Modeling the Motion of a Single Vehicle
The movement of a single vehicle can impact significantly the performance of a traffic stream. Consider a slow-moving vehicle at the front of a long line of vehicles traveling behind it, with no-passing opportunities. The performance of this lead vehicle
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Modeling the Motion of a Single Vehicle
The movement of a single vehicle can impact significantly the performance of a traffic stream. Consider a slow-moving vehicle at the front of a long line of vehicles traveling behind it, with no-passing opportunities. The performance of this lead vehicle significantly affects the speed and travel time of the following vehicles. Understanding the characteristics, performance, and movement of each vehicle type allows us to model groups of vehicles and to evaluate the performance of the traffic stream. Furthermore, the movement of individual vehicles allows us to develop better highway design and traffic control solutions. For example, understanding the acceleration and deceleration constraints of various vehicle types can help us design more effective passing zones and to allocate appropriate yellow and all-red intervals at signalized intersections. This chapter first discusses the basic equations of motion for a single vehicle. The second part of the chapter discusses vehicle, driver, and environmental characteristics and their effects on vehicle motion.
Motion of a Single Vehicle The motion of a single vehicle can be fully described mathematically using equations of motion. These are based on laws of physics and provide relationships between key parameters such as acceleration, speed, distance traveled, and travel time. This section derives and presents these equations of motion for various types of movement (constant speed, constant acceleration, and varying acceleration). The discussion in this section is based to a large degree on [1]. Figure 1.1 presents a diagram with the trajectory of a vehicle, i.e., a plot providing the vehicle’s position as a function of time. The horizontal axis of the figure indicates the time, while the vertical axis indicates the respective location of the vehicle. This type of diagram is called a time–space diagram. The trajectory of the vehicle is the line connecting the location–time points along the vehicle’s path. L. Elefteriadou, An Introduction to Traffic Flow Theory, Springer Optimization and Its Applications 84, DOI 10.1007/978-1-4614-8435-6_1, © Springer Science+Business Media New York 2014
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1 Modeling the Motion of a Single Vehicle
Fig. 1.1 Trajectory of a vehicle
The average speed of the vehicle between locations A and B (VAB) can be determined as follows: V AB ¼ dAB =ðt2 t1 Þ where dAB is the distance between points A and B (ft). Visually, the average speed of the vehicle is determined by the slope of the line connecting the two points as shown in Fig. 1.1. The instantaneous speed of the vehicle, v(t), i.e., the speed for a very small portion of the trajectory, is the respective slope of the line connecting the two points. The steeper the slope of the line, the higher the speed of the vehicle is, as it travels a longer distance in a shorter amount of time. As shown in Fig. 1.1, the speed of the vehicle near location A is lower than the average speed between points A and B, as the slope of that line (labeled instantaneous
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