GATE CE 2023 Set 2 — Question 50
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Transportation Engineering → Traffic Studies & Flow → Macroscopic Parameters
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Question
The figure presents the time-space diagram for when the traffic on a highway is suddenly stopped for a certain time and then released. Which of the following statements are true?
Correct answer
(B) Volume is lower in Region Q than in Region P; (C) Volume is higher in Region R than in Region P; (D) Density is higher in Region Q than in Region R
Solution
In a time-space diagram (Distance vs. Time):
1.The slope of a vehicle trajectory () represents the speed.
2.The horizontal spacing between trajectories at a fixed distance represents the time headway (). The volume is .
3.The vertical spacing between trajectories at a fixed time represents the distance spacing (). The density is .
Analysis of the regions:- Region P: Represents the initial steady-state flow.
- Region Q: Represents the jam condition where traffic is stopped. The trajectories are horizontal, meaning speed . Consequently, the volume . The trajectories are very close together vertically, indicating maximum (jam) density .
- Region R: Represents the release of traffic. The trajectories have a positive slope, but it is less steep than in Region P, so .
- (A) False: The slope in Region P is steeper than in Region R, so speed is higher in P than in R ().
- (B) True: In Region Q, traffic is stopped, so volume . In Region P, traffic is flowing, so . Thus, .
- (C) True: The horizontal spacing (time headway) between trajectories in Region R is smaller than in Region P (). Since , the volume in R is higher than in P ().
- (D) True: Region Q represents the jam condition where vehicles are at their closest possible spacing. Therefore, density in Q is the jam density, which is higher than the density in the moving traffic of Region R ().
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