PRE2016 3 Groep11

Introduction

With the expectations of the current car development as well as the current state of the art, it’s highly likely that autonomous cars will cooperate in traffic. The development steps, innovativity and the inventivity of big companies which support the production of autonomous cars, such as Tesla, BMW and Google, are - with an increasing rate of confidence - stating that it will be a matter of years before the first great share of autonomous vehicles on roads will be noticeable.

This will logically result in a mixture of both non-autonomous as well as self-driving vehicles. Autonomous vehicles have abilities with respect to reaction time and affiliation that are way advanced in comparison to human drivers. This will most likely be a cause of some interference between both of the vehicles with respect to the current traffic system. The differences that both vehicles have in reaction -and processing time can be unbeneficial for places where there is an almost continuous amount of much traffic.

This will especially occur in the rings of big cities, where the amount of traffic is big and chaotic most of the time. It is at this place in a city, where almost all other roads of the city can be reached. So these rings will be packed with traffic that has destinations in the city center, but also traffic from the city center that wants to reach out of the city bounds.

This report will be focusing on the development of a new system for traffic lights, so autonomous and non-autonomous vehicles will show more cooperation as well as an improved fluency. This project will look into the effects of a new traffic system that can be utilized on rings in the center of big cities. The density of traffic, the average speed, the passing time and CO2-emission are results that are aimed to look after in this report.

Authors

• 0960493 Tim Houthuijs
• 0934016 Kevin Jenniskens
• 0958509 Matthijs van Raaij
• 0948190 Sarah Rohder
• 0903327 Floris Tulner
• 0945501 Lars Verstraelen

Focus, Objectives and Approach

The goal of this project is to ultimately improve the traffic system which consists of several crossings by trying to add functionality to the individual traffic lights crossings to smartly create and use green waves. The new system tries to use this through the use of a time based order, similar to the path of a clock hand. In order to make sure that the new system compared to the old system is indeed better, it gets compared on five different variables:

• The average time it takes for an individual to drive to its destination
• How often a car has to stop during their trip
• How long a car has to stop when stopped
• How long a car has to stop on average for all cars
• The throughput of the system: How many cars pass the system within a set amount of time

These variables should lead to be able to answer the main question: Is the new system an improvement over the old traffic system?

Additionally, to answer this particular question, it has been divided into different sub-questions, which will ultimately lead to the conclusion to the final main question. The following sub-questions has been deemed interesting to answer:

• How does the old system work?
• How does the system take its different users into account?
• How does the old system work for more intersections?
• What exactly is a green wave?
• What exactly is the purpose of creating a green wave?
• What sensors are needed for this to work in the traffic system?

Focus

Requirements

• The traffic system is a ring
• 2-lane road, with near traffic lights left and right turn lanes
• Sensors in road around traffic lights to detect cars
• Speed and location of the cars can measured

Preferences

• Using green waving as much as possible
• The simulation needs to be as realistic as possible
• The spawning of the cars in the simulation needs to represent by realistic distribution

Constraints

• Cars cannot wait too long
• Emergency vehicles will not be simulated
• Each traffic light needs to make an estimation to determine the next traffic light state. This can be done with the Cost function of the previous group or an upgraded version of this.

Assumptions

• Cars do not drive through red
• All vehicles will stay below speed limitations

Approach

The project needed to be divided into several milestones:

• The old traffic system that was to be used as baseline needed to compare the new traffic system to needs to be extended to include more than one intersection.
• A first simple system using the new ‘clock’ based algorithm needs to be implemented.
• The simple system needs to be extended to a more advanced system, which is more realistic like.
• For every milestone background information and other relevant knowledge needs to be found, in order to successfully fulfil every milestone. A milestone should be completed before work on the following milestone can begin, however, in reality a lot of the background information and such will happen in parallel.

USE aspects

The situation that is developed in this Wiki is reminiscent of a situation that can be found in real life. Obviously, it is a simplified model of such a real life situation, but suitable for this project. However, even if the model is simplified, the different aspects of the real life equivalent should not be ignored. For instance, the role of the pedestrians that can be found trying to cross the ring are practically reduced to the assumption that that only happens when the light is red for the automobiles. However, to just ignore a such significant user of the traffic system in the Netherlands is quite brash. Thus, in this section the different USE aspects that are important to the specific simplified model of this project will be discussed, but also those in a similar real life situation, where the stakeholders should be the same.

Users

The users of the traffic system in the Netherlands consist of everyone participating in traffic. This ranges from users on wheels, such as automobiles and lorries, to pedestrians and cyclists. Even within these user groups there are different preferences and wishes to how the traffic system should look like. For instance, automobilists want to drive as fast as possible, while never having to stop for something else. Pedestrians want to safely walk alongside the faster traffic, such on curbs, and be able to cross the road where they need to. Obviously, this contradicts each other in a way. So, an overview of these different groups need to be made, such as can be seen in the list below.

Non-autonmous Car Owners

• Drive as fast as possible
• Nothing that slows down or stops their journey (such as traffic lights)
• If there is a waiting time, let it be as short as possible
• Good quality roads
• Everybody keeps to the traffic rules
• Pay as less as possible money for fuel

Autonomous Car Owners

• Drive as fast as possible
• Nothing that slows down or stops their journey (such as traffic lights)
• If there is a waiting time, let it be as short as possible
• Good quality roads
• Everybody keeps to the traffic rules

Pedestrians

• Safe place to walk
• Safe place to cross the road
• If there is a waiting time, let it be as short as possible
• Everybody keeps to the traffic rules

Cyclists

• Safe place to cycle
• Wants to cycle as fast as it can
• Nothing to slow down or stop their journey
• If there is a waiting time, let it be as short as possible
• Good quality roads
• Everybody keeps to the traffic rules

Special types of vehicles (ambulances, fire trucks)

• Being able to pass regular traffic in an emergency in a safe way
• Travelling time as short as possible
• Always green lights for any traffic light

Unfortunately, not all of these wishes can be granted, nor can all wishes be considered in this projects simplified model. For instance, a constraint of the model is that special vehicles, pedestrians, and cyclist will not be modeled into the system. Pedestrians and cyclist will be present, they will just not be separately simulated, as the assumption is that when the light is red for the ring users, then those two groups can safely cross the ring. Furthermore, since the simulation is based around optimising a traffic light-based system, it is difficult to grant the wish to all users that they never have to stop during their journey. However, the goal of this project is to try to optimise the waiting time, making it as short as possible for all present users. Additionally, this should also create a safer traffic environment for all involved, granting at least a few of the wishes of every user.

Society

The next important stakeholder in the ring-based traffic system is Society itself. Society also consists of the previous mentioned users, but also users that do not participate (at the moment) in the traffic system, thus keeping their wishes in mind as well. Furthermore, Society also has different interests and smaller stakeholders within, such as the environment, the economy, and ranking compared to other Societies (such as in a different country). An overview of the wishes in the Society needs be made, but it also needs to be clear what kind of different groups are represented in this projects Society,

Environment

• The CO2 emission should be lowered
• There should be less pollution
• No destroying the environment
• Society needs to be green, and look/see green (think planting trees and such)

Economy

• The quality of the traffic system should be at a minimum level, preferably higher
• Any change to the traffic system should be as cheap as possible
• Everybody needs to be able to reach their destination as fast as possible, since any delay costs *money

Compared to other Societies

• This Society needs to be the greenest
• It needs to have the safest roads
• It needs to have the highest quality of roads

Other User groups

• The roads need to be as safe as possible
• The roads need to be clean (think, no garbage from cars and such)
• The traffic should preferably be as far away from Society as possible

As can be seen, there are quite a few wide ranging wishes coming from Society. Some, such as the wish to have the highest quality of road material to be used in the roads are not relevant to this project in that it will not be simulated. However, the wish to make changes to the existing traffic system as low-cost as possible, and of course preferably even zero, is quite interesting. It will not be necessarily simulated or the goal of this project, but if the traffic system can be optimised using the concepts within this project without or barely changing the existing traffic system, then that would be quite a feat.

Enterprise

The last type of stakeholder are the entrepreneurs they are just as important to the traffic system as the User and Society stakeholders. The main stakeholders are the following:

• Car Manufacturers
  • they want to make as much money as possible
  • they want their product to be the most user friendly
• Oil companies
  • They want to sell their oil for the highest rate
  • They want cars to use much oil so they can sell more
  • They do not want cars to be energy sufficient
• Garages
  • They want to create trust between their customers
  • They want cars to be more fragile
• (GPS-manufactures)
• (Sensor-manufactures)

Car Manufacturers

Car manufactures like BMW, Audi, Kia, Tesla, and more all make new cars with new technology in them. One of these technologies is camera’s and park sensors, most new produced cars have them. These sensors can also be used to the to measure the distance between two cars. Some companies even use these kind of sensors to make the car semi self driving. These semi self driving cars have adaptive cruise control which works like a normal cruise control but now the car slows down when it comes to close to another car. This technology can be used to form a platoon. As we draw down to a conclusion it can be concluded that car manufacturers show their interest in these more autonomous kind of cars. To make sure their product stays top of the business.

The companies that will design and build the autonomous cars for instance, or the ones that will build any new updated traffic system will have quite an interest in an improved traffic system.

Literature research

For a project to be successful, research needs to be done. It is important to know what needs to be researched, which in this case includes information on how traffic lights gather information and how autonomous cars gather information.

Information gathering of traffic lights

Something that has to be taken into account, is the way the traffic lights have to interact or gain information from the moving vehicles. This means that there has to be a device which can communicate to the traffic light. Some ways of achieving this, might be to have a chip that interacts between the cars and the traffic lights, which may provide information both ends of the communication-cycle. However, the GPS chips at the time are not well-equipped for handling situations such as Eindhoven, as it is a big city. The focus of this project lies on the present day, so this limits the choice.

As the non-autonomous cars cannot be interacted with via signaling or other means of digital communication, it being a humanly driven vehicle, the requirements the device should have, can be reduced to it just scanning the environment. This can be done via sensors that exist in the world of today, but also in other ways. This includes ways such as a ultrasonic sensor system, image sensor system or the far infrared sensor system. Each of these has its perks and downfalls, but the image sensor system, while being least efficient on power usage, has the ability to check for the velocities of vehicles and the length of a jam, aside from just the number of vehicles and the occupancy, along with being able to check multiple lanes at once. One of the main subjects that is to be implemented and researched in this project, is the efficiency in terms of velocity, CO2 emission and more. As such, the most reliable way of scanning the environment in front of a traffic light, is the image sensor system.

The current system used in the Netherlands is by ways of a metallic sensor, that detects if a certain mass has been reached before allowing the detected object to be seen as a vehicle. This is not sufficient in terms of checking for velocity, or other important matters that need to be determined.

Information gathering of autonomous cars

Before implementing autonomous cars into the model and ultimately the real world, some background information is needed. So what are now a day cars capable to send and receive from the world ? To do so Tesla's autopilot was considered the best option since it is modern and gives a lot of open information. Unlike the WAYMO project of google. So what makes it possible that the Tesla model s , x and 3 all have semi-autonomous driving? The answer to that is sensors and a computer. All the Tesla’s are equipped with 8 different sensors: rear facing side cameras , front facing overview camera , main front facing camera , front facing distance camera , camera to drive backwards , ultrasonic system , front facing side cameras and radar. These sensors have the following properties:

• rear facing side cameras
  • max range of 100 meters
  • keep track of the blind spots
  • is used to safely switch lanes
• Front facing overview camera
  • max range is 60 meter
  • a 150 degree view detects traffic light signs and obstacles that are on the route the vehicle is taking
• Main front facing camera
  • max range is 150 meters
  • is mainly used to stay in lane and detect obstacles
• front facing distance camera
  • max range is 250 meters
  • this camera is handy when driving at high speed to spot a difference in environment ahead.
• camera to drive backwards

Algorithm

Currently a very standard model is being used fort he structuring of traffic. 90% of the traffic lights (in big cities as well as small villages) work as follows: when a car approaches a traffic light, it is either green or red. When it turned red, the traffic light waits for the traffic lights in the area to either turn red or to accommodate to a situation in which both this traffic light as well as the others can work. Then it will turn green with an initial green time. When no more traffic is passing through, the light will turn to red in less time than the green time was supposed to last. If traffic is passing continuously, then the green light will turn red after the green time has passed.

Algorithm by previous group

Group PRE2016 1 is a collection of students who were already working on creating on a new traffic system at intersections. This group didn’t necessarily concentrate on a system where lights are turned green or red when a car is waiting in front of it. They instead made a system in which the greentime and the moments when a light is turned green, is dependent off of the amount of cars that are waiting in front of the traffic light.

Content of Algorithm

In this chapter the contents of the algorithm will be explained in more detail.

States

To turn this system into a practise, the previous group first defined all state (in there case 18) that are possible. With a state is meant the combination of red and green lights at the intersection at a certain time. These state are:

• All pedestrians green, all car lights red;
• 4 rotations of one right turn car lane green, 2 pedestrian routes green;
• 4 rotations of two right turn car lane green, 1 pedestrian route green;
• All right turn car lanes green, all pedestrians red;
• 4 rotations of one left and straight car lane green, one right turn lane green and one pedestrian route green;
• 4 rotations of one left and straight car lane green, two right turn lanes green and all pedestrian routes red.

Of course this are not all states available but these are the states where no other light can’t be added without causing an accident.

Cost function

For each of the state the cost will be calculate by the costfunction. This cost function was defined which determined whether a light has a priority on other lights to turn green. This function is defined as follows for the car lanes:

Cost_Lane = Cost_traffic + Cost_waittime + Cost_waitlimit

= N + B + C_1 * t + P * e_1(t)

And for the pedestrians:

Cost_Pedestrianlane = Cost_waittime + Cost_waitlimit

= C_2 * t + P * e_2(t)

Here are:

C(t,N,B): The total cost dependent off of the amount of both non-autonomous vehicles and vehicles with human drivers as well as the waiting time

N: The amount of autonomous vehicles. The traffic system get this amount through communication with the autonomous vehicle.

B: the number of normal cars in the turn lane as reported by the autonomous cars (R is smaller or equal to the total number of normal cars in the turn lane).

C_1: The constant to provide the severity of the waiting time in front of a traffic light

t: The waiting time

P: A large value (in the order of thousands)

e_1(t): A function switching to 0 if t < T_maxcar and to 1 if t > T_maxcar

T_max: the maximum time a vehicle can be expected to wait at a intersection

e_2(t): A function switching to 0 if t < T_maxpedestrian and to 1 if t > T_maxpedestrian

T_maxpedestrian: the maximum time a pedestrian can be expected to wait at a intersection

So the bottom line of this function is: a green light is provided to the biggest row of cars in combination with their waiting time. This function is implemented in each traffic light at the intersection.

Algorithm in simulation

Packet loss

Due to the fact that the algorithm counts the amount of cars by communicating with the autonomous vehicles on the road, there is a chance that error in the communication. There for a packet loss was implemented in the simulation. This needed to make the simulation more realistic.

Spawning of Cars

In simulation the algorithm was implemented no real traffic data was used. The spawn time of new vehicles was composed out of three components: a base time that defines the minimum time between vehicles, a slider dependent time that allows the user of the simulation to determine the number of vehicles that arrive at the intersection and a random number, because vehicles arrive at an intersection in an unpredictable manner, or at least one should not assume it is predictable. This random number is a Gaussian distributed random variable.

Green wave

A Green Wave effect with several intersection wasn’t implemented in the simulation. However, a Green Wave like effect can be used in another way by just the one intersection that the autonomous vehicle is approaching. The car will receive an estimation of what state the intersection will be in when it arrives at the intersection. This method was used in the simulation.

The new Algorithm

The system that we are looking into, is mainly targeted to be used on rings of big cities. To describe this idea, an analogy with a clock is being proposed: a clock has a cursor which turns around its own axis. This pointer slides along the circumference of the clock. One can imagine the end of this cursor to be a car, which passes over a road with a constant speed. This is what we assume of a green wave: a state in which cars are allowed to pass sequent green traffic lights by traveling at a constant speed (within a degree of error in reality). This means that the traffic system can easily be corresponded with the speed of the car. The only thing for this system that we need to know, is what the speed limit should be of the road it’s traveling on. For instance when the speed limit is 60 km/h, and one has just past a green traffic light, and the next one is appearing in about 1 kilometer, then the next traffic light should turn green one minute after the previous one has turned green. This time is set that way because within this time, assuming a car will drive with a speed equal to the speed limit, then it will cover that one kilometer in one minute as well. This way, when the car is driving at a constant speed, it can always pass a green light. This is all because the moment the next light turns green, is slightly earlier (due to accelerating from 0 to the speed limit) then the moment where the car arrives at the traffic light. This way the car can drive further without pressing the brakes to slow down. This now introduced traffic system, will be crossed with the traffic system made by the previous groups. So on one hand, at the intersections the main focus is to give advantage to the longest row of vehicles. This whilst a green wave is being forced through the ring, so this green wave has a priority on the intersection system when it is about to pass through an intersection. This means that an alternate cost function needs to implement green waves as well. The new cost function for our system is:

C(t,A) = A^T(t) + c_1 * t + p_1 * e_1

Here are: C(t,A): The total cost dependent off of the amount of cars in a row and the waiting time of the car who has to wait the longest at the intersection to cross it.

A: The total amount of cars in an intersection row

T(t): A function that shows whether a row is in a green wave, and where

c_1: The constant to provide the severity of the waiting time in front of a traffic light

t: The waiting time

p_1: A large value (in the order of thousands)

e_1(t): A function switching to 0 if t < 30 and to 1 if t > 30

In this function it is implemented that a light is turned green earlier when a row at an intersection is in a green wave.

New Cost Function

As stated and defined above, a new cost function is presented to create the traffic algorithm. As one can see, there are a few differences. First of all N + B is being replaced with just a regular capital A, which stands for the total amount of cars (assuming that these are all man-driven). The rest of the constants that were already in the cost function made by group PRE2016 1 are still in the formula. A major difference however is the function T(t). This function provides to which the total amount of cars in a row at an intersection is put. Note that this function is always greater or equal to 1. This function behaves like a tent when the row is in a green wave (generated as a traveling signal through the total traffic system). When the green wave begin with its passing by the value starts to rise. It reaches its peak at the middle of the green wave signal (the green wave signal and the system is explained in the part about thew simulation). After the middle of the signal has passed, the values of the function start to linearly drop to 1. So now, when a green wave passes by, it has to seem, to the traffic light, that there are a lot of cars waiting to cross the street. This will have the traffic system which throughputs the green wave, give a priority on crossing in relativation to the the rows which have a relatively fewer amount of cars waiting. After all, the traffic light with the highest cost of all of the lights in the intersection, turns green first (as created by the past group). Depending on how big the value of c_1 is, the waiting time of the cars will also be weighed in the cost function. When this value is made larger, priority is given to the row which has the cars that are waiting the longest. So the weight will proportionally grow with the implementation of waiting time. p_1 is a large value (like 10000) which will only be put into the cost function, when the longest waiting car in the row had waited for 30 seconds or longer. This is obviously implemented to prevent one car from waiting to long, when a large amount of cars are on the other roads.

Simulation

A representation of a traffic system

To simulate the traffic situation a square road plan which will symbolize the “ring of Eindhoven” with a reduced amount of intersections will be simulated. There will be 24 intersections in the simulation to test how platooning will work over several intersections. For the traffic light system a new algorithm was imagined where all traffic lights in the ring are connected in a spinning wheel type. Imagine the hour slots on this clock to signify the intersections on the outer ring of the clock. The new algorithm would connect every 2 opposing intersections in figure [fignummer] to one state. This control system is used to make the simulation more responsive to platoons, as well as make the control of the intersections a bit easier. The state of the intersections depend on what the sensors between the previous and the one before that say, as well as the sensor before that. So for example the 12 and 6 o'clock positions are dependent on the sensors between 1-2 and 2-3. If a platoon is on its way it will try to make it possible for the platoon to be in the green wave.

A simulation was made in netlogo to figure out how different percentages of autonomous vehicles versus non autonomous vehicles would affect platooning. As outputs on the simulation a few values are important;

• Number of vehicles stopped in the simulation
• average time stopped(of vehicles going forward )
• average distance driven,
• average speed of cars
• average number of vehicles on the road.

Testplan

As seen in the ‘’dashboard’’ of the Netlogo program, some of the variables can be changed. The ones that matter the most in our program are focused on the use of the clock algorithm. Clocks are, in our program, expected to deliver positive changes in most of the parameters that can be measured, such as the total time stopped, the amount of cars stopped, the amount of cars on the road etc. In our clock system it is obvious that we needed to factor in two questions: how powerful should a clock be, and how many clocks should be on the ring? For this reason we implemented the following sliders in the program: Clock power and amount of clocks. For the test plan we needed to figure out how to run the program efficiently.

The clock power can be slid between 2 and 4, with a deviation of ½ . These numbers represent the power to which the amount of cars is raised at the start of the green wave. In the middle of the green wave this power will be 1½ times bigger. So the power will be raised from beginning to middle, and will be reduced from middle to end.

The amount of clock signals can be changed between 0 and 10 with a deviation of 1 clock. 0 meaning that there is no influence from green waves on the traffic on the ring, because there is no green wave signal. 10 meaning that 10 of these power function signals are sent through the intersection system, at the same speed as the cars in the program.

For the test plan of this program we decided to run the program as follows:

For 0 green wave signals we measure the parameters in one run. No green wave signal naturally means that there is no need for this amount to run in with different clock powers, because they won’t have effect when there is no green wave signal at all. This allows us to take a partial look into the results the previous group would have gotten, when the traffic lights with their cost function would be chained to more intersections. The rest of the results are obtained through running the program for 100.000 ticks for all remaining possible combinations of clock power with the amount of clocks. So every setting with a clock power between 2 and 4 and the amount can be changed between 1 and 10. This will give us 50 more results (5 power setting, 10 amount settings). The results of these runs are being put in an excel file which hands us the possibility to quickly see the best outcome per measured parameter. together, there are 51 different setting states that are worth exploring into. These are all ran twice. This is due to the random spawning of the cars on the road. By running them twice, we can take the average, so the deviations in spawn rate can be cancelled out a bit. The simulations are also ran with a focus on the parameters concentrating on ‘’cars at least a bit on the ring’’. This means that we exclude cars that just cross the ring from their spawn street to the opposite street.

The simulations with the lowest setting (0 green wave signals and any power) and the highest settings (10 wave signals and a clock power of 4) are being ran with test cars, which drive along the full ring once. These test cars are spawned every 1000 ticks. This is done because we want to obtain specific results for one car as well. We choose for these cars to be spawned after fixed times, so we can make an average, mainly because of the change of states at the intersections.

Planning and project information

In the beginning of the project, we had a certain planning that said what everyone had to do in a specific week. This was abbreviated with letters for the different people. The planning can be seen in table 1.

Table 1: Initial planning

	week 3	week 4	week 5	week 6	week 7	week 8
Understanding the current traffic system	All	All
The effects of autonomous vehicles on the traffic system		K M T	F T
What makes an autonomous vehicle better in traffic		S F L	S L
How are humans in the traffic affected			S F L	S L	S L
What can be changed to optimize traffic with autonomous vehicles			K M T	M T	M T
Model of the new traffic system		K F	K F	K F	K F
Complete the article					All	All
Work on final presentation					?	All

After a couple of weeks, there were some complications, and certain deadlines were not met. Because of this, and the fact that our initial approach turned out to be wrong, we changed our entire planning so that we could still finish the project in time and have time remaining to give some finishing touches. This can be seen in table 2.

Table 2: Eventual planning

	25-3	27-3	30-3	2-4	4-4	5-4	8-4	10-4	13-4
Programming in Netlogo	T K	T K	T K	T K
Rewriting focus, objectives, approach	F S	F S		T K
Literature study green waves, platooning, sensors vs chips, autonomous cars	M L	M L			L F
Results of program				L K T	L K T	L K T	L K T
Testplan				L K T
Final presentation				S	M L	M L
Description old system				T	T
Description new system				K	K	K
Peer-review				All	All	All	All	All
How the program works					T	T
Description clock system					S
Influence on the USE aspects					F
Analysis of results and conclusion					M	M	M	M
Writing discussion						F	F	F
Rewriting introduction								S
Finalisation									All

Because everyone writes their own parts, it still needs to be updated to the wiki. This has been delegated to Matthijs, while the final checker of for example grammar mistakes and of the wiki itself, has been delegated to Lars.

As part of the task division, there were not really special tasks that were given to certain people; everyone did their part of the project. There is however a small difference in the way people acted during meetings, or how they performed in the group itself.

Tim

Tim worked with Kevin on the program, but was also helpful in ways of contributing to the conversation with new ideas or solutions to problems that came up during meetings.

Kevin

Kevin, along with Tim, primarily focused on the programming part of the project. Because of this, they had the primary information and knew how the program works in its entirety. They did work with the others to gather information, such as how certain formulae should be formulated and what has to be searched in terms of constants needed in the model.

Matthijs

Sarah

Sarah focused on the USE aspects, but also tried to keep the conversation on track and come up with good solutions.

Floris

Lars

OUD

Currently a very standard model is being used fort he structuring of traffic. 90% of the traffic lights (in big cities as well as small villages) work as follows: when a car approaches a traffic light, it is either green or red. When it turned red, the traffic light waits for the traffic lights in the area to either turn red or to accommodate to a situation in which both this traffic light as well as the others can work. Then it will turn green with an initial green time. When no more traffic is passing through, the light will turn to red in less time than the green time was supposed to last. If traffic is passing continuously, then the green light will turn red after the green time has passed.

Traffic system by previous group

(Voor Matthijs Nieuw t.o.v. 26-3): Group PRE2016 1 is a collection of students who were already working on creating on a new traffic system at intersections. This group didn’t necessarily concentrate on a system where lights are turned green or red when a car is waiting in front of it. They instead made a system in which the greentime and the moments when a light is turned green, is dependent off of the amount of cars that are waiting in front of the traffic light. To turn this system into a practise, a cost function was defined which determined whether a light has a priority on other lights to turn green. This function is defined as follows: C(t,N,B) = N + B + c_1 * t + P_1 * e_1(t)

Here are:

C(t,N,B): The total cost dependent off of the amount of both non-autonomous vehicles and vehicles with human drivers as well as the waiting time

[math]\displaystyle{ N }[/math]: The amount of autonomous vehicles

[math]\displaystyle{ B }[/math]: The amount of non-autonomous vehicles

c_1: The constant to provide the severity of the waiting time in front of a traffic light

t: The waiting time

P_1: A large value (in the order of thousands)

e_1(t): A function switching to 0 if t<30 and to 1 if t>30

So the bottom line of this function is: a green light is provided to the biggest row of cars in combination with their waiting time. This function is implemented in each traffic light at the intersection.

City ring traffic system

The system that we are looking into, is mainly targeted to be used on rings of big cities. To describe this idea, an analogy with a clock is being proposed: a clock has a cursor which turns around its own axis. This pointer slides along the circumference of the clock. One can imagine the end of this cursor to be a car, which passes over a road with a constant speed. This is what we assume of a green wave: a state in which cars are allowed to pass sequent green traffic lights by traveling at a constant speed (within a degree of error in reality). This means that the traffic system can easily be corresponded with the speed of the car. The only thing for this system that we need to know, is what the speed limit should be of the road it’s traveling on. For instance when the speed limit is 60 km/h, and one has just past a green traffic light, and the next one is appearing in about 1 kilometer, then the next traffic light should turn green one minute after the previous one has turned green. This time is set that way because within this time, assuming a car will drive with a speed equal to the speed limit, then it will cover that one kilometer in one minute as well. This way, when the car is driving at a constant speed, it can always pass a green light. This is all because the moment the next light turns green, is slightly earlier (due to accelerating from 0 to the speed limit) then the moment where the car arrives at the traffic light. This way the car can drive further without pressing the brakes to slow down. This now introduced traffic system, will be crossed with the traffic system made by the previous groups. So on one hand, at the intersections the main focus is to give advantage to the longest row of vehicles. This whilst a green wave is being forced through the ring, so this green wave has a priority on the intersectionsystems when it is about to pass through an intersection. This means that an alternate cost function needs to implement green waves as well. The new cost function for our system is:

C(t,A) = A^T(t) + c_1 * t + p_1 * e_1

Here are:

C(t,A): The total cost dependent off of the amount of cars in a row and the waiting time of the car who has to wait the longest at the intersection to cross it.

A: The total amount of cars in an intersection row

T(t): A function that shows whether a row is in a green wave, and where

c_1: The constant to provide the severity of the waiting time in front of a traffic light

t: The waiting time

p_1: A large value (in the order of thousands)

e_1(t): A function switching to 0 if t<30 and to 1 if t>30

In this function it is implemented that a light is turned green earlier when a row at an intersection is in a green wave.

New Cost Function

As stated and defined above, a new cost function is presented to create the traffic algortihm. As one can see, there are a few differences. First of all N + B is being replaced with just a regular capital A, which stands for the total amount of cars (assuming that these are all man-driven). The rest of the constants that were already in the cost function made by group PRE2016 1 are still in the formula. A major difference however is the function T(t). This function provides to which the total amount of cars in a row at an intersection is put. Note that this function is always greater or equal to 1. This function behaves like a tent when the row is in a green wave (generated as a traveling signal through the total traffic system). When the green wave begin with its passing by the value starts to rise. It reaches its peak at the middel of the green wave signal (the green wave signal and the system is explained in the part aout thew simulation). After the middle of the signal has passed, the values of the function start to linearily drop to 1. So now, when a green wave passes by, it has to seem, to the traffic light, that there are a lot of cars waiting to cross the street. This will have the traffic system which throughputs the green wave, give a priority on crossing in relativation to the the rows which have a relatively fewer amount of cars waiting. After all, the traffic light with the highest cost of all of the lights in the intersection, turns green first (as created by the past group). Depending on how big the value of c_1 is, the waiting time of the cars will also be weighed in the cost function. When this value is made larger, priority is given to the row which has the cars that are waiting the longest. So the weight will proportionally grow with the implementation of waiting time. p_1 is a large value (like 10000) which will only be put into the cost function, when the longest waiting car in the row had waited for 30 seconds or longer. This is obviously implemented to prevent one car from waiting to long, when a large amount of cars are on the other roads.