Abstract
The movement of a single vehicle is a fundamental building block in traffic modeling. A single vehicle can significantly impact the performance of a traffic stream. Consider an on-ramp vehicle entering a busy freeway at a low speed: it can cause freeway mainline vehicles to abruptly change lanes, which – for the right amount of traffic – may lead to severe congestion and stop-and-go traffic. Consider also a slow-moving truck at the front of a long line of vehicles traveling behind it with no passing opportunities: the performance of this truck significantly affects the speed and travel time of the following vehicles. Understanding the characteristics, performance, and movement of each vehicle allows us to model groups of vehicles and estimate 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 allocate appropriate yellow and all-red intervals at signalized intersections.
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Problems
Problems
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1.
Solve Example 1.1 assuming that the vehicle’s reaction time is 1.5 s and its initial speed is 50 mph. How do the results compare to those of Example 1.1?
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2.
A driver is approaching a traffic signal at a speed of 40 mph. The driver’s perception and reaction time is 1.5 s. When the vehicle is at a distance of 300 ft prior to the stop bar, the signal turns to a yellow indication which has a duration of 3 s.
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(a)
If the vehicle’s deceleration function is −(9.5 + 0.6 t), will the vehicle be able to stop safely at the signal before it turns red?
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(b)
Plot the driver’s trajectory and discuss the adequacy of the yellow interval duration.
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(c)
Recalculate part (a) with a perception and reaction time of 5 s. How does the driver’s perception and reaction time affect your response to questions (a) and (b)?
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(a)
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3.
Identify three applications of the equations of motion in transportation-related manuals and applications (Green Book, HCM, etc.). Provide the derivation of the final equation used and discuss any assumptions employed.
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4.
Two vehicles approaching an uncontrolled intersection perpendicularly to each other start braking to avoid a collision. The driver of vehicle A has a reaction time of 2 s and the driver of vehicle B has a reaction time of 1 s. The distance of vehicle A from the potential collision point is 350 ft and that of vehicle B is 200 ft. The initial speed of vehicle A is 50 mph and its maximum deceleration is −10 ft/s2. The initial speed of vehicle B is 35 mph and its maximum deceleration is −8 ft/s2. Will the two vehicles collide? (A similar problem is provided in Ref. [1])
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5.
A crash occurred between a bus and a passenger vehicle at a stop-controlled T-intersection. It was determined that the passenger vehicle was traveling along the major roadway when the bus entered the traffic stream from the side street and the passenger vehicle rear-ended it. At the time of the impact, the speed of the passenger vehicle was 20 mph. Assuming that the maximum deceleration of the passenger vehicle is −10 ft/s2, what was the initial speed of the vehicle when it started decelerating? Pavement marks indicate that the braking distance was 40 ft. Given that the speed limit along the major roadway is 40 mph, was the passenger vehicle speeding?
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6.
Conduct a literature review on traffic psychology and summarize your findings regarding the relationship between individual driver characteristics and driving performance.
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7.
Obtain the most recent Green Book equation which estimates stopping sight distance for design purposes and discuss it in the context of the equations of motion presented above. Should this equation consider varying acceleration rather than constant acceleration?
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8.
Find in the literature one acceleration function for a passenger car and one for a heavy vehicle (truck or bus). Discuss their relative performance characteristics and the shape of their respective acceleration functions.
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Elefteriadou, L. (2024). Modeling the Motion of a Single Vehicle. In: An Introduction to Traffic Flow Theory. Springer Optimization and Its Applications, vol 84. Springer, Cham. https://doi.org/10.1007/978-3-031-54030-1_1
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DOI: https://doi.org/10.1007/978-3-031-54030-1_1
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