Analysis of Signal Intersection Design in Road and Traffic Engineering

This report delves into the principles of road and traffic engineering, focusing on the design and analysis of signalized intersections. It explores the importance of traffic signals in managing road users and mitigating traffic congestion in urban environments. The report covers key concepts such as phase design, cycle length determination, green splitting, saturation flow, and the calculation of lost time. It also highlights the application of Webster's method for signal timing design, providing a detailed methodology for analyzing and optimizing traffic flow at intersections. The report examines the calculation of cycle time, operational green time, and lane capacity, providing a comprehensive overview of intersection performance analysis. Through the use of mathematical representations and real-world examples, the report provides a practical understanding of the challenges and solutions involved in designing effective and efficient signalized intersections.

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ROAD AND TRAFFIC ENGINEERING
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Introduction
Many cities and town around the world highly depend on the application of traffic signal
to efficacy control the road users like pedestrians, vehicles, motorcycles among others (Stokes,
2014). Several towns worldwide have employed the principle of time-sharing to effectually
prevent problems that may arise in the roads as a result of the overwhelming number of traffic in
major cities (OECD, 2016). Many benefits arose from the usage of traffic signals to manage the
traffics, this includes but not limited to ensuring the traffic move orderly, various intersections
have increased in their effective capacity, and lastly design an intersection signal does not
require much rocket science, since designing such geometry is quite simple (Zyczkowski, 2013).
Notwithstanding the numerous advantages accrued to such intersections, some challenges
arise in their usage. This includes delays due to large stoppage times and their design and
implementation are relatively complex (Rampino, 2012). Regardless of the overall stoppage
being less compared to those in the rotary systems especially in higher volumes, so users have
cried foul due to they're characteristically delays in stoppages (Vogt, 2014).This report tries to
analyze the various concepts and theories in signal intersection design that encompasses matters
such as the design of phase, the design of cycle length and green splitting. The theory
surrounding the saturation flow is and calculating lost time are equally highlighted in the report.
This report adopts some notations and some technical definition that shall be used in the
subsequent sub-headings (Studies, 2013).
Glossary
The following notations and definition is deemed important to be used in interpreting the signal
design

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i. Intervals:
This shows alternations from one signal stage to the next. Two types exist in the interval domain,
change interlude and clearance interlude (trafikinstitut, 2017). Change duration similarly referred
to as time of the yellow signal shows the duration between red and green traffic signals during
one approach whereas go-ahead also referred to as all red is the duration when the traffic signal
shows all red mainly used to clear vehicles in the other side of the intersections (Guthrie, 2011).
ii. Phase:
This is a combination of green interval and the change plus clearance which follows. In the
green interval, the movement which is not conflicting gets assigned into their respective phases
(Peden, 2013).
iii. Lost Time:
This shows the time when a particular intersection does not fully get used for any traffic
movement. This is typical when a front driver takes too long to react to a new green signal and
takes some time to speed off.
iv. Green interval:
This is the duration when it is a go for a particular section of the intersection usually represented
by means of Gi. This is the real time when the light is turns green.
v. Red Interval:
This is the duration when the intersection signal shows red in a particular movement.

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vi. Cycle:
A complete cycle of the traffic through all the various points of indications used.
vii. Cycle length
Is the time measured in seconds for the traffic signal to finish all the indications in the cycle.
In other words, it measures the time taken for green light to reappear again. In the report, C
will denote it (Mohan, 2016).
Phase Design
Design of a signal is a typical ten Webster’s Method. This includes,
1. Design of Phase
2. determination of amber and the subsequent clearance time
3. Determination of length cycle
4. Green time apportionment
5. Requirements for pedestrian crossing
6. Evaluation of performance.
7. Checking the porotypes
8. Testing the workability
9. Webster analysis
10. Hypothesis of Webster
The main objective of the design is to give a difference in movement conflicts in the
underlying step. This warrants no conflict in the phases (Transport, 2011). It is the aim of a civil
engineer to develop a flawless design that has minimal conflicts in the intersection. A standard

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methodology has not been adopted for designing the intersections since it is a subject of the
geometry of the various intersections, and the flow magnitude (Pierse, 2011). The defector
standard has been a trial and error approach to the solution. However, the design of phase is quite
vital in the whole process and if not well-designed can adversely affect the other steps and hence
the whole intersection performance. And this can be illustrated in the diagram below for the four
lagged intersection.
Fig 1: Showing Four Legged Intersection
Cycle Time
Cycle time is actually the time a signal takes to complete a cycle. C represents cycle time,
Departure from the intersection illustrated in diagram above is as follows, immediately the signal
resets, the interval in time amid two motor vehicles also referred to as headway. The primary
headway denotes the interval of time from the beginning of green indication to the instantaneous
vehicle intersecting the restriction stripe other headways following are plotted as shown in the
figure above (Lucas, 2013). It is assessed that the opening movement will be comparatively
lengthier since much time is lost during the driver reaction time and his/her effective
acceleration. It is also assumed that the second driver's headway will be ahead of the first driver

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headway because of lower reaction time compared to the first drive. Once few vehicles have
crossed the intersections, the headways are deemed to be constant, until they reach a saturation
headway represented by the symbol h, which is the headway that can be reached at through a
constant movement of a pool of automobiles (Transport, 2014).
Operational Green Time
This is the available time an automobiles taken to cross safely an juction. It is a
summation of the effective green phase (Gi ) and yellow signal to border amount of lost time
(Stern, 2012). The time lost can be understood as per the summation of entirely the time lost
during start-up (l1) and time lost during clearance (l2) (Andersson, 2011). Therefore the actual
green time depicts the following formulae,
Gi=Gi+Yi-to . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lane Capacity
The calculation of the ratio between the effective green time and the length of the cycle gi/C
gives us the green ratio and as defined earlier, saturation flow is the number of automobile
flowing through an intersection in one hour with the assumption that it will always be green
throughout (Bartolomeos, 2012). Thus lane capacity is depicted as follows,
ci = si gi /C
Where the ci represent the lane capacity in a automobile for every hour, while si represent
capacity of traffic flow measured in a automobile for every hour per lane, C represents time of
cycle measured in seconds (Mohan, 2012).

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This report indicates the various steps to be followed in measuring the effectiveness and
efficiency of an intersection based on its lane capacity, saturation, the green ratio among other
mathematical representation. The above notation is vital in the analysis of the intersection shown
above in the assignment
Figure 2 Intersection Timing
Analysis of the Intersection
Several approaches have been developed to aid in developing algorithms to design signal timing
for intersections especially the four-legged type provided in the assignment, A typical algorithm
that encompasses ten steps was developed by a British Mathematician called Dr. Mehmet M.
Kunt. The algorithm is called Webster and detailed usage in the analyzing and design of the
timing of signals for the above intersection is explained below (Forum, 2014).
Webster’s Method for Signalization
Considering the below four-legged geometry of an intersection, //diagram. There are many
design issues in the above figure, first, the design necessities to be either a two, three even more

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phases for the intersection. And in this design, a four-phase signal design is ideal for
implementation purposes.
Methodology
The Webster method design assumes that the driver is able to make a stop at exactly the stoppage
line when the signal turns red (Lucraft, 2015). To calculate the change interval for the
intersection, the following algorithm has been adopted
y=t+ v 85 /2 a+19.6 g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Where y=duration of the yellow interludes in seconds
t=driver’s reaction time
v85=85th percentile speediness of impending vehicles in m/s
the a=braking rate of vehicles
g=rating of approach in decimal
Design of the Signal
To perfectly design timing of signal for a particular intersection, the aim of the designer
is to come up with the maximum effective traffic flow capacity approaching the intersection. The
design should also purpose at guaranteeing the smallest magnitude of interruptions and building
comparatively smaller queue and again providing the maximum chance of the traffic passing on

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the first particular period for mainstream users (Dawson, 2011). The timing of the signal should
take into a lot of consideration the general flow of traffic through the intersection. The length of
the cycle is generally 40 to 60 seconds for two-phase signal, longer ones are designed for more
complex traffic with more than two phases (Krul, 2011).
For a design to be achieved, the following algorithm should be used,
 First, find the volume of traffic for different roads and or directions
 Finding the breadth of the roads
 The product attained are key inputs for the results of the road traffic capacity, planning
signal timing centered on the procedures provided by a specific method of design
Calculations
The volume of the total traffic, Vt Is the summation of the individual traffics through the various
intersection approaches.
Volume traffic from the southern approach (Vs) is calculated as the summation of the total
number of vehicles passing from south
i.e V s = ( 70+8 ) + ( 550+66 ) + ( 15++5 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
=714 vehicles
The volume of traffic approaching from the western, WV side of the intersection is the
summation of all the traffic through the individual lanes of the approach.
V w= ( 30+8 ) +(450+50). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
=538 vehicles

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The amount of traffic flowing from the northern approach Vn of the intersection is the summation
of the traffic through the individual lanes through the northern approach.
V n= ( 38+6 ) + ( 470+ 81 ) + ( 55+12 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
=662
The volume of traffic flowing from the eastern approach V e is the summation of the individual
traffic in the lanes in the eastern approach of the intersection,
V e= ( 21+9 ) + ( 990+40 ) +(20+3)
¿ 1083
The total volume of the traffic V t = ( 714+538+662+1083 )
¿ 3001 vehicles
From the calculation, it is evident that the total number of vehicles to schedule to pass through
the intersection is 3001 vehicles, Both the commercial and other vehicles, To drill it down
further, the total number of commercial vehicles from different approaches can also be
determined from the above diagram.
The total volume of commercial vehicles V sc approaching the intersection from the southern
approach is the individual summation of the commercial vehicles in the individual lanes from the
southern approach,
V sc= ( 70+550+15 )
¿ 635

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The total volume of commercial vehicles approaching the intersection from the western V wc
appthe roach is the summation of the individual commercial traffic from the lanes from the
western approach,
V wc =(30+ 450)
¿ 480
The total volume of a commercial vehicle approaching the intersection from the northern
approach V nc of the intersection is in the individual sum of commercial vehicles in the individual
lanes in the intersection from the northern approach.
V nc=38+ 470+55
¿ 563
The total volume of the commercial vehicles approaching the intersection from the eastern
approach V ecof the intersection is the summation of the individual commercial vehices in the
individual lanes,
V ec=21+990+20
¿ 1031
Total number of commercial vehicles deemed to pass through the intersection V c is summation
of the individual commercial vehicles from the different approaches
V c=V sc+V wc +V nc+V ec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
= 635+ 480+563+1031
= 2709

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The noncommercial vehicles passing through the intersection from the given approaches is the
difference between the total vehicles through the specific approach and the commercial vehicles
through that approach.
The non-commercial through the southern approach V ns is given as follows
V ns=714−635
¿ 79
The non-commercial vehicles through the western approaching V nw is given as follows
V nw=538−480
¿ 58
The non-commercial vehicles through the northern approach V nn is given as follows
V nn=662−563
¿ 99
The noncommercial vehicles through the eastern approach V ne is given as follows
V ne=1083−1031
¿ 52
Width of Road
The width of the road is as well a significant parameter in the signal timing design and it
determines the rate of traffic flow, from the four-legged intersections in question, the width of
the two roads can be obtained using the following equations