Welcome back friends. Uh, we will now begin, uh, the next lecture. On non-motorized transportation, where we will look at pedestrian data collection and low character yeah. Lecture, we will, uh, show to you the different methods in which you can collect pedestrian data, as well as, uh, give you a detailed understanding about the different flow models that can be used, or that are used in modeling pedestrian, uh, data along with along different facilities. And also look at regression modeling and how you can use the regression modeling in developing these flow models. So when it comes to collecting, uh, pedestrian data, you can do it in various ways. Uh, the first, most, uh, common way of doing it is the man will count, but this is, uh, effective only when you have a facility that has. Very few pedestrians that walk. If you want to collect data on a residential street or a street, along with a language that are not very many people that walk, then it is easier to have a few data collectors who are, uh, uh, who, uh, will stand on the side of the road, who will stand on the side of the road and just collect. Uh, just count how many pedestrians are walking. So this is count data. Okay. So we are not collecting data on the type of people who are walking. Are they male, female? What is their age group? We are not going to hand out any survey questionnaires to them. We are just having a data collectors stand on the side of the road and count the number of people that are walking by him or her. So that's it. Very basic, uh, method of counting for pedestrians. Right. And you have to have all the count data because you have know the volume of people that walk along the street. So once you know the count, then you can submit up and say that, but our data and number of people that work or per day, there are a number of people that work, and then you can. Figure it out, which is the most congested period along the sidewalk, which is the, uh, lighter periods of along the sidewalk. And maybe if that sidewalk is connected to a signalized intersection, then you can go ahead and determine how much time maybe given for these pedestrians based on the volume of pedestrians that approach the, uh, crosswalk or the intersection, uh, how much signal timing should be given for them to cross across the streets. So this is the basic requirement of, uh, designing any facility is to understand how the volume of people walking and hence these counts are that it is very labor intensive. So you have to, uh, uh, maybe, uh, hire a lot of, uh, people who will do this manual counts and stand on the road side of the roads for that longer period or for a long period of time. However, now there are a lot of automatic, uh, data collector count collecting devices that are available. For example, the slab type device, which can be buried under the walkway. And it works on the principles of pressure. So pressure is applied on it. It will automatically count as a vehicle. Then there are something called, uh, pyro boxes that, uh, can be mounted on a, um, on a light pole and it can count. The number of people that are crossing, uh, crossing the, uh, uh, crossing the box. Uh, it has some, uh, infrared signals that, uh, it can count the number of people walking, uh, and it can, and you can have urban posts and fixed counters. This is an urban post that are fixed counters. These can be removed. These counters can be removed. Whereas these are fixed counters. That can also be, um, a sensor that can be put on some kind of a structure above a sidewalk or above a gate. So you will see a lot of, uh, automatic doors that are nowadays present, uh, in different facilities. They will have sensors on top so that when somebody walks in and out of a facility through that gate, they get recorded. So you can count the number of people that are. Coming in and out of a facility or so and so forth. I heard there are some constraints, uh, if it is especially, uh, uh, in outdoor situation that you are putting these, uh, automatic counters, then they have to be shielded from weather or theft and, uh, locations have to be selected very carefully. Now that you're going to install something, uh, for, uh, automatic counts for a longer period of time, better install it at the right place and the right angle. So it can count, uh, people, uh, correctly, uh, rather than double counting the same person or for example, uh, what often happens with automatic counting is that if, uh, there are two people that walk side by side and you have a device that is not overhead, but that is on the side of the road or the side of the foot path. Then, uh, both of the, both of the pedestrians are counted as one. So we call it as occlusion, uh, in many situation that, uh, two people are counted as one, then the volume counts get half almost. So it causes a problem. So the location and the placement of these automatic devices is very, very crucial. Again, they need a skilled labor now, uh, not only for installation, but for extraction of the data, you will have to have people who understand how to extract this data. And. Counted then. So, and the devices itself are a little bit costly. However, the accuracy of the counts if are done properly is very high and you almost do not need, uh, to have these people stand on the side of the road for a long period of time to count them manually. There are cameras also. So rather than having sensors, people also have. Cameras are take advantage of the cameras that are already existing in many of the intersections. For example, you would see here to count the number of people that are crossing the street. Uh, usually, uh, uh, these accountings are accounting is done manually, but usually nowadays there are a lot of, yeah. Computer vision techniques that can be used to, uh, count the number of people that are crossing, uh, that are captured on a video. Okay. now, uh, in the last lecture we introduced you to that basic three, uh, diagrams of, uh, flow parameters that are very fundamental to any traffic movement. And these are bottled from a motorized vehicular movement, but they can be applied in case of non-motorized us and pedestrian transport as well. So if you recall, the basic equation is. You is equal to U times K where Q is the flow. You is the velocity of speed and case density. So now you can also say two is equal to you, but you by S where S is nothing but the inverse of, uh, inverse of density. And that is called as pacing. So in. When it comes to looking at these diagrams for pedestrians, we usually use spacing as the parameter rather than density. So our, we use it, uh, alternatively in different kinds of cases. So if we look at each of these diagrams carefully, what we can see is that the speed and density have an inverse relationship. Right? So if there are N density, meaning. Number of people per square meter say, right? So if there is no people, no density, then you can walk at whatever speed you want to walk at. Right? So that is called free flow speed. You can work at whatever speed you want to. However, as the density starts increasing as more and more people start to walk along that given space or the sidewalk, then the speed off. The individuals walking starts decreasing, and it comes to a point where we call it jam density where not nothing moves, right? You are stuck. So you cannot, when there is congestion and the vehicles are not moving, you experienced that situation. And sometimes when you are in a very, very crowded area, maybe there is an event happening and nothing is moving. So that is kind of jam density. Right. So speed and density, however, inverse relationship. Now, when you look at flow and density, you start to see that it is it parabolic. So when there is again, when there is no density automatically means that there are no people at that point in time that are walking on the street, as density starts speaking up. Flow also starts picking up. Right? So as more and more people starting moving, there are more and more people moving. But minute that we will see what the flow units are, what the density units are in a little bit. What as per the, uh, characteristics of any parabolic, you will see that you will attain maximum density at. Exactly the mid point from gem density and zero density. Right? So at that point you will attain maximum flow. And then again, as your density starts, increasing keeps on increasing your flow does not increase anymore. Right? So there is a point at which there will be maximum people moving on that section per minute. Whereas if there are more and more people getting added, The speed get right people don't there's too much friction. There is too much condition. So there are the number of the number of people passing a point per minute decreases until again, you hit jam density. So there are as per uh, uh, characteristics of parabola, any flow unit at a particular flow point will be occurring at. Two different times based on two different, two different density numbers, right? That is how a parable works. Similarly, if you look at, uh, the relationship between speed and flow, it is also parabolic in nature where when the flow is zero again, when there are no people, you can essentially. Walk at whatever speed you want to walk, right? So free flow speed. Now as flow as number of people start increasing, your speed starts decreasing, right? Their speed start decreasing and their speed is maximum at your max at maximum flow. Your speed is maximum again at the same time. Your speed no longer increases after this point. And it goes back to, we will see how this works in the following slides. So I hope at least you understand the basic principles in the three different diagrams that are presented. So what is pedestrian speed? Usually the average pedestrian walking speed in terms of meters per second or meters per minute. Flow that I was talking about is the number of pedestrians passing a point. What unit of time we usually use number of pedestrians in every 15 minutes. Our pedestrians per minute also can be used. Density is the average number of pedestrians per unit area. So we usually use with a steel, what meter squared. And space is just the inverse of density. So it is the average area provided for each, but it's G meter square, but, but it's true. Okay. So when we talk about flow, what we are saying is that if this is a, a point, the number of pedestrians that crosses this point, but unit time, so per minute or per every 15 minutes, how many people cross this point? That is what is called flow. So there are different, uh, models that can, uh, uh, that have been developed over the years that captured the relationship between speed and density. Uh, the very simplistic model that I've shown you before, uh, which is a macro, which is a Greenfield Greenshields macroscopic stream model. That gives a very linear relationship between you and Kay. Whereas, uh, Greenberg's logarithmic model. Gives says that it is not linear, but the speed kind of is logarithmic in relationship with a density. And Underwood's exponential model now says that no, it is not logarithmic, but it is exponential in nature when it comes to the relationship between speed and density, we have already kind of explained to you, uh, uh, about this. Uh, about this figure, right. But the, but the relationship between between speed and density is given by this equation. So speed at any point will be equal to the free flow speed, uh, minus the, the ratio of the Freestore speed to jam density times. The density at that point in time. Okay. So this is the relationship between speed and density. The two values of free flow speed and jam density. Now what this equation, this equation usually is what we call regression Christian. Right? These are equations, which estimate the value of, uh, the speed off the pedestrian. You, once, you know, the relationship once you know what your free flow speed is, what your jam density is and what your given density is, you can estimate that speed spot, uh, speed of the pedestrians walking. So that technique is. Uh, used, uh, the technique used to, uh, estimate this skull regression technique. Now you already, uh, uh, you already know that the speed when there is no friction from other objects, K is equal to zero. You can reach, uh, free flow speed jam density at which no movement is possible. Jam density, intercept as UCF, and the slope is UFA KJ. Seven. Clearly we have also already looked at, uh, what is, uh, the greenfields microscopics, uh, stream model when it comes to the relationship between flow and density. So if you replace, since Q is equal to U times care, if you replace replacing you is equal to Q by K in this earlier equation, right? We already know this equation. Now, if you replace you is equal to Q by K in this equation. You'll get that equation of the parabola. So this gives you the relationship between Q N K. That is a relationship between Q N K again, density at which no movement is possible. That is jammed, right? Uh, max density occurs at midway, so K is equal to K jam by two. Okay. So this anywhere it is K jam by two. So this. Okay. Max is K two and max flow core set. K max max flow. Okay. Yep. Simple similarly, rewriting the equation of, uh, in terms of UN and Q, you can now get the relationship between you and queue. So basically if you understand this basic equation, Of you and density and knowing that Q is equal to you and to care, you can determine the parabolic equations of Q1 as well as Q1 you again, we have already seen at mean free speed. He was equal to zero and max flow occurs at a speed that is half of them. Speed up half of them mean three, uh, mean, uh, pretty close speed. Right? Our free flow speeds. So maximum speed. Ocker set. Half off free flow speed. This is half of the, and time speed. Now, for example, you are given this problem with these values of K N. Okay. So K is density. Whereas gen per meter squared and speed, uh, us speed meters per minute, determine the parameters or the flow model. Now you are told to estimate that or estimate or determined the parameters of the flow model and find the flow and density corresponding to a speed of 30 meter per minute. So you not only have to determine the equation, what the equation is, right. But you also have to, once you know the equation, you have to. Substitute U is equal to 30 meter per minute in order to estimate what is the flow and what is the density at that speed? Okay. So the greenfields macroscopic model, the relationship between UNK is a straight line and it resembles, uh, very basic linear regression for right. Y is equal to X plus B. Well, X is speed. And why is density? So this equation and you, we all know how you can solve a simple linear regression equation of Y is equal to X plus B. It is done by a technique called carpeting where B is given by this equation and a is given by this equation. So what, what are the elements of this equation? It says that all of the X values minus the mean of X value is multiplied by all of the Y values minus the mean of Y value. And the product of that is sum and divided by the, all of the X values minus the mean of the X values times two, which is again, summed up. So that gives you the B value. So in this case, what is X. In our case, which one is X and which one is, Y you have already told you that speed is X and density, is Y right. How did we tell you that you already know that speed Benson, right? We are looking at speed and density, or are we looking at. Speed. Yes, we are looking at speed and density. So speed is X as it is white. So we are going to find out, uh, first the parameter B, and then we are going to estimate parameter air, which is nothing but the mean of all the Y values minus B times the mean of all the X values. So let us see. So we have the X values and the Y values. So first we do the, uh, we sum all these up. Some, all the X values with some, all the Y values and find out the mean of X and mean of Y. And then we start for each row. We take the X value subtracted from its mean, we take the Y value subtracted from its mean, we sum these two columns or, uh, we, uh, have the product of those two columns. And then we also develop what is called the, uh, X minus. This should, this square should be outside, right? This one should be outside. So it is this column raised to the power to once we have developed these two columns, we sum them at the bottom and we find out that using the equation, given in the previous slide, we found out that B is minus 0.2 and a is 40.8. So then we get an equation, which says the relationship between speed and density is speed is equal to 40.8 minus 0.2 times density. So that is the relationship between speed and density. Now we also have to figure out the relationship, the other two relationships, the relationship between density and flow and speed and flow. So as we know. I mean free speed. If we know this, we can tell that mean free speed occurs when K is equal to zero. So mean free speed is equal to 40.8 kilometer per hour. And for you for the question of Q versus scale, the relationship now becomes Q is equal to point 40.8 K minus 0.2 K squared. Remember how we derived it? From, uh, earlier the relationship from, with how we moved from the relationship from you and Kate to relationship from two U N K, this is a parabolic relationship, whereas this is a linear relationship. Now we also know that at U is equal to zero K is equal to K jam. So if you put Q is equal to substitute, Q is equal to zero here we find we can find out what is the K Jamey question by solving this. Quadratic equation and found out that K M is equal to 204 pedestrian per meters per meter squared. This is when the footpath is completely crowded. And also we know that at Q at Q when Q is Q max K is equal to K done by two, right. We have already, uh, established that. So if you use the same and put it in this equation, we will get the Q Maxus. Two zero eight one pedestrians per minute. Now we have determined what is Q max? We have determined what is jam, and we also know the relationship between Q1 K. So now we can solve the second part of the question asked, what is the, uh, what is Q and K when the speed is 30 meters per minute? So using our relationship that we have already developed, we can find out, we can just substitute. It was able to 30 to find out what the case. And from this relationship, we can substitute a K a K S 54 to find out what the queue is. So you see what these equations help you to do? Is that now for a different facility, right? You only have to determine the speed of people walking at that facility. And it will automatically using these relations chips. You can find out what the you and the chaos you don't need to again, uh, do the calculations and figure out what the K and Q Q1 cares. You can just, you just have to know what the speed is and you can automatically determine the other two parameters. uh, there are, uh, like I said, uh, this is a very simple, uh, uh, relationship between, uh, speed and density, which is, uh, linear is what, uh, greenfields found out. However, well, there are two other relationships that are also used or the equations in that case are a bit different, uh, in Greenberg's model. Uh, the relationship between. Uh, speed and density is given in this fashion. Whereas, uh, in Underwood's model, the relationship has given him this passion as it is exponential. So if you are asked to solve a problem, given a certain method. So if we say that, find out the relationship using Greenberg's with the make model, you want to use this formula. Whereas if you, if you tell you to use a greenfields model, then you have to use the formula that was shown earlier. Now there are based on these. If you understand these three basic parameters flow parameters, uh, in, uh, uh, in pedestrian transport or in any forms of transport, you can then use these to build different models. Some models may be very specific to your, uh, your location, your country, your state, uh, some, maybe a homogeneous, some may be. Uh, the entire state, we follow a similar model in that country may follow a similar similar model, but, uh, you have to understand the basic three parameters that were discussed now, based on this, there are different types of models that already have been developed. So if you look at, uh, very broadly, these, uh, modeling techniques or softwares are classified under that two groups, one is behavioral models and one are movement related models. So the behavior models again, can be. Uh, classified two different ways, conceptual models, which usually follow, but it's, uh, a model that is developed based on the conceptual behavior model is called the social force model. Uh, and, uh, you can, but the other type are, uh, computer simulation models that simulates the behavior of individuals. So you have different kinds of softwares, uh, Legion root and simple. That does that. So, um, uh, modeling techniques or modeling softwares that are available that model individual pedestrians behavior, but they're all based on those three flow parameters, flow, speed, and density. Okay. Now, if you are, uh, looking at movement, uh, are the techniques and softwares that, uh, rely on movement, they do not consider any human factors or behaviors. There's this behavioral, uh, models. They do not, uh, focus on cloud dynamics. They are more dependent on individual behavior or individual concepts, right? These are more, uh, they do not consider individual behavior or human factors. They are more, uh, focused on the movement of groups of people. Now, even in the movement type of models, there are two different, uh, types, one which considers. Uh, a fluid or particle system. So it assumes that fluid behavior as per Boltzmann gas equation holds true, uh, in case of pedestrian movement. Whereas there are matrix based systems that are, uh, essentially used in, uh, the highway capacity manual 2000 and a different softwares that are listed here are based on each of those principles.
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