chapter three :- traffic engineering studies.pdf

traffic engineering studies

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Chapter Three
INTRODUCTION TO TRAFFIC FLOW THEORY
3.1 Introduction
Traffic Flow Theory is a tool that helps transportation engineers understand and express the
properties of traffic flow. At any given time, there are millions of vehicles on our roadways.
These vehicles interact with each other and impact the overall movement of traffic, or the traffic
flow. Whether the task is evaluating the capacity of existing roadways or designing new
roadways, most transportation engineering projects begin with an evaluation of the traffic flow.
Therefore, the transportation engineer needs to have a firm understanding of the theories behind
Traffic Flow Analysis. The functional effectiveness of a highway is measured in terms of its
ability to assist and accommodate the flow of vehicles with both safety and efficiency. In order
to measure its level of effectiveness, certain parameters associated with the highway must be
measured and analyzed. These properties include:
 The quantity of traffic
 The type of vehicles within the traffic stream
 The distribution of flow over a period of time (usually 24 hours)
 The average speed of the traffic stream
 The density of the traffic flow.
Analysis of these parameters will directly influence the scale and layout of the proposed
highway, together with the type and quantity of materials used in its construction. This process
of examination is termed traffic analysis and the sections below deal with relationships between
the parameters which lie at its basis.
3.2 Fundamental Characteristics of Traffic Flow
 Flow rate(q)
Traffic flow can be divided into two primary types. Understanding what type of flow is occurring
in a given situation will help you decide which analysis methods and descriptions are the most
relevant.

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The first type is called uninterrupted flow, and is flow regulated by vehicle-vehicle interactions
and interactions between vehicles and the roadway. For example, vehicles traveling on an
interstate highway or freeway are participating in uninterrupted flow. The second type of traffic
flow is called interrupted flow. Interrupted flow is flow regulated by an external means, such as a
traffic signal, stop or yield sign. Under interrupted flow conditions, vehicle-vehicle interactions
and vehicle-roadway interactions play a secondary role in defining the traffic flow.
The traffic flow, q, a measure of the volume of traffic on a highway, is defined as the number of
vehicles, n, passing some given point on the highway in a given time interval, t, i.e.:



In general terms, q is expressed in vehicles per unit time
Flow is one of the most common traffic parameters. Flow is normally given in terms of vehicles
per hour. The 15-minute volume can be converted to a flow by multiplying the volume by four.
If our 15-minute volume were 100 cars, we would report the flow as 400 vehicles per hour. For
that 15-minute interval of time, the vehicles were crossing the designated point at a rate of 400
vehicles per hour
 Density (k)
Density refers to the number of vehicles present on a given length of roadway. Normally, density
is reported in terms of vehicles per mile or vehicles per kilometer. High densities indicate that
individual vehicles are very close together, while low densities imply greater distances between
vehicles. The number of vehicles on a given section of highway can also be computed in terms of
the density or concentration of traffic as follows:



Where the traffic density, k, is a measure of the number of vehicles, n, occupying a length of
roadway, l

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 Speed(U)
The speed of a vehicle is defined as the distance it travels per unit of time. Most of the time, each
vehicle on the roadway will have a speed that is somewhat different from those around it. In
quantifying the traffic flow, the average speed of the traffic is the significant variable. For a
given section of road containing k vehicles per unit length l, the average speed of the k vehicles
is termed the space mean speed u (the average speed for all vehicles in a given space at a given
discrete point in time).
Therefore:
Where (li) is the length of road used for measuring the speed of the (i)th vehicle. Similarly, the
time mean speed can be determined as the arithmetic mean of the speed of vehicles passing a
point during a given time interval. It can be seen that if the expression for q is divided by the
expression for k, the expression for u is obtained:

Thus, the three parameters u, k and q are directly related under stable traffic conditions:

This constitutes the basic relationship between traffic flow, space mean speed and density. In
addition to the above parameters, the following parameters are also important in the study of
traffic flow.
 Volume
Volume and Rate of Flow are two different measures. Volume is the actual number of vehicles
observed or predicted to be passing a point during a given time interval. Rate of flow represents
the number of vehicles passing a point during a time interval less than 1 hour, but expressed as
an equivalent hourly rate.

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Volume is simply the number of vehicles that pass a given point on the roadway in a specified
period of time. By counting the number of vehicles that pass a point on the roadway during a 15-
minute period, you can arrive at the 15-minute volume. Volume is commonly converted directly
to flow (Q), which is a more useful parameter.
Hourly Volumes and Their Use
 While daily volumes are useful in highway planning, they cannot be used alone for
design or operational analysis purposes.
 Traffic volume varies considerably during the course of a 24-hr day.
 The single hour of the day that has the highest hourly volume is referred to as the
“peak hour”.
 Traffic volume within this hour is of greatest interest to traffic engineers in design or
operational analysis.
 The variation within a given hour is also of considerable interest for traffic design and
analysis.
 The quality of traffic flow is often related to short-term fluctuations in traffic demand.
 A facility may have capacity adequate to serve the peak hour demand, but short-term
peaks of flow within the peak hour may exceed capacity, thereby creating a breakdown.
The relationship between hourly volume and the maximum rate of flow within the hour is
defined by the Peak Hour Factor (PHF).
Peak Hour Factor (PHF)
The ratio of the hourly flow rate (Q60) divided by the peak 15 minute rate of flow expressed as
an hourly flow (Q15).

Where, V = hourly volume, and V15 = maximum 15- minute volume within the hour.

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Daily Volumes and Their Use
 A common time interval for volumes is a day.
 Daily volumes are frequently used as the basis for highway planning and general
observations of trends.
 Traffic volume projections are often based on measured daily volumes
There are four commonly used daily volume parameters:
1. Average Annual Daily Traffic (AADT): is the average 24-hr traffic volume at a given
location over a full 365-day year.
2. Average Annual Weekday Traffic (AAWT): is the average 24-hr traffic volume
occurring on weekdays over a full 365-day year.
3. Average Daily Traffic (ADT): is an average 24-hr volume at a given location for some
period of time less than a year, but more than one day.
4. Average Weekday Traffic (AWT): is an average 24-hr traffic volume occurring on
weekdays for some period less than one year.
Headway, spacing, gap, and clearance are all various measures for describing the space between
vehicles.
Headway (h)
Headway is a measure of the temporal space between two vehicles. Specifically, the headway is
the time that elapses between the arrival of the leading vehicle and the following vehicle at the
designated test point. You can measure the headway between two vehicles by starting a
chronograph when the front bumper of the first vehicle crosses the selected point, and
subsequently recording the time that the second vehicle’s front bumper crosses over the
designated point. Headway is usually reported in units of seconds.
Spacing (s)
Spacing is the physical distance, usually reported in feet or meters, between the front bumper of
the leading vehicle and the front bumper of the following vehicle. Spacing complements
headway, as it describes the same space in another way. Spacing is the product of speed and
headway.

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Gap (g)
Gap is very similar to headway, except that it is a measure of the time that elapses between the
departure of the first vehicle and the arrival of the second at the designated test point. Gap is a
measure of the time between the rear bumper of the first vehicle and the front bumper of the
second vehicle, where headway focuses on front-to-front times. Gap is usually reported in units
of seconds.
Clearance (c)
Clearance is similar to spacing, except that the clearance is the distance between the rear bumper
of the leading vehicle and the front bumper of the following vehicle. The clearance is equivalent
to the spacing minus the length of the leading vehicle. Clearance, like spacing, is usually
reported in units of feet or meters.
3.3. Speed-density relationship
In a situation where only one car is travelling along a stretch of highway, densities (in vehicles
per kilometer) will by definition be near to zero and the speed at which the car can be driven is
determined solely by the geometric design and layout of the road; such a speed is termed as free-
flow speed as it is in no way hindered by the presence of other vehicles on the highway.
As more vehicles use the section of highway, the density of the flow will increase and their speed
will decrease from their maximum free-flow value (uf) as they are increasingly more inhibited by
the driving maneuvers of others. If traffic volumes continue to increase, a point is reached where
traffic will be brought to a stop, thus speeds will equal zero (u = 0), with the density at its
maximum point as cars are jammed bumper to bumper (termed jam density, kj). Thus, the
limiting values of the relationship between speed and density are as follows:
When k = 0, u = uf
When u = 0, k = kj.
Various attempts have been made to describe the relationship between speed and density
between these two limiting points. Greenshields (1934) proposed the simplest representation
between the two variables, assuming a linear relationship between the two (see Fig. 1).

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Fig -1 Illustration of speed- density relationship
In mathematical terms, this linear relationship gives rise to the following equation

This assumption of linearity allows a direct mathematical linkage to be formed between the
speed, flow and density of a stream of traffic. This linear relationship between speed and
density, put forward by Greenshields (1934), leads to a set of mathematical relationships
between speed, flow and density as outlined in the next section.
The general form of Greenshields’ speed-density relationship can be expressed as:
u = c1 + c2k
Where c1 and c2 are constants
However, certain researchers (Pipes, 1967; Greenberg, 1959) have observed non-linear behavior
at each extreme of the speed-density relationship, i.e. near the free-flow and jam density
conditions. Underwood (1961) proposed an exponential relationship of the following form:

Using this expression, the boundary conditions are:
 When density equals zero, the free flow speed equals c1
 When speed equals zero, jam density equals infinity.

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The simple linear relationship between speed and density will be assumed in all the analyses
below.
3.3.1 Flow-density relationship
Combining the equations for u and relations between flow, density and speed, the following
direct relationship between flow and density is derived:
Therefore

This is a parabolic relationship and is illustrated below in Fig. 2.
In order to establish the density at which maximum flow occurs, the above equation is
differentiated and set equal to zero as follows:

Since uf ≠ 0, the term within the brackets must equal zero, therefore

km, the density at maximum flow, is thus equal to half the jam density, kj. Its location is shown in
Fig. 2.

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Fig 2.2: Illustration of flow-density relationship
3.3.2 Speed-flow relationship
In order to derive this relationship, Equation above is rearranged as:

By combining this formula with u, the following relationship is derived:

This relationship is again parabolic in nature. It is illustrated in Fig. 3


Figure .3 Illustration of speed-flow relationship
In order to find the speed at maximum flow, Equation above is differentiated & put equal to zero:

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Since kj ≠ 0, the term within the brackets must equal zero, therefore

um, the speed at maximum flow, is thus equal to half the free-flow speed, uf. Its location is shown
in Fig. 3.
Combining um and km the following expression for maximum flow is derived: