 So my name is Sander Sleeman and I'm from Denmark. I work for the University of Aarhus in Yeah, well Aarhus most specifically I'm employed in the Aarhus School of Engineering. So just Quick agenda. So first I'll talk a little bit about why we think it's important to do this work and then go more into the traffic modeling part Which is the bulk of It turns out that it's actually the hardest part of the pollution modeling stuff So why is it a good why do we think it's important to try to model traffic pollution? Well, there's actually two reasons for it the first one is of course the pollution and And in in the bottom corner of the slide you can see a special a special situation in a In a street where we have Pollution in the street and we have a wind coming Across the streets and because of the high buildings in the street we get what we call a canyon effect. So You can imagine that if you want to have a precise model of the street level pollution this is quite a Challenging problem to actually model how much of the pollution is going to be concentrated on the lee side of the road so so One part of this is To be able to model precisely how much pollution how much the concentrations of the pollutants are at the street level Because of course, it's not healthy to to be in a very polluted street So the other The other reason why we think it's a good idea to model a Pollution from traffic is because we have an obligation to report our climate gas emissions in Denmark well Through the Kyoto protocol we all have have these obligations to to be able to Measure or model our climate gas emissions and in Denmark it turns out that 24% of all climate gas emissions actually comes from the transportation system. So so it's it's important to know That is how much it is of course, but it's also important to know where we have this pollution and how we can mitigate or how we can adapt to to these pollutant emissions so one idea was to use smartphones as a way of register how people are moving in the transport system because Before we before we try to use smartphones. We have really didn't have very very precise information on on on people's movement in in the traffic system because We have part measurements with the tubes on the streets We have coils in the streets are also point measurements And then we have surveys where we ask people how they move around in and how they use the transportation system So which modes of transportation they are using and when they move when they travel Which also has some problems with coverage and with people not remembering correctly which routes they take and stuff like that. So so there's There's also Also people have tried to use Data from cell phone towers where we can measure how many cell phones are in the neighborhood of a given tower which also can if we can track the The cell phone IDs we can see not very precisely, but we can see how these Cell phones move from towers to cell towers So that's also been a source of information about how people travel But now we have smartphones and they are with people all the time and they have a Several sensors and maybe we could use these sensors to get more precise idea on how people are moving around in the transport system and in the upper right hand of the slide there's a spectrogram of the The accelerometer in a cell phone in a smartphone Which is inside a Car in idle and what you can see here is actually the the vibrations from the engine. So in the start there is as I don't know if you all know what a spectrogram is, but On the I axis we have frequencies and we have a time on the X axis. So this is a 10-minute measurement on on a Car in idle so in the beginning there are some red bars Which is the handling of the phone and then it's green means there is no vibrations and then that we get these red almost horizontal lines which Which is the frequency of the idling car So it it was in a cold day. So in the start motor is cold and then the The rotation speed of the motor is high and then when it gets warmer it slows the Idle speed of the motor down. So that's what you can see from from these data from a smartphone. So We wanted to see if we can use these Smartphones for for getting more data so No more precise data of course we'd We turn it turns out that not all people use smartphones and not all people using smartphones in traffic systems want to give us the data. So we end up with a Not complete coverage of Our transport system. So how can we fill in the missing the blanks? And that's what we can use traffic modeling for so and this traffic modeling is actually a science that goes Back like six sixty years or something like that and It has been used to so the the basic use of it is to try to To model how much traffic there is on each road in a transport network and we can use this this knowledge of the traffic flows to to predict where and when there will be congestion and it has been used for planning the effects of new roads If we want to make a Large roadwork, how could we do that with a? Minimal Inconvenience and something like that It has also been used before for pollution predictions And well with quite some success I must say and In we can also use it If we are planning or want to see the effects of new Resent residential areas of business areas. So if we build new new parts of the city, how will that? What will the effect be on the transportation network? But in the core of it is to try to find out how much How big are the traffic loads on each road in the network? So let's go to something So some of the basics in traffic Assignments, so we have this idea of Of a transportation network and what the basic the the smallest part of the transportation network We call a link so a link is the connection between two points and There can the traffic that flows into a link has to flow out of the link. It can't disappear in in between two nodes, so That's the definition of a link and we then Look at routes for for travels and travels are a router then a combination of links which The travels are used to to navigate through the network so a travel Transport network is actually a graph and we can use the individual streets Cut them up in in links and then we have the the edges of our graph So a route is We start somewhere in our origin and it ends in a destination and we the transport the transportation modeling tries to find out what what are the the Used links to serve that the travel demand for for that origin to that destination So of course we we don't expect people to to go We expect them to go the Shortest path through through our network. So we don't want to have any loop signal network So so every route is a simple Simple route so a Part of of the travel model is is to look at We try to model how people are choosing the routes route and the network to serve this that their wishes to come to a specific place so When we talk about route choice we also talk about How to assign traffic flows to specific routes So And you can imagine that if you have People coming from different places going to different destinations They might share links at some point in in the journey and that means that our that the flow on an individual link is a The sum of of all the routes that use that link so we need to model all the routes and then we have to take care of all the The links that are used that more than one route So and and we try to model how how our travelers are using their free choice and We will we will try to find an equilibrium rules state some ideas on how we think that people are choosing routes and In that there were way of choice. We will try to find the equilibrium of all travelers in the network so so And one of the challenging Thing about route choice is that there is a very large number of routes which can serve A demand from one origin to one destination There is another Science of which is called discrete choice, but that Field is really more about only a few choices so if you only have like a handful of different choices and there are ways to model that quite efficiently so one example is What are you going to use for the transport? Are you going to bike or going by car or going by bus or train or whatever? so that there's only a few different choices when you're you consider which Transportation mode you want to do but here in in the route choice. There's a very large number of of routes to choose from so So how many are there actually they are going to go through a small artificial example just to show That this number is going to be very large so So how many routes are in the first figure? We have four points A and B so how many ways are there to come from A to B? Exactly two so let's make it more difficult with nine nodes Anyone can count how many routes there are Simple routes without loops How many? Yes, actually there is 12 So they are here all 12 so just for For going from two for now nodes to nine nodes you get from two routes to 12 routes And actually if you go to the next one where we have 16 nodes We are going to get 184 routes and you can see if you if you of course, it's an artificial example, but you can see that even for for and Equal seven you get this very large number 575 million different routes and that's for a very small network So of course, we don't have to consider all the routes maybe because we have Dijkstra and A star methods to to find shortest path algorithms, but there's still it's it's still not It's not that easy so we could just Ask Dijkstra to give us the shortest path and then we are gone are done because Well, when well, you know, of course that if we have When we have a large number of travelers on the road then the speed goes of the of the road the travel speed goes Down what we what is called congestion? So so what we we experience that as many as more and more people use the same road our travel time increases so Of course, if you notice that in the traffic you will ask yourself if there's a alternative route with less of travel time, so our model here should be able to To model this That so that before that we get the demand distributed or more routes so that Links are not completely congested So we'll come come back to that later so Of course, we all It will also be nice if we had a way to calculate the travel times for congested links So we we need to have a function of of the travel time as a function of the amount of congestion and then we we should Figure out a way to formulate of equilibrium so that we could Distribute the flows in order to to obtain this equilibrium. So The classic way of doing that is through looking at it can econometric so in Econometry you consider all the access in a in a market You assign an utility to So We are considered to be selfish Actors in this marketplace and we want to maximize our utility by doing the best thing we can So and then another way of looking at the utility is that we We could maximize our utility, but we could also try to minimize our costs and we consider the time we use in travel as a cost so we can actually we can put a special number on how much we Consider the cost of Of our travel of course are fixed cost and variable costs But so yeah But the interesting thing here is the variable cost the travel time mostly of course the the travel length is also an issue Because we have to account for the extra fuel that we have to to spend to travel that extra length but this is the basic model of every traveler in the network we Try to minimize our cost That is try to minimize our travel time so I'm not going to go into this too much There is this idea of a value of time and So and we can measure that actually so Let's talk about congestion instead. So so what happens when more and more travels are using the same link Well, the travel time goes up and this is what the figure here in the right-hand side shows so we have in the to the left we have the We have no No cars and we have the what we call a free free flow travel time and then as more and more cars comes on the link the travel time Right increases and we use this formula here the Which is actually a very old formula Defined by the Bureau of Public Roads in America, but it turns out that it actually works pretty well in in a lot of cases so and So the We have the zero which is the free flow time And then we have the X is the amount of cars on the link and then C is the capacity of the link So we see that when we reach a capacity so X equals C we we add an extra alpha to our travel time, but the beta is Normally a very large number or very large not it's for most of time so so it The increase is going to be quite dramatic when we go when we cross over the capacity of the road so and the The figure shows how we can find an equilibrium in this case because we have two links connecting the two points and as We have a fixed number of cars wanting to go from A to B and we see that if if we at the Crossing point we we see that the travel time on each of the link is the same and that means that it Doesn't make sense to Change your route if you're Because everyone has the same travel time. So that's the equilibrium that we are going to look for we want to We want to find the assignment of traffic to each link in such a way that Every traveler has the same travel time. This is what we call the deterministic user equilibrium. So If everyone has the same travel time, it doesn't make sense to try to change your your route Okay Simple enough except that you have to you have to Have to go through all the links and make sure that it's true for everyone so so but is it really a realistic Condition for this equilibrium because in order to to make sure that we all have the same travel time it you kind of You you expect everyone to know everything about the travel system So you have to you you know where the the shortest path is and you know where everyone else is going to drive at this point in time so It's it means that that the travelers need to have perfect knowledge about the transport system So maybe it's not completely realistic so Maybe we could do something else Well, we could try to randomize it a bit so with we instead of Demanding full or perfect knowledge about the transport systems. We can we can act like our model it as at all Travelers think that they have a little lowest travel time. So we this think introduces a Randomness into The equation that we can use this to to statistically model the the travel Assignment So we instead of only conceal the value of time and travel time we add a a small and Random variable the EPS here which Which is Going to model this randomness of this uncertainty on On how we are going to do so now we have two different equilibrium conditions so There are some of course known with some some problems with that so in the statistical user into equilibrium we We need to consider every route in the in the Transportation system and we have seen that that can be a very large number of that So it's it takes a long time actually to when you consider the statistical use of equilibrium so so But on the other hand that the deterministic use equilibrium is a bit unrealistic So so what can we do? Well recently we there have been research into Combining the deterministic use equilibrium Statistic user equilibrium, so we can We can reduce the choice set that we have that we consider in the statistic user Equilibrium in such a way that we don't need to to consider all routes in in every Iseration of the model and in that way we can Save a lot of computations I'm not going into that too much there so, but I implemented that model and tried it for a large city Very large city actually. It's number 35 on the list of of Large cities in the world so there are Three hundred thousand links which I convert into one-way links so that I'm I don't it's easier when you when you do the The modeling to only have one way links instead of considering which way we are going through that link and Then I Then I had these I made some synthetic data to to to see if I couldn't could make it work on this large example and what you see in the and the figure is that all the green stuff is all the links in Istanbul and I don't know if you know Istanbul, but the the The white part in the middle is the bus the straighter bus bus and you can see that are two bridges They are working on a third one, but I think it's not completed yet and The red part in the in the figure is all the used roads and you can clearly see all the highways Which span the city so? that was I I Yeah, I could talk a lot about the implementation, but but the next step in this work is to To use the smartphone data the location data that we collect from the smartphones to create these origin destination destination matrix is that This is how we we spell out the traffic demand in the system And there is really one of the points where we are not Well, we don't have very very good data. So so if we could get traffic demand from the The location data from from the smartphones. It would be great and the figure shows the origin and destinations for a local experiment we did in in Denmark So it seems promising that you can You can use these data even though even though that we only have a small percentage of the of the total number of travelers it seems that we can We can get this origin destination matrix going so Thank you questions alright, so We have time for a couple of questions Thanks for the talk. Can you tell us which kind of? Data processing module you have used for for finding equilibrium so the the the model the transfer the traffic model is implemented by In post-quest, so I Got the data from the OpenStreetMap project and So it lends itself to a database Implementation so and then instead of pulling out data from from the Road network, I just keep all the data in the Postgres database and and do all the processing Driven by Python scripts So the heavy lifting is a postgres All right one more question over there Thanks for your talk if I understood rightly you didn't consider any time-faring aspects so like Dynamically adapting to congestion lanes being closed accidents things like that Was it possible to investigate that and I was also curious if you had any access to other data sets like say uber To sort of test algorithms on that So as far I can understand the question is about time aspects and if if I had access to uber data or More yeah, but just to the first part like and I think you were you're just assuming that a fixed number of people are Trying to travel on the network, but if people know that congestion is really bad They might either delay their trip or take the very indirect route or switch to an alternative mode of transport like train Or time-shifted or just cancel their trip It depends on how bad the congestion is and what the cause is if the road is completely closed They might it was a possible to algorithmically investigate any of those well, I think that you as I've understood your question, I think you are right that The people know more about the the road situation now than they did before because they have They have access to Google maps and Ways and and stuff like that. So an Intelligence transport systems are also more available in at least in larger cities. So maybe Maybe our travels are coming becoming more like in the deterministic user equipment that they actually know exactly what's going on in the transportation system, but on the same time it seems that Even though we have access to to these systems in our daily commute we we tend to only use that road that that we are used to so so Maybe maybe we when we are Doing things that we always do we are only using the habits that we have Been used to so so but With respect to to timing information we we we consider The most interesting things are of course when there are congestion So we we consider only the times of day where we have the most traffic. That's that makes the most sense And we have the data that we we collect Has this time timing information? So we can we can see how people are moving through today when the The congestion is there Okay, okay. Well, let's thank the speaker again Thank you and