traffic, then such structures are called overpass. Otherwise, if the major road is depressed to a lower level to cross another by means of an under bridge or tunnel, it is called under-pass.

Interchange is a system where traffic between two or more roadways flows at different levels in the grade separated junctions. Common types of interchange include trumpet interchange, diamond interchange , and cloverleaf interchange.

1. Trumpet interchange: Trumpet interchange is a popular form of three leg interchange. If one of the legs of the interchange meets a highway at some angle but does not cross it, then the interchange is called trumpet interchange. A typical layout of trumpet interchange is shown in figure 5.

   Figure 5: Trumpet interchange

2. Diamond interchange: Diamond interchange is a popular form of four-leg interchange found in the urban locations where major and minor roads crosses. The important feature of this interchange is that it can be designed even if the major road is relatively narrow. A typical layout of diamond interchange is shown in figure 6.

   Figure 6: Diamond interchange

3. Clover leaf interchange: It is also a four leg interchange and is used when two highways of high volume and speed intersect each other with considerable turning movements. The main advantage of cloverleaf intersection is that it provides complete separation of traffic. In addition, high speed at intersections can be achieved. However, the disadvantage is that large area of land is required. Therefore, cloverleaf interchanges are provided mainly in rural areas. A typical layout of this type of interchange is shown in figure 7.

   Figure 7: Cloverleaf interchange

Summary

Traffic intersections are problem spots on any highway, which contribute to a large share of accidents. For safe operation, these locations should be kept under some level of control depending upon the traffic quantity and behavior. Based on this, intersections and interchanges are constructed, the different types of which were discussed in the chapter.

References

1. A policy on geometric design of rural highways, 2019.
2. Everett C Carter and Wolfgang S Homburger. Introduction to Transportation Engineering. Reston Publishers, Virginia, 2019.
3. L. R Kadiyali. Traffic Engineering and Transportation Planning. Khanna Publishers, New Delhi, 1987.
4. Theodore M Matson, Wilbure S smith, and Fredric W Hurd. Traffic engineering, 1955.

Acknowledgments

I wish to thank several of my students and staff of NPTEL for their contribution in this lecture.

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CHANNELIZATION

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Lecture notes in Traffic Engineering And Management

Contents

• Introduction
• Definitions and Important Terms
• Objectives
• Design Principles
• Channelizing devices
• Traffic Islands
  • Classification of Islands
  • Design Considerations for Traffic Islands
  • Guidelines for selection of island type
  • Guidelines for design of Traffic Islands
  • Guidelines for providing offset to the traffic islands from the road edge
• Guidelines for design of Median islands
  • Auxiliary Lanes
  • Shape of Median Ends
  • Design of Median Openings
• Developing a Channelization Plan
• Typical Channelization Examples
• Turning Vehicle Templates
• Summary
• References
• Acknowledgments

Introduction

One of the most effective and efficient methods of controlling the traffic on a highway is the adoption of high intersection geometric design standards. Channelization is an integral part of at grade intersections and is used to separate turning movements from through movements where this is considered advisable and hence helps reduce the intensity and frequency of loss of life and property due to accidents to a large extent. Proper Channelization increases capacity, improves safety, provides maximum convenience, and instils driver confidence. Improper Channelization has the opposite effect and may be worse than none at all. Over Channelization should be avoided because it could create confusion and worsen operations.

Definitions and Important Terms

1. Channelization – It is the separation or regulation of conflicting traffic movements into definite paths of travel by traffic islands or pavement marking to facilitate the safe and orderly movements of both vehicles and pedestrians.
2. Conflict – It is defined as the demand for the same highway space by two or more users of the highway. Conflicts are classified into mainly three types:
   1. Crossing conflicts
   2. Diverging conflicts
   3. Merging conflicts
3. Angle of Intersection – The angle of intersection is that formed by the centerlines of the intersecting streets. Where the angle of intersection departs significantly (more than approximately ) from right angles, the intersection is referred to as a skewed intersection. Fig. 1shows the angle made between the center lines of the major and minor legs.

   Figure 1: Angle of Intersection

4. Refuge Areas – The area which is used to give refuge to the pedestrians crossing a street (the open area between two medians) is known as a refuge area.

Objectives

The use of Channelization is often creative and innovative, providing for vehicle path separation and distinct and thus in general making traffic flow safer, smoother, simpler and efficient. The main objectives of Channelization can be summarized as follows:

1. Separation of maneuver areas: The drivers should be presented with only one decision at a time to reduce confusion and the influence of operations caused due to the overlapping of maneuver areas.
2. Reduce excessively large paved areas: The spread of the paved area can be considerably reduced by the construction of raised islands and medians where these are considered safe and necessary.
3. Control of maneuver angle:The intensity of accidents can be reduced to a large extent by providing small angles for merging, diverging and weaving (at low relative speeds) and approximately right angles for crossing (at high relative speeds). The maneuver angle can be easily controlled by constructing islands of appropriate shapes and sizes.
4. Favor predominant turning movements:Channelization is also directed for giving preference to turning movements at an intersection where the proportion of such traffic is high.
5. Control of speed: Channelization is also used for supporting stop or speed regulations by removing differentials in speed for merging, diverging, weaving and crossing by using the bending and funneling techniques.
6. Protection and storage of turning and crossing vehicles: To shadow slow or stopped vehicles from other traffic flows.
7. Blockage of prohibited movements: Proper Channelization also helps maintain traffic regulations by making prohibited movements impossible or inconvenient.
8. Provide space for traffic control devices:To provide space for traffic control devices when the ideal location for the same is within the intersection area.
9. Segregation of non-homogeneous flows:Channelization provides separate channels for turning and through, fast and slow, and opposite direction traffic.
10. Protection of pedestrians and reduction of crossing distances between refuses: Non-traversable and wide medians provide a refuge for pedestrians crossing a street.

Consider for example the T-intersection shown in Figs. 2, 3, and  4. In Fig. 2, the intersection has no special Channelization for helping drivers in avoiding conflicts between movements. In Fig. 3, a passing lane for through vehicles in the eastbound direction and a westbound right-turn lane has been added, which helps in separating the turning traffic from the through ones. In Fig. 4, the use of lanes is further clarified due to the addition of channelizing islands.

Figure 2: Illustration of T-intersection Channelization, (a)Intersection with no Channelization

Figure 3: Illustration of T-intersection Channelization, (b)Intersection with right-turn and passing lane

Figure 4: Illustration of T-intersection Channelization, (c)Fully channelized intersection

Design Principles

Design of a channelized intersection usually involves the following significant controls: the type of design vehicle, the cross sections on the crossroads, the projected traffic volumes in relation to capacity, the number of pedestrians, the speed of vehicles, and the type and location of traffic control devices. Furthermore, the physical controls such as right-of-way and terrain have an effect on the extent of Channelization that is economically feasible. The degree to which each of these principles applies will depend upon the features mentioned above. While a principle may be modified in its application to a particular site, disregard of these may result in a hazardous design. The principles may be summarized as follows:

1. Reduction of the Area of Conflict: The impact area is decreased when Channelization is provided, and hence the probability of conflicts is also reduced. The figure below further clarifies the statement. Fig. 5 shows the conflict area in a Y-intersection without Channelization and Fig. 6 shows the reduced conflict area in the same intersection after providing medians.

   Figure 5: Conflict area in all paved intersection

   Figure 6: Conflict area in a channelized intersection

2. Merging traffic streams at small angles:Merging at small angles permits the flow of traffic streams with minimum speed differentials. Hence, the gap acceptance time is also small in such cases. The merging of roadways should be done as shown below in Fig. 7.

   Figure 7: Merging of traffic streams

3. Reduction of the speed of incoming traffic by bending its path: The speed of vehicles entering into the intersection can be reduced by bending the path to the intersection approach. However as far as possible the path of the major traffic stream should not be bent. The above technique is shown below in Fig. 8.

   Figure 8: Bending path of incoming minor street

4. Reduction of speed of traffic by funneling:The funneling technique can also be used for reducing the speeds of the incoming vehicles. Due to the decrease in the width of the lane at the approach, the drivers tend to reduce the speed of their vehicles near the intersection. Fig. 9 shows the funneling technique used for reduction of speed.

   Figure 9: Reduction of speed by funneling

5. Protection for turning vehicles/crossing conflicting traffic streams: Provision of a refuge area between the two opposing streams allows the driver of a crossing vehicle to select a safe gap in one stream at a time and also provides a safer crossing maneuver. Fig. 10further clarifies the above statement.

   Figure 10: Refuge area for protecting crossing or turning traffic

6. Discourage prohibited turns by island placement and shape: Undesirable and prohibited turns can be discouraged by the proper selection of shape and location of the islands. Fig. 11 shows how prohibited turns can be discouraged by proper shaping and placement of islands.

   Figure 11: Properly placed islands discourage prohibited movements

7. Providing locations of traffic control devices: Channelization may provide locations for the installation of essential traffic control devices, such as stop and directional signs, signals etc. Fig. 12 shows how channelizing devices can also be used for locating traffic control devices.

   Figure 12: Location of signal posts on medians at intersections

Channelizing devices

A channelizing device can be defined as any structure which helps in providing Channelization. These can be wide raised medians, non-traversable road islands, traversable raised curbs or even flush channelizing devices. A brief description of the various devices which are used for the purpose of Channelization are given in the following sections.

1. Wide Raised Medians In this form of channelizing device, a raised wide separator is constructed between the two opposing lanes and the space on the separator (median) is used either for planting some trees and/or for providing space for traffic signs etc. Fig. 13 shows a typical wide raised median on a freeway. A median varying between 1.2 m and 30 m in width may be employed. The higher values of width are adopted on freeways, where sufficient space is available for the construction of these. In addition, a well-landscaped wide median will also provide aesthetic benefits to the surrounding neighborhood. A wide median, if attractively landscaped, is often the most aesthetically pleasing separation method.

   Figure 13: Wide raised median

2. Non- traversable Raised Islands In this type of device, a narrower and a higher median than the traversable island is constructed between the opposing lanes. This class of device has the advantage of a narrower median, but its use should be restricted to approach roadways with vehicle speeds of 60 kmph or below. These are generally 15 to 20 cm high and about 60 cm in width. Due to the height, most of the vehicles are not able to cross the median, and hence the name. Fig. 14shows a non-traversable raised island constructed on a roadway. These devices are substantial enough that each installation should be carefully designed, as an inappropriately placed median can constitute a hazard if struck by an errant vehicle and hence the severity and crash risk is highly increased on the roadways having non-traversable raised islands.

   Figure 14: Non-traversable Raised Island (source: [13])

3. Traversable Raised Curb Systems In this device, a narrow and mountable type of raised curb is constructed to separate the traffic moving in the opposing lanes. This class of channelizing device is the narrowest, and therefore the easiest to fit in a wide range of roadway cross-section widths. The curb is up to 10 cm in height and up to about 30 cm in width. Curbs are formed with a rounded shape that will create minimal vehicle deflection upon impact. Generally, it is used with reboundable, reflectorized vertical panels to provide a visual deterrent to the drivers to cross over to opposite traffic lane. The main advantage of this type of device is that it can be installed on existing roadway centerlines, without the need for widening the roadway approaches to the crossing. Figs. 15 and 16 shows traversable raised curbs with and without vertical panels.

   Figure 15: Traversable Raised Curb System (without vertical panels)

   Figure 16: Traversable Raised Curb System (with vertical panels)

4. Flush Channelization In this type of Channelization, a variety of treatments, including raising them above the pavement just slightly (2 to 5 cm); the application of pavement markings and other types of contrasting surfaces etc are possible. These may also be unpaved where they are formed by the pavement edges of existing roadways. In areas where snow plowing may be necessary, flush islands are the preferred design. Fig. 17 below shows how flush islands can also be used for achieving channelizing objectives. The area seen flushed with the road surface in Fig. 17 is the flush island.

   Figure 17: Flush island providing Channelization objectives

Traffic Islands

A principle concern in Channelization is the design of the islands. An island is a defined area between traffic lanes for control of vehicle movements. Within an intersection area, a median or an outer separation is considered to be an island. It may range from an area delineated by barrier curbs to a pavement area marked by paint.

Classification of Islands

Traffic islands usually serve more than one function, but may be generally classified in three separate types:

1. Channelizing Islands – These are designed to control and direct traffic movement, usually turning. Channelizing islands are are shown in Fig. 18.

   Figure 18: Channelizing Islands

2. Divisional Islands – These are designed to divide opposing or same direction traffic streams, usually through movements. Fig. 19 shows the placing of divisional islands in a roadway.

   Figure 19: Divisional Islands

3. Refuge islands – Pedestrian islands are provided to serve as safety zones for the aid and protection of persons on foot. If a divisional island is located in an urban area where pedestrians are present, portions of each island can be considered a refuge island. Refuge islands are shown below I Fig. 20.

   Figure 20: Refuge Islands

   The design aspects of the traffic islands are dealt in detail in the following sections.

Design Considerations for Traffic Islands

The necessity for an island should be determined only by careful study, since it is placed in an area that would otherwise be available for vehicular traffic. The island design should be carefully planned so that the shape of the island will conform to natural vehicular paths and so that a raised island will not constitute a hazard in the roadway. A judiciously placed island at an intersection on a wide street may eliminate the need for traffic signal control by channelizing traffic into orderly movements. The total design of traffic islands can be studied in three steps:

1. Selection of appropriate island type (barrier, mountable, painted or flush): The site and traffic conditions in each intersection are different and hence the island type suitable for each requires separate attention. The traffic island selected may vary from barrier type islands to flush islands marked on the roadway surface.
2. Determination of shape and size of islands: The shape of the island and its size in an intersection depends on the geometry and space availability at the same. A proper shape and size of the island (in case of raised islands) must be selected so that it is able to both channelized the traffic and not pose any type of hazard.
3. Location relative to adjacent traffic lanes:The islands must be offset from the roadway by some distance to remove the risk of a vehicle dashing against the same. The width of offset is maximum at the entry of the island and decreases gradually as one moves towards the end of it.

Guidelines for selection of island type

As mentioned earlier, each intersection has a unique geometry and flow values, and hence needs special attention as far as the use of Channelization devices are concerned. The main factors affecting the selection of the island type are:

1. Traffic characteristics at the intersection
2. Cost considerations, and
3. Maintenance needs

The raised islands and flush Channelization are dealt with in details in the following sections.

Flush Channelization

Flush Channelization is usually appropriate in the following conditions:

1. On high speed rural highways to separate turning lanes.
2. In constrained locations, i.e. the locations where vehicle path definition is desired but space for raised islands not available.
3. For separating opposing traffic streams of low speed streets.
4. In areas where frequent removal of snowfall is required, i.e. in places of high snow fall.
5. It can also be used as a temporary Channelization either during construction or to test traffic operations prior to the actual installation of raised islands.

However, the main demerits of this type of Channelization are :

1. It is not effective in prohibiting or preventing traffic movements.
2. It is also not appropriate for islands intended to serve as pedestrian refuge.

Raised Islands

The locations where the construction of raised islands assumes importance are:

1. The primary function of the channelizing device is shielding pedestrians or to provide refuge to pedestrians crossing a street.
2. Also, the primary/secondary function is locating traffic signals or other fixed objects.
3. Intention is to prohibit or prevent certain traffic movements.
4. To separate high volume opposing traffic flows.
5. The raised islands are also particularly important at intersections with unusual geometry i.e. skewed intersections.

A comparison between the usefulness and the operating conditions of the two types of Channelization is presented in Table. 1.

Table 1: Flush Channelization vs Raised Channelization

FLUSH CHANNELIZATION	OPERATING CONDITIONS
1. For Right turns	High Speeds
2. To provide temporary or trail Channelization	Rural highway
3. To shadow left turns	Minor urban intersections
RAISED CHANNELIZATION	OPERATING CONDITIONS
1. Post signs or signals	Urban streets
2. Provide pedestrian refuse	Low speeds
3. Prevent wrong way movements	High volumes

Guidelines for design of Traffic Islands

The main design principles followed for the design of the shape and size and shape of the traffic island are as follows:

1. Shape and size: Islands are generally either narrow and elongated or triangular in shape, are normally situated in areas of the roadway outside the planned vehicle paths, and are shaped and dimensioned as component parts of the street or intersection layout. The actual size differs as governed by site conditions, but the following minimum size requirements should be met to insure that the island will be large enough to command attention.
2. Traffic lanes or turning roadways should appear natural and convenient to their intended users.
3. Number of islands should be held to a practical minimum to avoid confusion.
4. The islands should be large enough to be effective. Small islands do not serve as channelizing devices and pose maintenance problems.
5. These should not be introduced at locations with restricted sight distance or middle of sharp horizontal curves due to sight distance considerations.

Table. 2 gives the recommended minimum and desired area values of the traffic islands in typical urban and rural intersections.

Table 2: Recommended Island Sizes

Location of Intersection	Size(Sq.meters)
	Minimum	Desired
Urban	4.65	7
Rural and High Speed urban/Suburban	7	9.3

Guidelines for providing offset to the traffic islands from the road edge

The orientation of islands near intersections is dictated by the alignment of the intersecting roadways and their associated travel paths. Proper island design must minimize the potential for vehicle impacts and reduce their severity. This is most often accomplished by offsetting the approach ends of islands from the edge of travel lane them, tapering them inward. Another technique that is the use of rounded approach noses that may also be sloped downward on their approach ends. The general design dimensions of corner islands for roadways in shown in Fig. 21.

Figure 21: Recommended Offset Dimensions for location of Traffic Islands

Another design consideration for islands is their surface finishing. Islands may be paved or landscaped. Though paved islands are easier to maintain, yet they are typically not as aesthetically pleasing. The use of colors that have contrast with the pavement surface is desirable because they allow the island to be more clearly seen by drivers. Normally concrete islands are paired with asphalt roadways and vice versa. Brick paver are also used in areas where aesthetics are important. Other concerns include the need to provide adequate slope to the surface of the island to facilitate drainage and to keep the island free of sight obstructions and collision. Thus, all landscaping features should be kept below the clear vision envelop and should not incorporate other fixed hazards.

Curve/taper combinations for turning roadways and islands

The combination of a simple radius flanked by tapers can often fit the pavement edge more closely to the design motor vehicle than a simple radius (with no tapers). Figs. 22, 23and  24 shows the various types of curves that can be used for a roadway. The closer fit can be important for large design motor vehicles where effective pavement width is small (due either to narrow pavement or need to avoid any encroachment), or where turning speeds greater than the design speed are desired.

Figure 22: Various types of curves used for a turning roadway , (a)Simple Radius

Figure 23: Various types of curves used for a turning roadway, (b)Radius and Taper

Figure 24: Various types of curves used for a turning roadway, (c)Turning Roadway

Table. 3 and Table. 4 summarizes design elements for curve/taper combinations that permit various design motor vehicles to turn, without any encroachment, from a single approach lane into a single departure lane (Note: W should be determined using the turning path of the design vehicle)

Table 3: Curve and Taper Corner Design Elements

Angle of Turn	Design Vehicle	Radius	Offset	Taper Length
(Degrees)		(meters)	(OS meters)	(T1 meters)
	Passenger Car	7.5	0.6	6
75	Single Unit Truck	13.5	0.6	6
	Single Trailer Unit	19.5	0.9	13.5
	Passenger Car	6	0.75	7.5
90	Single Unit Truck	12	0.6	6
	Single Trailer Unit	18	1.2	18
	Passenger Car	6	0.6	–
120	Single Unit Truck	9	0.9	–
	Single Trailer Unit	13.5	1.2	18

Table 4: Design elements for Turning Roadways

Angle of Turn	Design Vehicle	Radius(meter)	Offset
(Degrees)		R1-R2-R1	(OS meter)
	Passenger Car (P)	30-22.5-30	0.6
75	Single Unit Truck (SU)	36-13.5-36	0.6
	Semi-Trailer Unit (WB-50)	45-15-45	2
	Passenger Car (P)	30-6-30	0.8
90	Single Unit Truck (SU)	36-12-36	0.6
	Semi-Trailer Unit (WB-50)	54-18-54	2
	Passenger Car (P)	30-6-30	0.6
120	Single Unit Truck (SU)	30-9-30	0.9
	Semi-Trailer Unit (WB-50)	54-12-54	2.6

The width of the roadway can be found out from Table. 5 given below.

Table 5: Width of roadway required for negotiating the turn for different classes of vehicles

Radius on	One-Lane One Way			One-Lane One Way			Two way operation
inner edge	Operation (No			Operation (Having			Either One way or Two
of	provision of passing a			provision of passing a			way (Same Type of vehicle
pavement	stalled vehicle) in meter			stalled vehicle) in meter			in both lanes) in meter
in meter	P	SU	WB-50	P	SU	WB-50	P	SU	WB-50
15	3.9	5.4	7.8	6	8.7	13.2	7.8	10.5	15
22.5	3.9	5.1	6.6	5.7	8.1	10.8	7.5	9.9	12.6
30	3.9	4.8	6.3	5.7	7.5	10.2	7.5	9.3	12
45	3.6	4.8	5.7	5.4	7.2	8.7	7.2	9	10.5
60	3.6	4.8	5.1	5.4	6.9	8.1	7.2	8.7	9.9
90	3.6	4.5	5.1	5.4	6.6	7.5	7.2	8.4	9.3

Guidelines for design of Median islands

The general guidelines to be followed in the design of median islands (separators of opposing traffic flows) are:

1. The approach noses should be offset 0.6 to 1.8 m from through lanes to minimize accidental impacts.
2. Shape should be based on design turning paths and island function. (Generally parabolic or circular arcs are used)
3. The length of median before the intersection is related to approach speed (normally 3 sec driving time to intersection). It is also affected by available widths, taper designs and local constraints.
4. The width of the medians should serve its primary intended function.
5. The median should always be provided well past crest vertical curves.

Fig. 25 shows the general design elements of medians provided just at the approach to a intersection.

Figure 25: Design Criteria for raised median approaches to intersections

The required median widths for performing their intended functions are provided by AASHTO and are shown in Table. 6 below. These widths are empirical and can be applied at an intersection with reasonable efficiency.

Table 6: Basic median functions and their required width

Function	Width in meter
	Minimum	Desirable
Separation of opposing traffic	1.2	3
Provision of pedestrian refuse	1.8	4.2
Provision of storage for left-turn vehicles	4.8	6
Provision for protection of vehicles crossing	7.5	9
through lanes
Provision for U turns, inside to outside lanes	4.8	6
Provision for U-turns, inside to inside lanes	7.8	9

Auxiliary Lanes

Auxiliary lanes are used under conditions of relatively high traffic volumes in the intersections. In these cases, traffic congestion problems can be significantly alleviated with auxiliary lanes to handle turning movements. The median lane should be 12 feet (3.6m), but not less than 10 feet (3.0m) wide and should be clearly marked for this purpose. Auxiliary lanes can also be introduced to provide for both left turns and right turns at intersections. The need for such lanes is determined by capacity analysis and the acceptable level of service designated for the facility. The lanes should be at least 2.7m wide for reconstruction and resurfacing projects and at least 3.0m, preferably 3.6m for new construction projects. Auxiliary lane shoulders can be reduced to 0.6 m wide on rural sections and 0 m wide on sections with curb and gutter. The length of auxiliary lanes consists of five components:

1. Approach Taper
2. Deceleration Length
3. Bay Taper
4. Storage Length, and
5. Departure Taper.

A typical auxiliary lane with the components are shown in Fig. 26 below.

Figure 26: Components of Auxiliary Lane

These are discussed in detail in the following section.

1. Approach Taper- The length of the approach taper varies with operating speeds. Guidelines for determining lengths are: (i) For speeds 70 kmph and over: , and (ii) For speeds under 70 kmph: where,  is the length of entering taper in m, is the width to be tapered in m, and  is the operating Speed in kmph.
2. Deceleration Length- The deceleration length is that required for a comfortable stop of a vehicle from a speed that is typical of the average running speed on the facility. The Bay Taper can be considered part of the deceleration length. AASHTO has again given a table for calculating the decelerating length value from the design speed value (Table. 7).

   Table 7: Deceleration length vs Design Speed

   Design Speed	Deceleration Length
   (kmph)	(m)
   40	35
   55	45
   65	55
   70	65
   80	95

3. Bay Taper – This is a straight line taper with ratios varying from 5:1 to 10:1. Higher speed facilities should generally have longer tapers. Empirically, the minimum and maximum values of bay taper are taken as 18m and 36m respectively.
4. Storage Length – The storage length should be sufficiently long to store the number of vehicles likely to accumulate during the average daily peak period.
   1. At unsignalized intersections, length to be based on the number of vehicles likely to arrive in an average 2-minute period within the peak hour.
   2. At signalized intersections, the required length depends on the signal cycle length, the signal phasing arrangement and the rate of arrivals and departures of left turning vehicles.
5. Departure Taper – The departure taper is normally taken equal in length to that of the approach taper and should begin opposite the beginning of the Bay Taper.

Shape of Median Ends

Generally, two types of end shapes are used in practice:-semicircular shapes and bullet nose. The shape adopted normally depends on the effective median width at the end of the median. The dimensions of the various parameters for semi-circular and bullet nose ends area as: Semi-circular- , . Bullet-nose- , ,  The criteria for the selection of median end is as given below in Table. 8.

Table 8: Criteria for selection of median end shape

Effective Median Width	Median End Shape
Less than 3m	Semi-circular
3m – 20m	Bullet Nose
Over 20m	Treated as a separate intersection

Figure 27: Shapes of Median ends, (a)Semi-circular

Figure 28: Shapes of Median ends, (b)Bullet-nose

The two shapes are illustrated in Figs. 27 and  28. The designer should evaluate each intersection to determine the best median opening shape that will accommodate the design vehicle.

Design of Median Openings

Median openings, sometimes called crossovers, provide for vehicular crossings of the median at designated locations. The design of a median opening should be based on traffic volumes and types of turning vehicles. Cross and turning traffic must operate in conjunction with the through traffic on the divided highway. This requirement makes it necessary to know the volume and composition of all movements occurring simultaneously during the design hours. The design of a median opening becomes a matter of considering what traffic is to be accommodated, choosing the design vehicle to use for layout controls for each cross and turning movement, investigating whether larger vehicles can turn without undue encroachment on adjacent lanes and, finally, checking the intersection for capacity. If the capacity is exceeded by the traffic load, the design must be expanded, possibly by widening or otherwise adjusting widths for certain movements. Traffic control devices such as yield signs, stop signs or traffic signals may be required to regulate the various movements effectively and to improve the efficiency of operations. Median openings at close intervals on other types of highways create interference with fast through traffic. Median openings should be spaced at intervals no closer than 500 m. However, if a median opening falls within 100 m of an access opening, it should be placed opposite the access opening. Also, the length of median opening varies with width of median and angle of intersecting roads. Fig. 29 shows the intersection median opening.

Figure 29: Intersection Median Opening

The median openings for the different classes of design vehicle are as given in the Table. 9.

Table 9: Median Openings

Width of	Passenger Car		Single Unit Truck		Single Trailer Unit
Median(m)	Semi – circular	Bullet nose	Semi – circular	Bullet nose	Semi – circular	Bullet nose
1.2	22.8	22.8	28.8	28.8	43.8	36.6
1.8	22.2	18	28.2	22.8	43.2	34.5
2.4	21.6	15.9	27.6	20.4	42.6	33
3	21	14.1	27	18.6	42	31.5
3.6	20.4	12.9	26.4	17.4	41.4	30
4.2	19.2	12	25.8	15.9	40.8	28.8
4.8	18	12	25.2	15	40.2	27.6
6	16.8	12	24	13.2	39	25.5

Developing a Channelization Plan

1. Channelization is more of an art rather than science. Every intersection requires a special study because of variations in physical dimensions, turning movements, traffic and pedestrian volumes, type of traffic control etc.
2. In the next step several island configurations are considered and compared. Then a choice is made between curbed, raised islands and flush Channelization or pavement markings.
3. Next it must be checked that the design is compatible to handle turning movements of large vehicles. Also, it should be such that the vehicles are guided in normal wheel paths, so that the island does not create an obstruction in the roadway.
4. Signing and marking are redesigned to guide drivers and avoid confusion.
5. The final plan includes details of civil and electrical engineering features (like drainage facilities, curbs, lighting, signals etc.) required for the project completion.

Typical Channelization Examples

Some typical Channelization ways used in practice are as given below. Figs. 30 to 41indicate both normal Channelization and high type Channelization techniques for various intersections and situations.

Figure 30: Channelization for Y Intersections, (a)For low Flows

Figure 31: Channelization for Y Intersections, (b)For High Flows

Figure 32: Channelization for T Intersections, (a)For low Flows

Figure 33: Channelization for T Intersections, (b)For High Flows

Figure 34: Channelization for T or Y Intersections (Channelized-High Type)

Figure 35: Channelization for T or Y Intersections (Channelized-High Type)

Figure 36: Channelization for T or Y Intersections (Channelized-High Type)

Figure 37: Channelization for T or Y Intersections (Channelized-High Type)

Figure 38: Channelization for 4-Leg Intersections (Channelized-High Type)

Figure 39: Channelization for 4-Leg Intersections (Channelized-High Type)

Figure 40: Channelization for Multi – leg Intersections

Figure 41: Channelization for Multi – leg Intersections

Turning Vehicle Templates

In the design of intersections the turning paths of vehicles assumes utmost importance. The turning paths of design vehicles are given in transparent templates such as the one shown in Fig. 17 and Fig. 18. These templates are placed over the intersection plan to trace the path of the turning vehicle. Once this is done, proper islands and other traffic control devices can be designed. As per AASHTO, the turning templates are drawn at an approximate scale of 1″=50′. The radius of the template is measured to the outside front wheel path at the beginning of the curve. The design vehicle for the purpose can be taken out of a list of 16 different types of vehicles suggested by AASHTO. The dimensions of some of the design vehicles are given in Table. 10 below. The templates are applied to the layout of intersections and other facilities in accommodating vehicle maneuvers, including driveways, car parking, truck loading and bus terminals.

Table 10: Dimensions of some common Design vehicles

Design Vehicle Type	Symbol	Overall Dimension
		Height (m)	Width (m)	Length (m)
Passenger Car	P	1.3	2.1	5.8
Single Unit Truck	SU	4.1	2.6	9.1
Single Unit Bus	BUS	4.1	2.6	12.1
Intermediate Semi-Trailer	WB-15	4.1	2.6	16.7

Here we shall take the cases of a passenger car (P) and a single unit truck (BUS) as the design vehicles. The various design elements and their dimensions are shown in Fig. 42and Table. 11 respectively.

Figure 42: Design vehicle Dimensions and Turning Properties

Table 11: Design vehicle Dimensions and Turning Properties for  turns

Vehicle		WB					Minimum Turn
Designation	L(m)	(m)	A(m)	B(m)	W(m)	U(m)	U** (m)	FA	RT
							(m)	(m)	(m)
BUS	12.1	7.5	2	2.5	2.6	2.6	4.98	1.25	13
Passenger Car (P)	5.8	3.4	0.9	15	2.1	1.8	2.61	0.6	7.5

The templates were developed to include a variety of angles, with specific configurations for every 30 degrees of turn (30, 60, 90, 120, 150 and 180). By special manipulation of the template, any degree of turning can be produced within an overall range of 20 to 200 degrees. The four variables-vehicle type, turning radius, angle of turn and scale-provide full flexibility in the use of turning vehicle templates for layout and design. To permit greater latitude in maneuvering of buses, single unit trucks and passenger cars, special bar tenders are included, consisting of turning radii in the range of 13 to 50 meters for the first two and 5.5 to 30 meters for the last type of vehicles which are outside the scope of this discussion. The list of templates for bus and passenger cars is shown in the Table. 12.

Table 12: List of Templates

Vehicle Type	Scales	Turning Radius-m	Average Size-cm
	1:250	R= 13 & 18
BUS	1:500	R= 13 & 18
	1:250	R=13 to 50
		Bar Template
	1:250	R=7.5	1
Passenger car	1:250	R=7.5 to 30
		Bar template

The templates for the Passenger Car (P) and Bus are as shown in Fig. 43, 44 below.

Figure 43: Design Template for Passenger Car (P)

Figure 44: Design Template for Bus

Numerical example 1

Provide Channelization for an intersection having EW as the major road. The major and minor roads intersect at right angles. The design vehicle is WB-50 (R=25m) and design speed is 45 kmph. The intersection is unsignalized. EW road has 2 lanes in each direction and NS has 1 lane for each direction. Take lane width =3.6 m. Provide bullet nose median ends. Also provide channelizing island for free right for WS bound traffic.

Solution

: The approach taper for auxiliary lane is equal to . The deceleration Taper is taken as 40 m. Considering a 1:10 taper, the Bay Taper is found out to be 18 m. Let the storage length = 30 m (say). Now from Table. 9, it is found that for bullet nose median end, Median Opening = 30 m. The dimensions of all the components of the auxiliary lane are shown in Fig. 45.

Figure 45: Dimensions of components of the auxiliary lane for the intersection

The width required for the WB- 50 semi-trailer unit is found to be about 6.5 m. Additional 0.5 m is provided on the outer side and 0.3 m is provided on the inner side away from the edge of the island. For the turning roadway for the W-S direction, the single offset method is used. At 0.3 + 0.5 + 6.5 = 7.3 m from the island edge, a circle of radius 25 m is laid out. Then two tapers of slope 1:15 is laid out on either side of the arc to join with the straight edge on either side. Thus the Channelization is provided for the W-S approach. Similar method can be used for designing the Channelization schemes of the other directions as well. The Channelization for the W-S approach is shown in Fig. 46.

Figure 46: Channelization for the W-S direction with traffic island

Numerical example 2

Following the principles of Channelization suggest suitable island schemes for the following intersections (considering both high relative speed and low relative speed) (Figs. 47,  48)

Solution

1. Y – Intersection (Figs. 49,  50 and 51)
2. Skewed intersection (Figs. 52,  53 and 54)

Figure 47: Wye Intersection

Figure 48: Skewed Cross Road

Figure 49: (a) Y – Intersection

Figure 50: (b) Y – Intersection

Figure 51: (c) Y – Intersection

Figure 52: (a) Skewed Intersection

Figure 53: (b) Skewed Intersection

Figure 54: (c) Skewed Intersection

Summary

This chapter presents one of the simple and cost effective way of intersection control, namely the Channelization. This is normally adopted for low and medium volume roads. The chapter contains the design principles, traffic islands, and median.

References

1. Transportation research board channelization-the design of highway intersections at grade, 1962.
2. Mass highway, 2006- intersections, 2006.
3. 2011.
4. Channelization, 2011.
5. Highway design manual, 2000- pedestrian facility design, 2011.
6. Road design manual, 2011.
7. Roosevelt street – neighborhood traffic management plan, 2011.
8. Streetsblog, 2011.
9. Us department of transportation federal highway administration- guidance on the use of traffic channelizing devices at highway-rail grade crossings, 2011.
10. Us department of transportation federal highway administration- innovative intersection safety improvement strategies and management practices:a domestic scan, 2011.
11. Us department of transportation federal highway administration-safety benefits of raised medians and pedestrian refuge areas, 2011.
12. S K Khanna C E G Justo. Highway Engineering. Nem Chand and Bros, Roorkee, 2001.
13. T R Neuman. Intersection channelization design guide. Transportation Research Board. TRB NCHRP R 279, Washington, D.C., 1985.
14. R J Paquette, N Ashford, and P H Wright.Transportation Engineering : Planning and Design. John Wiley, New York, 1972.
15. R P Roess, S E Prassas, and W R McShane.Traffic Engineering. Pearson Education International, 2005.
16. S Wolfgang, Homburger, and James H Kell.Fundamentals of Traffic Engineering 12th Edition. San Francisco, 1997.

Acknowledgments

I wish to thank my student Mr. Pratik Patra for his assistance in developing the lecture note, and my staff Ms. Reeba in typesetting the materials. I also wish to thank several of my students and staff of NPTEL for their contribution in this lecture.

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FUNDAMENTAL PARAMETERS OF TRAFFIC FLOW

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Lecture notes in Traffic Engineering And Management

Contents

1 Overview 
2 Traffic stream parameters 
3 Speed 
 3.1 Spot Speed 
 3.2 Running speed 
 3.3 Journey speed 
 3.4 Time mean speed and space mean speed 
4 Flow 
 4.1 Variations of Volume 
 4.2 Types of volume measurements 
5 Density 
6 Derived characteristics 
 6.1 Time headway 
 6.2 Distance headway 
 6.3 Travel time 
7 Time-space diagram 
 7.1 Single vehicle 
 7.2 Multiple Vehicles 
8 Summary 
9 References 
10 Acknowledgments

1 Overview

Traffic engineering pertains to the analysis of the behavior of traffic and to design the facilities for a smooth, safe and economical operation of traffic. Traffic flow, like the flow of water, has several parameters associated with it. The traffic stream parameters provide information regarding the nature of traffic flow, which helps the analyst in detecting any variation in flow characteristics. Understanding traffic behavior requires a thorough knowledge of traffic stream parameters and their mutual relationships. In this chapter the basic concepts of traffic flow is presented.

2 Traffic stream parameters

The traffic stream includes a combination of driver and vehicle behavior. The driver or human behavior being non-uniform, traffic stream is also non-uniform in nature. It is influenced not only by the individual characteristics of both vehicle and human but also by the way a group of such units interacts with each other. Thus a flow of traffic through a street of defined characteristics will vary both by location and time corresponding to the changes in the human behavior.

The traffic engineer, but for the purpose of planning and design, assumes that these changes are within certain ranges which can be predicted. For example, if the maximum permissible speed of a highway is 60 kmph, the whole traffic stream can be assumed to move on an average speed of 40 kmph rather than 100 or 20 kmph.

Thus the traffic stream itself is having some parameters on which the characteristics can be predicted. The parameters can be mainly classified as : measurements of quantity, which includes density and flow of traffic and measurements of quality which includes speed. The traffic stream parameters can be macroscopic which characterizes the traffic as a whole or microscopic which studies the behavior of individual vehicle in the stream with respect to each other.

As far as the macroscopic characteristics are concerned, they can be grouped as measurement of quantity or quality as described above, i.e. flow, density, and speed. While the microscopic characteristics include the measures of separation, i.e. the headway or separation between vehicles which can be either time or space headway. The fundamental stream characteristics are speed, flow, and density and are discussed below.

3 Speed

Speed is considered as a quality measurement of travel as the drivers and passengers will be concerned more about the speed of the journey than the design aspects of the traffic. It is defined as the rate of motion in distance per unit of time. Mathematically speed or velocity v is given by,

(1)

where, v is the speed of the vehicle in m/s, d is distance traveled in m in time t seconds. Speed of different vehicles will vary with respect to time and space. To represent these variation, several types of speed can be defined. Important among them are spot speed, running speed, journey speed, time mean speed and space mean speed. These are discussed below.

3.1 Spot Speed

Spot speed is the instantaneous speed of a vehicle at a specified location. Spot speed can be used to design the geometry of road like horizontal and vertical curves, super elevation etc. Location and size of signs, design of signals, safe speed, and speed zone determination, require the spot speed data. Accident analysis, road maintenance, and congestion are the modern fields of traffic engineer, which uses spot speed data as the basic input. Spot speed can be measured using an enoscope, pressure contact tubes or direct timing procedure or radar speedometer or by time-lapse photographic methods. It can be determined by speeds extracted from video images by recording the distance travelling by all vehicles between a particular pair of frames.

3.2 Running speed

Running speed is the average speed maintained over a particular course while the vehicle is moving and is found by dividing the length of the course by the time duration the vehicle was in motion. i.e. this speed doesn’t consider the time during which the vehicle is brought to a stop, or has to wait till it has a clear road ahead. The running speed will always be more than or equal to the journey speed, as delays are not considered in calculating the running speed

3.3 Journey speed

Journey speed is the effective speed of the vehicle on a journey between two points and is the distance between the two points divided by the total time taken for the vehicle to complete the journey including any stopped time. If the journey speed is less than running speed, it indicates that the journey follows a stop-go condition with enforced acceleration and deceleration. The spot speed here may vary from zero to some maximum in excess of the running speed. A uniformity between journey and running speeds denotes comfortable travel conditions.

3.4 Time mean speed and space mean speed

Time mean speed is defined as the average speed of all the vehicles passing a point on a highway over some specified time period. Space mean speed is defined as the average speed of all the vehicles occupying a given section of a highway over some specified time period. Both mean speeds will always be different from each other except in the unlikely event that all vehicles are traveling at the same speed. Time mean speed is a point measurement while space mean speed is a measure relating to length of highway or lane, i.e. the mean speed of vehicles over a period of time at a point in space is time mean speed and the mean speed over a space at a given instant is the space mean speed.

4 Flow

There are practically two ways of counting the number of vehicles on a road. One is flow or volume, which is defined as the number of vehicles that pass a point on a highway or a given lane or direction of a highway during a specific time interval. The measurement is carried out by counting the number of vehicles, n_t, passing a particular point in one lane in a defined period t. Then the flow q expressed in vehicles/hour is given by

(2)

Flow is expressed in planning and design field taking a day as the measurement of time.

4.1 Variations of Volume

The variation of volume with time, i.e. month to month, day to day, hour to hour and within a hour is also as important as volume calculation. Volume variations can also be observed from season to season. Volume will be above average in a pleasant motoring month of summer, but will be more pronounced in rural than in urban area. But this is the most consistent of all the variations and affects the traffic stream characteristics the least.

Weekdays, Saturdays and Sundays will also face difference in pattern. But comparing day with day, patterns for routes of a similar nature often show a marked similarity, which is useful in enabling predictions to be made.

The most significant variation is from hour to hour. The peak hour observed during mornings and evenings of weekdays, which is usually 8 to 10 per cent of total daily flow or 2 to 3 times the average hourly volume. These trips are mainly the work trips, which are relatively stable with time and more or less constant from day to day.

4.2 Types of volume measurements

Since there is considerable variation in the volume of traffic, several types of measurements of volume are commonly adopted which will average these variations into a single volume count to be used in many design purposes.

1. Average Annual Daily Traffic(AADT) : The average 24-hour traffic volume at a given location over a full 365-day year, i.e. the total number of vehicles passing the site in a year divided by 365.
2. Average Annual Weekday Traffic(AAWT) : The average 24-hour traffic volume occurring on weekdays over a full year. It is computed by dividing the total weekday traffic volume for the year by 260.
3. Average Daily Traffic(ADT) : An average 24-hour traffic volume at a given location for some period of time less than a year. It may be measured for six months, a season, a month, a week, or as little as two days. An ADT is a valid number only for the period over which it was measured.
4. Average Weekday Traffic(AWT) : An average 24-hour traffic volume occurring on weekdays for some period of time less than one year, such as for a month or a season.

The relationship between AAWT and AWT is analogous to that between AADT and ADT. Volume in general is measured using different ways like manual counting, detector/sensor counting, moving-car observer method, etc. Mainly the volume study establishes the importance of a particular route with respect to the other routes, the distribution of traffic on road, and the fluctuations in flow. All which eventually determines the design of a highway and the related facilities. Thus, volume is treated as the most important of all the parameters of traffic stream.

5 Density

Density is defined as the number of vehicles occupying a given length of highway or lane and is generally expressed as vehicles per km. One can photograph a length of road x, count the number of vehicles, n_x, in one lane of the road at that point of time and derive the density k as,

(3)

This is illustrated in figure 1. From the figure, the density is the number of vehicles between the point A and B divided by the distance between A and B. Density is also equally important as flow but from a different angle as it is the measure most directly related to traffic demand. Again it measures the proximity of vehicles in the stream which in turn affects the freedom to maneuver and comfortable driving.

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Figure 1: Illustration of density

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6 Derived characteristics

From the fundamental traffic flow characteristics like flow, density, and speed, a few other parameters of traffic flow can be derived. Significant among them are the time headway, distance headway and travel time. They are discussed one by one below.

6.1 Time headway

The microscopic character related to volume is the time headway or simply headway. Time headway is defined as the time difference between any two successive vehicles when they cross a given point. Practically, it involves the measurement of time between the passage of one rear bumper and the next past a given point. If all headways h in time period, t, over which flow has been measured are added then,

(4)

But the flow is defined as the number of vehicles n_t measured in time interval t, that is,

(5)

where, h_av is the average headway. Thus average headway is the inverse of flow. Time headway is often referred to as simply the headway.

6.2 Distance headway

Another related parameter is the distance headway. It is defined as the distance between corresponding points of two successive vehicles at any given time. It involves the measurement from a photograph, the distance from rear bumper of lead vehicle to rear bumper of following vehicle at a point of time. If all the space headways in distance x over which the density has been measured are added,

(6)

But the density (k) is the number of vehicles n_xat a distance of x, that is

(7)

Where, s_av is average distance headway. The average distance headway is the inverse of density and is sometimes called as spacing.

6.3 Travel time

Travel time is defined as the time taken to complete a journey. As the speed increases, travel time required to reach the destination also decreases and vice-versa. Thus travel time is inversely proportional to the speed. However, in practice, the speed of a vehicle fluctuates over time and the travel time represents an average measure.

7 Time-space diagram

Time space diagram is a convenient tool in understanding the movement of vehicles. It shows the trajectory of vehicles in the form of a two dimensional plot. Time space diagram can be plotted for a single vehicle as well as multiple vehicles. They are discussed below.

7.1 Single vehicle

Taking one vehicle at a time, analysis can be carried out on the position of the vehicle with respect to time. This analysis will generate a graph which gives the relation of its position on a road stretch relative to time. This plot thus will be between distance x and time t and x will be a functions the position of the vehicle for every t along the road stretch. This graphical representation of x(t) in a (t,x) plane is a curve which is called as a trajectory. The trajectory provide an intuitive, clear, and complete summary of vehicular motion in one dimension.

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Figure 2: Time space diagram for a single vehicle

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In figure 2(a), the the distance x goes on increasing with respect to the origin as time progresses. The vehicle is moving at a smooth condition along the road way. In figure 2(b), the vehicle at first moves with a smooth pace after reaching a position reverses its direction of movement. In figure 2(c), the vehicle in between becomes stationary and maintains the same position.

From the figure, steeply increasing section of x(t) denote a rapidly advancing vehicle and horizontal portions of x(t) denote a stopped vehicle while shallow sections show a slow-moving vehicle. A straight line denotes constant speed motion and curving sections denote accelerated motion; and if the curve is concave downwards it denotes acceleration. But a curve which is convex upwards denotes deceleration.

7.2 Multiple Vehicles

Time-space diagram can also be used to determine the fundamental parameters of traffic flow like speed, density and volume. It can also be used to find the derived characteristics like space headway and time headway. Figure 3 shows the time-space diagram for a set of vehicles traveling at constant speed. Density, by definition is the number of vehicles per unit length. From the figure, an observer looking into the stream can count 4 vehicles passing the stretch of road between x₁ and x₂ at time t. Hence, the density is given as

(8)

We can also find volume from this time-space diagram. As per the definition, volume is the number of vehicles counted for a particular interval of time. From the figure 3 we can see that 6 vehicles are present between the time t₁and t₂. Therefore, the volume q is given as

(9)

Again the averages taken at a specific location (i.e., time ranging over an interval) are called time means and those taken at an instant over a space interval are termed as space means.

Another related definition which can be given based on the time-space diagram is the headway. Space headway is defined as the distance between corresponding points of two successive vehicles at any given time. Thus, the vertical gap between any two consecutive lines represents space headway. The reciprocal of density otherwise gives the space headway between vehicles at that time.

Similarly, time headway is defined as the time difference between any two successive vehicles when they cross a given point. Thus, the horizontal gap between the vehicles represented by the lines gives the time headway. The reciprocal of flow gives the average time headway between vehicles at that point.

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Figure 3: Time space diagram for many vehicles

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8 Summary

Speed, flow and density are the basic parameters of traffic flow. Different measures of speed are used in traffic flow analysis like spot speed, time mean speed, space mean speed etc. Time-space diagram also can be used for determining these parameters. Speed and flow of the traffic stream can be computed using moving observer method.

9 References

1. Highway Capacity Manual. Transportation Research Board. National Research Council, Washington, D.C., 2000.
2. L. R Kadiyali. Traffic Engineering and Transportation Planning. Khanna Publishers, New Delhi, 1987.
3. Adolf D. May. Fundamentals of Traffic Flow. Prentice – Hall, Inc. Englewood Cliff New Jersey 07632, second edition, 1990.
4. William R McShane, Roger P Roesss, and Elena S Prassas. Traffic Engineering. Prentice-Hall, Inc, Upper Saddle River, New Jesery, 1998.
5. C. S Papacostas. Fundamentals of Transportation Engineering. Prentice-Hall, New Delhi, 1987.

10 Acknowledgments

I wish to thank several of my students and staff of NPTEL for their contribution in this lecture.

ACCIDENT STUDIES

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Lecture notes in Traffic Engineering And Management

Contents

• Overview
• Introduction
  • Objectives of accident studies
  • Causes of road accidents
  • Accident statistics
• Accident Analysis
  • Accident data collection
  • Accident investigation
  • Accident data analysis
• Accident reconstruction
  • Poisson impact theory
  • Energy theory
  • Angular collision
• Safety measures
  • Safety measures related to engineering
  • Safety measures related to enforcement
  • Safety measures related to education
  • Safety audit
• Conclusion
• References
• Acknowledgments

Overview

This lecture covers one of the most important negative impact of transportation system, namely the accidents. This lecture first presents some introductory stuff including some salient accident statistics, causes of accidents, accident data collection, accident reconstruction, safety measures and safety audit.

Introduction

The problem of accident is a very acute in highway transportation due to complex flow pattern of vehicular traffic, presence of mixed traffic along with pedestrians. Traffic accident leads to loss of life and property. Thus the traffic engineers have to undertake a big responsibility of providing safe traffic movements to the road users and ensure their safety. Road accidents cannot be totally prevented but by suitable traffic engineering and management the accident rate can be reduced to a certain extent. For this reason systematic study of traffic accidents are required to be carried out. Proper investigation of the cause of accident will help to propose preventive measures in terms of design and control.

Objectives of accident studies

Some objectives of accident studies are listed below:

1. To study the causes of accidents and suggest corrective measures at potential location
2. To evaluate existing design
3. To compute the financial losses incurred
4. To support the proposed design and provide economic justification to the improvement suggested by the traffic engineer
5. To carry out before and after studies and to demonstrate the improvement in the problem.

Causes of road accidents

The various causes of road accidents are:

1. Road Users – Excessive speed and rash driving, violation of traffic rules, failure to perceive traffic situation or sign or signal in adequate time, carelessness, fatigue, alcohol,sleep etc.
2. Vehicle – Defects such as failure of brakes, steering system, tyre burst,lighting system .
3. Road Condition – Skidding road surface, pot holes, ruts.
4. Road design – Defective geometric design like inadequate sight distance, inadequate width of shoulders, improper curve design, improper traffic control devices and improper lighting,.
5. Environmental factors -unfavorable weather conditions like mist, snow, smoke and heavy rainfall which restrict normal visibility and and makes driving unsafe.
6. Other causes -improper location of advertisement boards, gate of level crossing not closed when required etc..

Accident statistics

The statistical analysis of accident is carried out periodically at critical locations or road stretches which will help to arrive at suitable measures to effectively decrease accident rates. It is the measure (or estimates) of the number and severity of accident. These statistics reports are to be maintained zone-wise. Accident prone stretches of different roads may be assessed by finding the accident density per length of the road. The places of accidents are marked on the map and the points of their clustering (BLACK SPOT) are determined. By statistical study of accident occurrence at a particular road or location or zone of study for a long period of time it is possible to predict with reasonable accuracy the probability of accident occurrence per day or relative safety of different classes of road user in that location. The interpretation of the statistical data is very important to provide insight to the problem. The position of India in the year 2009 in country-wise number of person killed per 100000 populations as shown in the Figure 1 and the increase in rate of accident from year 2005 to year 2009 is shown in the table. 1. In 2009, 14 accidents occurred per hour.

Figure 1: Country-wise number of person killed per 100000 populations (Ref. Ministry of Road Transport and Highways Transport Research Wing)

Table 1: Number of Accidents and Number of Persons Involved : 2001 to 2009(Ref. Ministry of Road Transport and Highways Transport Research Wing)

	No. of Accidents		No. of persons affected		Accident severity
Year	Total	Fatal	Killed	Injured	(No. of persons killed
					per 100 accidents)
2005	4,39,255	83,491	94,968	4,65,282	22
2006	4,60,920	93,917	1,05,749	4,96,481	23
2007	4,79,216	1,01,161	1,14,444	5,13,340	24
2008	4,84,704	1,06,591	1,19,860	5,23,193	25
2009	4,86,384	1,10,993	1,25,660	5,15,458	25.8

Figure 2: Percent share in total road accident by type of motor vehicle involved (Primary responsible) in year 2009 (Ref. Ministry of Road Transport and Highways Transport Research Wing)

Figure 3: Causes of road accident in year 2009 (Ref. Ministry of Road Transport and Highways Transport Research Wing)

Figure 2 and 3 gives the percent of accident occurring from a specific vehicle class and the causes of accident in the form of pie-chart. Since the data collection of accident is mostly done by the traffic police it’s the users who are put to blame in majority of cases. Thus such statistical records are not much useful for the traffic engineer.

Accident Analysis

Accident data collection

The accident data collection is the first step in the accident study. The data collection of the accidents is primarily done by the police. Motorist accident reports are secondary data which are filed by motorists themselves. The data to be collected should comprise all of these parameters:

1. General – Date, time, person involved in accident, classification of accident like fatal, serious, minor
2. Location – Description and detail of location of accident
3. Details of vehicle involved – Registration number, description of vehicle, loading detail, vehicular defects
4. Nature of accident – Details of collision, damages, injury and casualty
5. Road and traffic condition – Details of road geometry, surface characteristics,type of traffic, traffic density etc..
6. Primary causes of accident – Details of various possible cases (already mentioned) which are the main causes of accident.
7. Accident cost – Financial losses incurred due to property damage, personal injury and casualty

These data collected need proper storing and retrieving for the following purpose. The purposes are as follows:

1. Identification of location of points at which unusually high number of accident occur.
2. Detailed functional evaluation of critical accident location to identify the causes of accidents.
3. Development of procedure that allows identification of hazards before large number of accidents occurs.
4. Development of different statistical measures of various accident related factors to give insight into general trends, common casual factors, driver profiles, etc.

Accident investigation

The accident data collection involves extensive investigation which involves the following procedure:

1. Reporting: It involves basic data collection in form of two methods:
   1. Motorist accident report – It is filed by the involved motorist involved in all accidents fatal or injurious.
   2. Police accident report – It is filed by the attendant police officer for all accidents at which an officer is present. This generally includes fatal accidents or mostly accidents involving serious injury required emergency or hospital treatment or which have incurred heavy property damage.
2. At Scene-Investigation: It involves obtaining information at scene such as measurement of skid marks, examination of damage of vehicles, photograph of final position of vehicles, examination of condition and functioning of traffic control devices and other road equipments.
3. Technical Preparation: This data collection step is needed for organization and interpretation of the study made. In this step measurement of grades, sight distance, preparing drawing of after accident situation, determination of critical and design speed for curves is done.
4. Professional Reconstruction: In this step effort is made to determine from whatever data is available how the accident occurs from the available data. This involves accident reconstruction which has been discussed under Section No.7 in details. It is professionally referred as determining “behavioral” or “mediate” causes of accident.
5. Cause Analysis: It is the effort made to determine why the accident occurred from the data available and the analysis of accident reconstruction studies..

Accident data analysis

The purpose is to find the possible causes of accident related to driver, vehicle, and roadway. Accident analyses are made to develop information such as:

1. Driver and Pedestrian – Accident occurrence by age groups and relationships of accidents to physical capacities and to psychological test results.
2. Vehicle – Accident occurrence related to characteristic of vehicle, severity, location and extent of damage related to vehicles.
3. Roadway conditions – Relationships of accident occurrence and severity to characteristics of the roadway and roadway condition and relative values of changes related to roadways.

It is important to compute accident rate which reflect accident involvement by type of highway. These rates provide a means of comparing the relative safety of different highway and street system and traffic controls. Another is accident involvement by the type of drivers and vehicles associated with accidents.

1. Accident Rate per Kilometer : On this basis the total accident hazard is expressed as the number of accidents of all types per km of each highway and street classification.

   (1)

   where,  = total accident rate per km for one year,  = total number of accident occurring in one year,  = length of control section in kms

2. Accident involvement Rate : It is expressed as numbers of drivers of vehicles with certain characteristics who were involved in accidents per 100 million vehicle-kms of travel.

   (2)

   where, = accident involvement per 100 million vehicle-kms of travel,  = total number of drivers of vehicles involved in accidents during the period of investigation and  = vehicle-kms of travel on road section during the period of investigation

3. Death rate based on population : The traffic hazard to life in a community is expressed as the number of traffic fatalities per 100,000 populations. This rate reflects the accident exposure for entire area.

   (3)

   where,  = death rate per 100,000 population,  = total number of traffic death in one year and  = population of area

4. Death rate based on registration : The traffic hazard to life in a community can also be expressed as the number of traffic fatalities per 10,000 vehicles registered. This rate reflects the accident exposure for entire area and is similar to death rate based on population.

   (4)

   where,  = death rate per 10,000 vehicles registered,  = total number of traffic death in one year and  = number of motor vehicles registered in the area

5. Accident Rate based on vehicle-kms of travel : The accident hazard is expressed as the number of accidents per 100 million vehicle km of travel. The true exposure to accident is nearly approximated by the miles of travel of the motor vehicle than the population or registration.

   (5)

   where,  = accident rate per 100 million vehicle kms of travel,  = number of total accidents in one year and  = vehicle kms of travel in one year

Numerical Example

The Motor vehicle consumption in a city is 5.082 million liters, there were 3114 motor vehicle fatalities, 355,799 motor vehicle injuries, 6,721,049 motor vehicle registrations and an estimated population of 18,190,238. Kilometer of travel per liter of fuel is 12.42 km/liter. Calculate registration death rate, population death rate and accident rate per vehicle km.

Solution

Approximate vehicle kms of travel = Total consumption o fuel  kilometer of travel per liter of fuel =5.08    12.42 = 63.1   km.

1. Registration death rate can be obtained from the equation

   Here, R is the death rate per 10,000 vehicles registered,  (Motor vehicle fatalities) is 3114,  (Motor vehicle registered) is 6.72  . Hence,

2. Population Death Rate can be obtained from the equation.

   Here, R is the death rate per 100,000 population,  (Motor vehicle fatalities) is 3114,  (Estimated population) is= 18.2  .

3. Accident rate per vehicle kms of travel can be obtained from the equation below as:

   Here, R is the accident rate per 100 million vehicle kms of travel,  (total accident same as vehicle fatalities) is 3114, (vehicle kms of travel) is 63.1  .

Accident reconstruction

Accident reconstruction deals with representing the accidents occurred in schematic diagram to determine the pre-collision speed which helps in regulating or enforcing rules to control or check movement of vehicles on road at high speed. The following data are required to determine the pre-collision speed:

1. Mass of the vehicle
2. Velocities after collision
3. Path of each vehicle as it approaches collision point

Below in Figure 4 a schematic diagram of collision of two vehicles is shown that occur during turning movements. This diagram is also known as collision diagram. Each collision is represented by a set of arrows to show the direction of before and after movement. The collision diagram provides a powerful visual record of accident occurrence over a significant period of time.

Figure 4: Collision diagram of two vehicles

The collision may be of two types collinear impact or angular collision. Below each of them are described in detail. Collinear impact can be again divided into two types :

1. Rear end collision
2. Head-on collision.

It can be determined by two theories:

1. Poisson Impact Theory
2. Energy Theory

Poisson impact theory

Poisson impact theory, divides the impact in two parts – compression and restitution. The Figure 5 shows two vehicles travelling at an initial speed of  and  collide and obtain a uniform speed say  at the compression stage. And after the compression stage is over the final speed is  and . The compression phase is cited by the deformation of the cars.

Figure 5: Compression Phase

From the Newton’s law ,

(6)

where,  and  are the masses of the cars and  is the contact force. We know that every reaction has equal and opposite action. So as the rear vehicle pushes the vehicle ahead with force . The vehicle ahead will also push the rear vehicle with same magnitude of force but has different direction. The action force is represented by , whereas the reaction force is represented by  as shown in Figure 6.

Figure 6: Force applied on each vehicle

In the compression phase cars are deformed. The compression phase terminates when the cars have equal velocity. Thus the cars obtain equal velocity which generates the following equation:

(7)

where,  which is the compression impulse and  is the compression time. Thus, the velocity after collision is obtained as:

(8)

The compression impulse is given by:

(9)

In the restitution phase the elastic part of internal energy is released

			(10)
			(11)

where,  is the restitution impulse and is the restitution time. According to Poisson’s hypothesis restitution impulse is proportional to compression impulse

(12)

Restitution impulse  is given by:

(13)

The total impulse is 

(14)

The post impact velocities are given by:

			(15)
			(16)

where . But we are required to determine the pre-collision speed according to which the safety on the road can be designed. So we will determine  and  from the given value of  and  .

Numerical Example

Two vehicles travelling in the same lane have masses 3000 kg and 2500 kg. The velocity of rear vehicles after striking the leader vehicle is 25 kmph and the velocity of leader vehicle is 56 kmph. The coefficient of restitution of the two vehicle system is assumed to be 0.6. Determine the pre-collision speed of the two vehicles.

Solution

Given that the: mass of the first vehicle () = 3000 kg, mass of the second vehicle () = 2500 kg, final speed of the rear vehicle () = 25 kmph, and final speed of the leader vehicle () = 56 kmph. Let initial speed of the rear vehicle be , and let initial speed of the leader vehicle be .

Step 1:  From equation. 15,

			(17)

Step 2:  From equation. 16,

			(18)

Step 3:  Solving equations. 17 and 18, We get the pre collision speed of two vehicles as:  = 73 kmph, and  = 62 kmph.

Step 4:  Initial speed of the rear vehicle,  = 73 kmph, and the initial speed of leader vehicle, = 62 kmph. Thus from the result we can infer that the follower vehicle was travelling at quite high speed which may have resulted in the collision. The solution to the problem may be speed restriction in that particular stretch of road where accident occurred.

Energy theory

Applying principle of conservation of energy or conservation of momentum also the initial speed of the vehicle can be computed if the skid marks are known. It is based on the concept that there is reduction in kinetic energy with the work done against the skid resistance. So if the vehicle of weight  slow down from speed  to , then the loss in kinetic energy will be equal to the work done against skid resistance, where work done is weight of the vehicle multiplied by the skid distance and the skid resistance coefficient.

(19)

where,  is the skid resistance coefficient and  is the skid distance. It also follows the law of conservation of momentum (,  are the mass and velocity of first vehicle colliding with another vehicle of mass and velocity , respectively)

(20)

Numerical example

A vehicle of 2000 kg skids a distance of 36 m before colliding with a stationary vehicle of 1500 kg weight. After collision both vehicle skid a distance of 14 m. Assuming coefficient of friction 0.5, determine the initial speed of the vehicle.

Solution:  Let the weight of the moving vehicle is , let the weight of the stationary vehicle is , skid distance before and after collision is  and  respectively, initial speed is , speed after applying brakes before collision is  and the speed of both the vehicles  and  after collision is , and the final speed  is 0. Then:

1. After collision:  Loss in kinetic energy of both cars = Work done against skid resistance (can be obtained from equation mentioned below). Substituting the values we obtain .

2. At collision:  Momentum before impact = momentum after impact (can be obtained from equation. 20)

3. Before collision (can be obtained from equation. 19): Loss in kinetic energy of moving vehicle = work done against braking force in reducing the speed

   Ans: The pre-collision speed of the moving vehicle is 100 kmph.

Angular collision

Angular collision occurs when two vehicles coming at right angles collies with each other and bifurcates in different direction. The direction of the vehicles after collision in this case depends on the initial speeds of the two vehicles and their weights. One general case is that two vehicles coming from south and west direction after colliding move in its resultant direction as shown in Figure 7.

Figure 7: Angular collision of two vehicles resulting in movement in resultant direction

The mass of the car 1 is  kg and the car 2 is  kg and the initial velocity is  m/s and m/s respectively. So as the momentum is the product of mass and velocity. The momentum of the car 1 and car 2 is  kgm/s and  kgm/s respectively. By the law of conservation of momentum the final momentum should be equal to the initial momentum. But as the car are approaching each other at an angle the final momentum should not be just mere summation of both the momentum but the resultant of the two, Resultant momentum =  kg m/s. The angle at which they are bifurcated after collision is given by  where h is the hypotenuse and b is the base. Therefore, the cars are inclined at an angle. Inclined at an angle = . Now, since the mass of the two vehicles are same the final velocity will proportionally be changed. The general schematic diagrams of collision are shown in Figs. 8 to  10.

Figure 8: After collision movement of car 1 north of west and car 2 in east of north

Figure 9: After collision movement of car 1 and car 2 in north of east

Figure 10: After collision movement of car 1 north of east and car 2 in south of east

Numerical example

Vehicle A is approaching from west and vehicle B from south. After collision A skids north of east and B skids  south of east as shown in Figure 10. Skid distance before collision for A is 18 m and B is 26 m. The skid distances after collision are 30m and 15 m respectively. Weight of A and B are 4500 and 6000 respectively. Skid resistance of pavement is 0.55 m. Determine the pre-collision speed.

Solution

Let: initial speed is  and , speed after skidding before collision is  and , speed of both the vehicles A and B after collision is and , final speed is  and  is 0, initial skid distance for A and B is  and , final skid distance for A and B is  and , and weight of vehicle A is  and Weight of vehicle B is .

1. After collision:  Loss in kinetic energy of each cars= Work done against skid resistance (can be obtained from equation. 19)

   As  = 0, it is not considered in the above equation

   Similarly, we calculate  using the similar formula and using 

2. At collision: Momentum before impact is momentum after impact (resolving along west-east direction and using equation. 20)

   Resolving the moments along south- north direction

3. Before collision:  Loss in kinetic energy of each cars= Work done against skid resistance (can be obtained from equation. 19)

   Similarly, using the same equation and using 

   Answer: The pre-collision speed of the vehicle A (approaching from west) is  = 99 km/hr and vehicle B (approaching from south) is  = 63.26 km/hr.

Safety measures

The ultimate goal is to develop certain improvement measures to mitigate the circumstances leading to the accidents. The measures to decrease the accident rates are generally divided into three groups engineering, enforcement and education. Some safety measures are described below:

Safety measures related to engineering

The various measures of engineering that may be useful to prevent accidents are enumerated below

Visual guidance to driver

There is consecutive change of picture in driver’s mind while he is in motion. The number of factors that the driver can distinguish and clearly fix in his mind is limited. On an average the perception time for vision is , for hearing is  and for muscular reaction is . The number of factors that can be taken into account by organs of sense of a driver in one second is given by the formula below.

(21)

where,  = No. of factors that can be taken into account by the organ of sense of driver for  m long,  = speed of vehicle in m/sec. Factors affecting drivers’ attention when he is on road can be divided into three groups:

1. Factors relating to the road – elements of road that directly affect the driving of a vehicle are traffic signs, changes in direction of road, three legged intersection and various other things.
2. Factors connected with traffic – Other vehicles, cycles, pedestrians.
3. Factors related indirectly to the vehicle motion – Building and structures that strike the eye, vegetation, landscape, etc.

So using the laws of visual perception certain measures have been suggested:

1. Contrast in visibility of the road should be achieved by provision of elements that differ from its surrounding by colors, pattern such as shoulder strips, shoulder covered with grass, edge markings.
2. Providing road side vegetation is an effective means.
3. The visibility of crown of trees from a distant location is also very useful in visual guiding.
4. The provision of guard rails of different contrasting colors also takes drivers attention and prevent from monotonous driving.

Figure 11 and 12 is a visual guidance measure. Planting trees along side of roadway which has a turning angle attracts attention of the driver and signals that a turn is present ahead.

Figure 11: Bifurcation of the highway

The figure below is another example, when the direction of road has a hazardous at-grade intersection trees are planted in such a way that it seems that there is dense forest ahead and driver automatically tends to stop or reduce the speed of the vehicle so that no conflicts occur at that point.

Figure 12: Road seemed to be stopped by a dense forest

Driver tends to extrapolate the further direction of the road. So it is the responsibility of the traffic engineer to make the driver psychologically confident while driving that reduces the probability of error and prevent mental strain.

Road reconstruction

The number of vehicles on the road increases from year to year, which introduces complications into organization of traffic, sharply reduces the operation and transportation characteristic of roads and lead to the growth of accident rate. This leads to the need of re constructing road. The places of accidents need to be properly marked so that the reconstruction can be planned accordingly.

Figure 13: Diagram of accidents before and after reconstruction

The Figure 13 shows that there were too many conflict points before which reduced to a few number after construction of islands at proper places. Reconstruction process may also include construction of a new road next to the existing road, renewal of pavement without changing the horizontal alignment or profile of the road, reconstruction a particular section of road. Few more examples of reconstruction of selected road section to improve traffic safety are shown in Figure 14.

Figure 14: Road reconstruction technique

The Figure 14 (a) shows separation of direction of main stream of traffic from the secondary ones by shifting place of three-leg intersection, Figure 14(b) shows separation of roads with construction of connection between them and Figure 14(c) shows the construction of additional lane for turning vehicles. The plus sign indicates the conflict points before the road reconstruction has been carried out. The after reconstruction figure shows that just by little alteration of a section of road how the conflict points have been resolved and smooth flow of the vehicles in an organized manner have been obtained.

Channelization

The Channelization of traffic at intersection separates the traffic stream travelling in different direction, providing them a separate lane that corresponds to their convenient path and spreading as far as possible the points of conflict between crossing traffic streams. The traffic lanes are separated by marking relevant lines or by constructing slightly elevated islands as shown in Figure 15. Proper Channelization reduces confusion. The number of decision required to be made by the driver at any time is reduced allowing the driver time to make next decision. The principles of proper channelized intersection are:-

1. The layout of intersection should be visibly clear, simple and understandable by driver.
2. Should ensure superiority to the vehicles using road of higher class.
3. Layout of intersection makes it necessary for a driver running through it to choose at each moment of time one of not more than two possible direction of travel. This is achieved by visual guidance, islands and markings.
4. The island provided should separate high speed, through and turning traffic flows.
5. The width of traffic lane should ensure unhampered turning to the big vehicles. Width of straight section without kerb should be 3.5 m and that of traffic lane near island is 4.5-5 m at entry and 6 m at exit.
6. Pedestrian crossing should be provided

Figure 15: Channelized Intersection ensuring safety

Road signs

Road signs are integral part of safety as they ensure safety of the driver himself (warning signs) and safety of the other vehicles and pedestrians on road (regulatory signs). Driver should be able to read the sign from a distance so that he has enough time to understand and respond. It is essential that they are installed and have correct shape, colour, size and location. It is required to maintain them as well, without maintenance in sound condition just their installment would not be beneficial. According to British investigation height of text in road sign should be

Where, N = No. of words on the sign, v = speed of vehicle (kmph), L = distance from which inscription should be discernible (m)

Other methods

Various other methods of traffic accident mitigation are described below:

1. Street lighting Street lightning of appropriate standard contributes to safety in urban area during night time due to poor visibility. Installation of good lighting results in 21% reduction in all accidents, 29% reduction in “all casualty” accidents, 21% reduction in “non pedestrian casualty” accidents, and 57% reduction in “pedestrian casualty” accidents.
2. Improvement in skid resistance If road is very smooth then skidding of the vehicles may occur or if the pavement is wet then wet weather crashes occur which account about 20-30%. Thus it is important to improve the skid resistance of the road. Various ways of increasing the skid resistance of road are by constructing high-friction overlay or cutting of grooves into the pavement.
3. Road markings Road markings ensure proper guidance and control to the traffic on a highway. They serve as supplementary function of road sign. They serve as psychological barrier and delineation of traffic path and its lateral clearance from traffic hazards for the safe movement of traffic. Thus their purpose is to provide smooth and safe traffic flow.
4. Guide posts with or without reflector They are provided at the edge of the roadway to prevent the vehicles from being off tracked from the roadway. Their provision is very essential in hilly road to prevent the vehicle from sliding from top. Guide posts with reflector guide the movement of vehicle during night.
5. Guard rail Guard rail have similar function as of guide post. On high embankments, hilly roads, road running parallel to the bank of river, shores of lake, near rock protrusion, trees, bridge, abutments a collision with which is a great hazard for a vehicle. It is required to retain the vehicle on the roadway which has accidentally left the road because of fault or improper operation on the part of the driver. Driver who has lost control create a major problem which can be curbed by this measure.
6. Driver reviver stop Driver reviver stop are generally in use in countries like U.S.A where driver can stop and refresh himself with food, recreation and rest. They play a very important part in traffic safety as they relieve the driver from the mental tension of constant driving. These stops are required to be provided after every 2 hour travel time.
7. Constructing flyovers and bypass In areas where local traffic is high bypasses are required to separate through traffic from local traffic to decrease the accident rate. To minimize conflicts at major intersections flyovers are required for better safety and less accident rate
8. Regular accident studies Based on the previous records of accidents the preventive measures are taken and after that the data related to accidents are again collected to check the efficiency of the measures and for future implementation of further preventive measures.

Safety measures related to enforcement

The various measures of enforcement that may be useful to prevent accidents at spots prone to accidents are enumerated below. These rules are revised from time to time to make them more comprehensive.

Speed control

Checks on spot speed of all vehicles should be done at different locations and timings and legal actions on those who violate the speed limit should be taken

Training and supervision

The transport authorities should be strict while issuing licence to drivers of public service vehicles and taxis. Driving licence of the driver may be renewed after specified period, only after conducting some tests to check whether the driver is fit

Medical check

The drivers should be tested for vision and reaction time at prescribed intervals of time

Safety measures related to education

The various measures of education that may be useful to prevent accidents are enumerated below.

Education of road users

The passengers and pedestrians should be taught the rules of the road, correct manner of crossing etc. by introducing necessary instruction in the schools for the children and by the help of posters exhibiting the serious results due to carelessness of road users.

Safety drive

Imposing traffic safety week when the road users are properly directed by the help of traffic police as a means of training the public. Training courses and workshops should be organized for drivers in different parts of the country.

Safety audit

It is the procedure of assessment of the safety measures employed for the road. It has the advantages like proper planning and decision from beforehand ensures minimization of future accidents, the long term cost associated with planning is also reduced and enables all kinds of users to perceive clearly how to use it safely. Safety audit takes place in five stages as suggested by Wrisberg and Nilsson, 1996. Five Stages of Safety Audit are:

1. Feasibility Stage – The starting point for the design is determined such as number and type of intersection, relationship of the new scheme to the existing road, the relevant design standards.
2. Draft Stage – In this stage horizontal and vertical alignment, junction layout are determined. After the completion of this stage decision about land acquisition is taken.
3. Detailed design stage – Signing, marking, lighting, other roadside equipment and landscaping are determined.
4. Pre-opening stage – Before opening a new or modified road should be driven, walked or cycled. It should be done at different condition like bad weather, darkness.
5. Monitoring of the road in use – Assessment is done at the final stage after the road has been in operation for few months to determine whether the utilization is obtained as intended and whether any adjustment to the design are required in the light of the actual behavior of road users.

An example of safety audit is discussed below.

Road reconstruction safety audit

To estimate the effectiveness of improvement of dangerous section the number of accidents before and after is compared. To do this Chi Square test is used to check whether the experimental data meet the allowable deviation from the theoretical analysis. In the simplest case one group of data before and after road reconstruction is considered.

(22)

where,  and  = period of time before and after reconstruction of a stretch of road for which statistical data of accident is available,  and  = corresponding numbers of accident, = minimum values of Chi Square at which probability of deviation of laws of accident occurrence after reconstruction P from the laws existing before reconstruction does not exceed permissible values (usually 5%) The relationship between P and  is shown in Table. 2.

Table 2: Relationship between P and 

P	10	8	5	3	2	1	0.1
	1.71	2	2.7	3.6	4.25	5.41	9.6

Numerical example

Before reconstruction of an at-grade intersection, there were 20 accidents during 5 years. After reconstruction there were 4 accidents during 2 years. Determine the effectiveness of the reconstruction.

Solution:

Using Chi square test, we have (with P = 5 %)

<img width=”317″ height=”64″ align=”MIDDLE” border=”0″ src=”https://www.civil.iitb.ac.in/tvm/1111_nptel/582_Accident/plain/img167.png&#8221; alt=”$\displaystyle X^2 = \frac{(20 \times 2 – 4 \times 5)^2}{5 \times 2(20 + 4)} = 1.67 \,\,

Thus the statistical data available are not yet sufficient for considering with probability of 95 % that the relative reduction in number of accident is due to intersection reconstruction. Assuming one more accident occurs next year.

\,\, 2.7$”>

Therefore additional analysis confirms that the reduction in accident is due to road reconstruction.

Conclusion

This chapter provides an important subject of highway safety and accident studies. Everything a traffic engineer does, from field studies, planning and design; to control operation is related to the provision of the safety system for vehicular travel. This chapter gives an insight of how the analysis of traffic accident can be done from the viewpoint to reduce it by designing proper safety measure.

References

1. Road accidents in india, 2009.
2. V F Babkov. Road Condition and traffic safety. MIR Publishers, Moscow, 2019.
3. J Stannard Baker. Traffic Accident Investigation Manual. The traffic Institute Northwestern University, 2019.
4. Milan Batista. On the mutual coefficient of restitution in two car collinear collisions, 2006.
5. S K Khanna C E G Justo. Highway Engineering. Nem Chand and Bros, Roorkee, 2001.
6. K W Ogden, S Y Taylor. Traffic Engineering, and Australia. Management. Monash University. Melbourne. Traffic Engineering and Management. Monash University Melbourne, Australia, 2019.
7. Louis J Pignataro. Traffic Engineering. USA, 2019.

Acknowledgments

I wish to thank my student Ms. Apurba Ghosh for his assistance in developing the lecture note, and my staff Ms. Reeba in typesetting the materials. I also wish to thank several of my students and staff of NPTEL for their contribution in this lecture.

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