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.

Bibliography

Bocarejo, J., Tafur, L. (2013). Urban Land Use Transportation Driven by an Innovative

Transportation Project, Bogotá, Colombia. Global Reports on Human Settlements,

2013.

Wu, N., & Giuliani, S. (2016). Capacity and Delay Estimation at Signalized

Intersections under Unsaturated Flow Condition Based on Cycle Overflow Probability.

Transportation Research Procedia Vol. 15, pp.63-74.

Beauchamp-Baez, G., Rodriguez-Morales, E., & Muniz-Marrero, E. (1997). A Fuzzy

Logic Based Phase Controller for Traffic. Proceedings of the Sixth IEEE International

Conference on Fuzzy Systems Vol. 3, pp. 1533-1539.

Zakariya A., & Rabia S. (2016). Estimating the minimum delay optimal cycle length

based on a time-dependent delay formula. Alexandria Engineering Journal Vol. 55. Pp-

2509-2514

Li, M., Boriboonsomsin, K., Wu, g., Zhang, W., Barth, M. (2009). Traffic Energy and

Emission Reductions at Signalized Intersections: A Study of the Benefits of Advanced

Driver Information. International Journal of ITS Research, Vol. 7, No. 1, June 2009

Fajardo, C. (2010). Optimización del Tiempo Efectivo de Verde por Medio del Cambio

del Orden de las Fases y Recalculo de los Tiempos Entreverde para la Intersección de la

Calle 94 con Carrera 9 de Bogotá, Colombia. Universidad de los Andes.

Retzko, H., & Boltze, M. (1987). Timing of Inter-green Periods at Signalized

Intersections: The German Method. ITE Journal, pp. 23-26.

Road and Transportation Research Association. (1992). Guidelines for Traffic Signals

RiLSA. Darmstadt, Germany.

Robles, D., Ñañez, P., Quijano, N. Control y simulación de tráfico urbano en Colombia:

Estado del arte. Universidad de los Andes, 2009.

TRB. (2000). Highway Capacity Manual. National Research Council.

Wolfermann, A. (2009). Influence of Inter-green Times on the Capacity of Signalised

Intersections, Doctoral Thesis, Chair of Transport Planning and Traffic Engineering,

TU Darmstadt, 2009.

Unda, R., and A. Rodriguez-Valencia. Operational Effects for Pedestrian and Motorized

Traffic of Channelized Right-Turn Lanes at Urban Signalized Intersections.

Universidad de los Andes, 2016.

Tovar, S., and A. Rodriguez-Valencia. Effect of phase sequence in capacity in

signalized intersections. Universidad de los Andes, 2010.