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UNIVERSIDAD DE LOS ANDES
EFFECT OF GEOMETRY AND PHASE ORDER ON CAPACITY AND
DELAYS IN SIGNALIZED INTERSECTIONS
Author: Nicolás Jaramillo M. Student Civil Engineering n.jaramillo12@uniandes.edu.co
Supervisor: Alvaro Rodriguez–Valencia Assistant Professor Department of Civil and Environmental Engineering
A thesis submitted in fulfillment of the requirements for the degree of Civil Engineering
in the
Engineering Faculty Universidad de los Andes
December 14, 2018
Abstract Bogota has designed traffic networks according to the design manual used and developed
in Colombia. However, it is based on the German guidelines RiLSA, which will be briefly
explained through this document. Additionally, the method for calculating inter-green
times using the same guidelines will be described. On the other hand, it has been found
that changing the phase order sequence of the traffic lights in signalized intersections has
a positive impact on interaction capacity and traffic delays. This paper evaluates the
impact of changing the phase order sequence of traffic lights by changing the geometry
of the medium size separator of a four access, 4-phase, all-green intersection which
provides all possible turns, at the same time. This analysis uses the German
microsimulation software PTV-Vissim, considering six signal plans varying the phase
order, and five different scenarios changing the dimension of one axis of the intersection,
which for practical terms will be the width of the separator. Results have been focused on
the vehicle delay and capacity of the intersection. Finally, one real case study will be
exposed, and the potential resulting improvement will be presented.
Keywords Intersections, traffic lights, geometry, phase order, capacity, delay.
Introduction
Urban signalized intersection capacity is linked to the traffic signal lights. However, it
also depends on the movements and turns the vehicles are allowed to do in each
intersection, taking into account that left turns are one of the most critical maneuvers
(Wolfman, 2009). Since inter-green times depend on the geometry of the intersection,
Wolfman found that these times can deteriorate the capacity (Wolfman, 2009).
According to the article “A Fuzzy Logic Based Phase Controller for Traffic”, in signalized
intersections that have poorly designed traffic lights, inter-green times contribute to the
increase of time delay, accidents, pollution and fuel consumption (Beauchamp-Baez,
Rodriguez-Morales, & Muniz-Marrero, 1997). Therefore, inter-green times can be
optimized without safety concerns for three reasons: Low traffic flow that does not justify
some inter-green times; conflicts leading to long inter-green times that can be prevented;
the variability of the inter-green times parameters can be reduced.
Since the intersection’s geometry affects entering and clearing times as they are function
of the distance, then inter-green times will be affected as well. Consequently, the effective
green time is also influenced. Taking into consideration the following relationship, for
longer inter-green times the capacity will be reduced, and delays will increase; on the
other side, for longer effective green times the capacity will increase, and delays will
decrease. Thus, there is a latent capacity in signalized intersections that can be exploited
(Wolfman, 2009).
This research project assesses the simultaneous effect of geometry and phase order in a
four phase intersection with all-green times for each entrance, on the capacity and delays
of the intersection. In order to answer the question, first it will be introduce the German
Guidelines to design traffic signal lights, which inspires the Colombian Guidelines. Then,
it analyzes the effect of the inter-green times and effective green time calculated by this
method, for five intersections having different geometries. Finally, we designed an
experiment with the five intersections aiming to isolate the effect of the geometry in the
inter-green times which then affects the capacity of the intersections. Results have been
focused on delay reduction and will be analyzed and concluded.
Background
Throughout decades there has been numerous studies in signalized intersections, which
shows how the capacity can be improved. In fact, Tovar demonstrates in the article Effect
of phase sequence in capacity in signalized intersections that the capacity of the
intersection can be increased by changing the phase order of the signal lights (Tovar,
2010). Tovar found out that, specifically for the intersection of the street 94 with 9, in
Bogota Colombia, if the phases are assigned in a clockwise sequence, there is an increase
of approximately 10% in the capacity.
RiLSA
The RiLSA are the German guidelines for traffic signal lights and intersections (Robles,
D., Ñañez, P., Quijano, N., 2009). Currently, Colombia uses a specific manual1 for the
planning and design of the administration of traffic and transport, which is based on the
RiLSA. Specifically, for signalized intersections, this Manual uses the same rules and
equations of RiLSA that are going to be explained next.
The RiLSA guidelines define the inter-green time as “the interval between the end of the
green time for one traffic stream and the beginning of the green time for the next, crossing
or entering traffic stream” (Road and Transportation Research Association, 1992). It is
important to mention that the German guidelines consider the trajectories of the current
cars and the entering movements to the worst conflict area in the interior of the
intersection, in pursuance of calculate safe operation, placed on kinematic straightforward
procedures.
To clarify, the joint surface where both trajectories overlap is known as the conflict area
of disagreeing movements between vehicles at the interior of the intersection. Now, those
inter-green times are calculated for all possible movements and summarized in a matrix
called inter-green times matrix.
RiLSA define inter-green time as 𝑡𝑧:
𝑡𝑧 = 𝑡ü + 𝑡𝑟 − 𝑡𝑒
Where:
𝑡ü = 𝑂𝑣𝑒𝑟𝑟𝑢𝑛 𝑡𝑖𝑚𝑒
𝑡𝑟 = 𝐶𝑙𝑒𝑎𝑟𝑖𝑛𝑔 𝑡𝑖𝑚𝑒
𝑡𝑒 = 𝐸𝑛𝑡𝑒𝑟𝑖𝑛𝑔 𝑡𝑖𝑚𝑒
Now, it is important to know how the guidelines define each of the terms mentioned
above. First, the clearing time is the time required for the last vehicle passing the stop line
to drive the clearing distance before the signal light turns to red. Then, it is essential to
know the clearing distance, it is defined as the distance from the stop line to the conflict
area adding the approximate length of the vehicle.
𝑡𝑟 =𝐿𝑟+𝐿𝑣
𝑣𝑟
On the other hand, the entering time is the time required for the vehicle to drive from the
stopline to the conflict area just after the traffic light turns to green. The Manual and the
RiLSA recommended to use a velocity of 40 km/h.
1 Manual de Planeación y Diseño para la Administración del Tránsito y el Transporte
𝑡𝑒 =3.6 𝐿𝑒
40
One of the most difficult variables to contemplate and analyze is the behavior of drivers,
which can be imprudent, careless or neglectful. Due to this situation, some safety factors,
that work as a buffer for the entrance and clearance times in the intersection, have to be
taken into consideration. For example, the clearing speed for straight-ahead movements
is 𝑣𝑟=10m/s (according to guidelines aplication), which is 1.4 times lower than the regular
speed limit for urban roads 𝑣𝑚𝑎𝑥=50km/h. Furthermore, the time that the entering
vehicule takes from standstill condition to start when the light turns green and pass the
stop line it’s assumed as 40km/h.
Now, the overrun time refers to the period between the end of green light time and the
moment when the last vehicle passes over the stop line at the end of that green light time.
It is also known as amber time, defined as the time between green and red light. This fact
points towards the fact that the last car which is exiting the intersection, after crossing the
stop line, will be holding the interaction even though the light is already red. Moreover,
yellow time 𝑡𝑣 is well defined as the permissible speed of the access, so the amber time
depends on and it is proportional to the permissible speed of the vehicle as it shows the
next table:
𝒕𝒗 (s) Speed (km/h)
3 50 km/h or lower
4 60 km/h
5 70 km/h
Table 1 Yellow time for permissible speed
Context
Bogota has approximately 1400 signalized intersections. Nowadays, the city is in the
process of replacing all the traffic lights. For the second semester of 2019, they must
finish building 54 new signalized intersections and adapt 240 in order to have greater
security for citizens. Additionally, for the same period, all maintenance must be
completed, and every signalized intersection must be in operation.
Bogota has around 10 million inhabitants including the nearby municipalities. This is one
of the reasons why there are severe traffic congestions everywhere. This is a disheartening
prospective, as the actual mobility secretary of Bogota mentioned in Urban Land Use
Transformation Driven by an Innovative Transportation Project, Bogota, Colombia, “the
growing wealth of the population is generating an accelerated increase in motorization”
(Bocarejo, J., Tafur, L., 2013). For this reason, an increase in capacity in signalized
intersections becomes part of a solution that the city can adopt, in order to reduce traffic
congestions and to improve the quality of life of Bogota citizens.
Problem Definition
This paper analyses the inter-green times for several, theoretically calculated, scenarios
to see what the impact of phase order in the signal lights in each scenario is. Then, using
the software PTV-Vissim 9, we analyze a four access, 4-phase, all-green intersection
which provides all possible turns to evaluates intersection by using microsimulation to
explore what the improvements of phase sequence are, when the geometry and the effects
on delays and capacity of the signalized intersections are taken into account.
The following figure, shows our object of study, a four-entrance intersection. The
possible maneuvers are also illustrated as well as the nomenclature used to label those
movements. The subsequent table summarize the phases and movements.
Figure 1 Phase Order
Phase Movements
Phase I 1
2
3
Phase II 4
5
6
Phase III 7
8
9
Phase IV 10
11
12 Table 2 Phase Order and Vehicle Movements
Then, it is going to be explained the six signal plans within each scenario. This means
each signal plan has a different phase sequence of the traffic lights. The next table shows
all the possible combinations between the phases.
Additionally, we studied the effects of the inter lane distance x, on the performance of the
intersection. These effects will be studied while varying the distance x in only one
direction, as illustrated in the figures that follow. The results of the computations are
shown in the next figures, one for each scenario. The lane separation distance is
represented by the yellow rectangle. In the figures that follow.
Figure 2 Scenario 1: X = 0 Meters
Signal Plan Phase Sequence
1 I II III IV
2 I II IV III
3 I III II IV
4 I III IV II
5 I IV II III
6 I IV III II
Table 3 Signal Plans within each scenario
Table 4 Inter-green Times Scenario 1: X = 0 Meters
Figure 4 Scenario 3: X = 10 Meters
Table 5 Inter-green Times Scenario 2: X = 5 Meters
Figure 3 Scenario 2: X = 5 Meters
Table 6 Inter-green Times Scenario 3: X = 10 Meters
Figure 5 Scenario 4: X = 15 Meters
Figure 6 Scenario 5: X = 20 Meters
Method
To explore what the benefits and improvements of changing the phase order of the signal
lights could be and what the impact of the geometry is, two main criteria have been
chosen. The first one is the vehicle delay, which is defined as the additional time that the
drive will experience, or the difference between the time traveled with traffic or
interruptions and the theoretical time without interruptions. (Wu, N., & Giuliani, S.,
2016). The vehicle average delay is calculated with the following formula.
𝑉𝐴𝐷 = ∑ 𝑚𝑜𝑑𝑒 𝑢𝑠𝑒𝑟𝑠 ∗ 𝑚𝑜𝑑𝑒 𝑎𝑣𝑎𝑟𝑎𝑔𝑒 𝑑𝑒𝑙𝑎𝑦
Table 7 Inter-green Times Scenario 4: X = 15 Meters
Table 8 Inter-green Times Scenario 5: X = 20 Meters
The second criteria selected is capacity, specifically the capacity of the intersection. This
means how many more vehicles could travel through the intersection in one cycle. Yet,
the capacity undoubtedly depends on the vehicle delay as it can be seen with the following
relationship.
𝑑 (𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦)
𝑑 (𝐷𝑒𝑙𝑎𝑦)< 0
As we can see on the previous equation, the derivate of capacity over the derivate of delay
is negative. In other words, it can be said that to increase the capacity of any intersection,
it can be done by reducing the average vehicle delay on the same intersection. In
conclusion, the delay is inversely proportional to the capacity of the intersection as the
next equivalence shows.
< 𝐷𝑒𝑙𝑎𝑦 → > 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦
> 𝐷𝑒𝑙𝑎𝑦 → < 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦
Experiment Design The following table shows the assumptions with its corresponding conditions taken into
consideration with the experiment design. It is necessary to mention that pedestrians were
not taken into account for the microsimulation in the software PTV-Vissim 9. Another
important condition is the vehicle speed chosen, considering Bogota’s context, traffic and
speed limits, 50km/h is the most adequate speed. However, it is reduced to 30km/h, for
vehicles that turn. This is the speed recommended in the manual used in Bogota for
planning and design for traffic and transport.
Assumptions Conditions
Time signal phase All traffic lights phases are 120s.
Lane width 3.6m
Vehicle composition 100% Cars
Vehicle approach speed 50 km/h
Vehicle turning speed 30 km/h
Proportion of turns 25% Left – 50% Straight – 25% Right
Controlled Range
Geometric design
Scenario 1: X = 0 Meters
Scenario 2: X = 5 Meters
Scenario 3: X = 10 Meters
Scenario 4: X = 15 Meters
Scenario 5: X = 20 Meters
Traffic Volume Saturated Table 9 Simplifications and controlled variables
Additionally, it is essential to indicate that the traffic is saturated during the whole
experiment, this means there is always a row of vehicles in all the four entrances waiting
for the traffic light to change to green, it has been chosen scenario 2: X = 5 meters to
show that the traffic volume is saturated. The subsequent figure demonstrates the previous
affirmation,
Figure 7 Scenario 2: X = 5 Meters. Software: Vissim 9
Microsimulation
In order to perform all the simulations in the experimental design, the German software
PTV-Vissim 9 has been used since microsimulation models have a stochastic component,
random variables are considered. Nevertheless, each scenario could not be run just one
time; to get reliable results each scenario must be run a certain amount of times. Hollander
and Liu present a formula for calculating the number of runs required for the experiment
(Hollander and Liu., 2008)
𝑅 = (𝑠. 𝑡𝛼
2⁄
𝑥. 𝜀)
2
Where:
𝑅 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑢𝑛𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡
𝑠 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑟𝑎𝑓𝑓𝑖𝑐 𝑚𝑒𝑎𝑠𝑢𝑟𝑒
𝑥 = 𝑀𝑒𝑎𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑟𝑎𝑓𝑓𝑖𝑐 𝑚𝑒𝑎𝑠𝑢𝑟𝑒
𝜀 = 𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦, 𝑎𝑠 𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑥
𝑡𝛼2⁄ = 𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑆𝑡𝑢𝑑𝑒𝑛𝑡´𝑠 𝑡 − 𝑡𝑒𝑠𝑡
On the contrary, the vehicle delay and capacity calculation depend on several factors,
described in the experiment design. However, are all the possible factors that affect the
outflow rate of each approach entrance, for example randomness of traffic and lane
changing, were not mentioned previously (Wolfmann, 2009)
Results and analysis As it has been mentioned before, is important to have in mind which are the different
scenarios and the several signal plans that we are studding in order to comprehend the
succeeding results. Hence, table number three and figures from two to six summarizes
both, the scenarios and the signal plans. Taking into account that the geometry is the
variable that increase five meters for each scenario, additionally the phase order of the
signal plan (each signal plan is defined as a different sequence combination of the traffic
lights) changes within each scenario, all the six signal plans have been studied in each
scenario.
Scenario Signal Plan Phase Sequence
1
X = 0 Meters
1 I II III IV
2 I II IV III
3 I III II IV
4 I III IV II
5 I IV II III
6 I IV III II
2
X = 5 Meters
1 I II III IV
2 I II IV III
3 I III II IV
4 I III IV II
5 I IV II III
6 I IV III II
3
X = 10 Meters
1 I II III IV
2 I II IV III
3 I III II IV
4 I III IV II
5 I IV II III
6 I IV III II
4
X = 15 Meters
1 I II III IV
2 I II IV III
3 I III II IV
4 I III IV II
5 I IV II III
6 I IV III II
5
X = 20 Meters
1 I II III IV
2 I II IV III
3 I III II IV
4 I III IV II
5 I IV II III
6 I IV III II Table 10 Summarize of Scenarios and Signal Plans
The following tables show the results specifically for scenario number one. This
demonstrates the benefits of changing the phase order in a traffic light. As it can be seen,
signal plan number six is the one that has less vehicle delay, in fact it improves in
approximately 8.6% in comparison to the worst case, signal plan number one. This
indicates that for scenario one the phases order clockwise is the one that gives less delays.
Figure 8. Vehicle Delay Signal Plan 1
Figure 9. Vehicle Delay Signal Plan 2
Figure 10. Vehicle Delay Signal Plan 3
Figure 11. Vehicle Delay Signal Plan 4
Figure 12. Vehicle Delay Signal Plan 5
Figure 13. Vehicle Delay Signal Plan 6
Then, it is important to explore the impact of the phase order in the traffic lights taking
into account the geometry of the signalized intersection, the following graphics shows the
vehicle delay for the different movements as the geometry of the x-axis is changed, for
each scenario.
Figure 14. Vehicle delay scenario 0 meters.
Figure 15. Vehicle delay scenario 5 meters
Figure 16. Vehicle delay scenario 10 meters
Figure 17. Vehicle delay scenario 15 meters
Figure 18. Vehicle delay scenario 20 meters
These results show that increasing the geometry of the separator on the x axis of the
intersection increases the inter-green times which have a negative impact on the effective
green time. At the same time this has an influence on the delay times. As it can be seen
in the tables above the delay time increases with each scenario. However, signal plan 6
(clockwise phase order) is the one that leads to the shorter vehicle delays. This implies
that ordering the traffic lights in a clockwise sequence gives the best results. It is
important to mention that those are the ones that have the minor vehicle delay, which
means greater capacity, as the figure 20 displays.
CAPACITY IMPROVEMENT
Scenarios Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 5
Vehicles mean worst signal plan (Signal Plan 1)
830 808 783 764 742
Vehicles mean best signal plan (Signal Plan 6)
943 916 883 855 822
% of improvement 11.98% 11.79% 11.33% 10.64% 9.73%
Table 11 Capacity Improvement
The table above shows the capacity improvement of changing the phase order of the
traffic lights in each scenario. Specifically, it demonstrates how many more vehicles are
allowed to pass in the same amount of time. It can be seen that the geometry affects
negatively the number of vehicles that pass through the intersection, in fact in scenario
number one in the best signal plan there are 943 vehicles, meanwhile in scenario number
five only 822 vehicles passed leading to a difference of 121 vehicles, 10.6% which can
be significant for reducing travel times.
Next, a specific movement will be analyzed under each scenario. Movement 1 has been
chosen, since it is affected by enlarging the x axis of every intersection. From the graphic
below, we seek to explore what the effect of geometry is on the vehicle delay and,
consequently, on the capacity.
Figure 19 Movement 1
Figure 20. Vehicle Delay movement 1
Movement 1
Figure 20 shows the vehicle delay for movement 1, for all six signal plans and five
scenarios, the same ones that we have been working on. It demonstrates that signal plan
number six is the one that gives less vehicle delay, even though we take into account the
geometry evaluated in each scenario, it is the one that gives the best results. However, it
strongly proves that geometry does affect the vehicle delay. There are clear differences
between scenarios, as the x dimension of the intersection is enlarged, the vehicle delay
increases. Nonetheless, it can be improved by changing the phase order of the traffic
lights, since it is the one that provides shortestinter-green times and more effective green
time (signal plan number six).
Applications Currently there are signalized intersections which are similar to the ones studied in this
document, one of them is situated in the north of Bogota Colombia, precisely in the street
116 with 15 avenue. Figure 21 shows the intersection, as it can be seen it is a four-entrance
intersection which has 20.71 meters of platform, this includes a walking space and a
bicycle lane, this platform can be seen as the “x - dimension” of each scenario analyzed.
Figure 21 Actual Intersection Street 116 Avenue 15 Bogota, Colombia
Now, in figure 22, it can be seen an example of how the intersection can be transformed
in order to improve its capacity using the results found. We decided to channel the right-
turn lanes and reduce the platform dimension. This reduces the distance that is used as a
variable for calculating the inter-green times; it has been decided to leave it with 5 meters
for pedestrians and bike users. Consequently, inter-green times will be reduced, and
effective green time will be incremented. Therefore, vehicle delay will decrease, and the
capacity of this intersection will increase theoretically by 8.17%, which is the benefit of
passing from scenario number five to scenario number two.
Figure 22 Proposal Intersection Street 116 Avenue 15 Bogota, Colombia
Conclusions
Summarizing the experiments done, basically we designed 5 scenarios, having different
geometries. The separator located at the x axis enlarges five meters by each intersection.
Within each scenario we tried 6 different signal plans, to explore what is the best plan
depending on the geometry. This was conceivable through the use of the German software
Vissim 9 using microsimulation.
In conclusion, signal plan number six leads to the best results among the plans considered.
Is the one that minimizes vehicle delay. Additionally, scenario number 1 gives the greater
capacity for the intersection. The combination of these two variables leads to find out the
positive effect of geometry and phase order on capacity and delays in signalized
intersections. Setting x=0meter separator in the x dimension and phasing the traffic lights
clockwise yields a specific improvement of 12.8% in comparison to the larger scenario
where x=20 meters.
It has been found out that, for similar intersections, the geometrical design should
consider that, enlarging the dimensions will have a negative impact on the vehicle delay
and on the capacity. Thus, signalized intersections should be as small as possible without
affecting other actors, as pedestrians, cyclist or even drivers. Finally, it has been identified
that, independently of the geometry, the sequence of the traffic lights should be
configured clockwise for a better use of the signalized intersection.
Finally, this study opened an important discussion about the priority of the actors in the
intersections, since nowadays many countries are focusing all the benefits and facilities,
such as, larger walking lanes, ramps, longer walking times and wider crosswalks to the
pedestrians. Then, reducing the dimensions of the intersection could create conflicts and
polemical opinions about who needs more space and what policy is more beneficial to the
city.
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