A MTM is a mathematical model that compares the time it would take to get from point A to point B under certain conditions. These conditions could be traffic speeds, congestion, turningarounds, and other typical driving conditions. The model uses the standard deviation of the mean as its mean. This is a logistic regression that compares the predicted time against the actual time.
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The deviation is calculated by taking the arithmetic mean of all the deviations. That is, it divides the expected time by the actual time and calculates the deviation. That way, we have a way of measuring how far the car would go when going at a certain speed. It can also be used to find the range of possible speeds. Traffic data is collected over time from areas around the United States. Here’s how to use the MTM in practice.
We first need to plot the data. This is called a trendline, which is just a line connecting two points on a plotted map, or points on a histogram. The trendline can be used to draw a general picture of the area.
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Now plot the data along the mean line. The color of the line indicates the time trend, while the size of it indicates the magnitude of the trend. The larger the size of the line, the steeper the trend. The bigger the size, the wider the average speed. In general, the bigger the size of the line, the faster the average speed.
Finally, plot the data along the median line. This is called the concentration curve, and it can be thought of as a high-shelf curve. Here the concentration of traffic occurs close to the mean, so the speed is slower near that mean than further away. This effect is especially useful if you are trying to forecast where the speed will be less as you drive through slower conditions.
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One thing to be aware of though is that the slope of the concentration curve could be different depending on whether it is moving up or down. If it is moving up, the speed will be higher closer to the mean. But if it is moving down, the speed will be lower closer to the mean. You may wish to plot the data in this way when you want to estimate how fast the average vehicle speed will change, or if you want to see how fast individual cars are likely to travel in a different area.
One other way to plot the mean median driving time is with the aid of a model based on mathematical algorithms. The algorithm can be used to extrapolate past data to predict the future. So for example, if you know that vehicle speeds are about to increase across a major highway, then using the formula can calculate how long it will take for each vehicle to reach a particular point, and thus calculate the average speed. Of course this only works well if the roads have a flat rate of speed.
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To conclude, you should look at the data plot in figure 3. In the lower plot you have plotted the actual data mean driving time for vehicles of similar weight. The upper plot shows what would occur if the road was altered in one way or another, such as reducing speed. The lower curve shows what would happen if you just let the car travel at its own pace. By understanding the formula and how it works, you can use it to your advantage when studying real data.
One last way to plot the mean driving time is by using a least squares regression. In this method you plot a line representing the data mean. Each point on the line is the difference in the predicted value of speed from the actual data. Use the data to see where the problem might lie, and then look for the area between two extreme points.
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When choosing a regression, you need to choose a relatively simple function. It needs to be something like the slope of the x-axis. This allows you to quickly identify points that are out of range. Using the data from earlier, find the points that are most out of range. Then place these points within the next larger range, and so forth.
Finally, there is another way to plot the mean driving time data, using a least squares curve. In this method you plot the data against a least square curve. The y-intercept of the function is your predicted value for the speed at any given time. You can plot this for any desired interval. Use the data to find the points that are most out of range, and then place these points within the next larger interval.
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