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GATE 2022 CE (CE1) – Question 44

Traffic Engineering and Transportation Planning · Fundamental relationships of traffic flow · 2 marks · Multiple choice

Consider the four points P, Q, R, and S shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by kP, kQ, kR, and kS, respectively. The correct order of these densities is

Speed–flow curve with four labelled points P,Q,R,S. See the attached source image.
  1. $k_P>k_Q>k_R>k_S$
  2. $k_S>k_R>k_Q>k_P$
  3. $k_Q>k_R>k_S>k_P$
  4. $k_Q>k_R>k_P>k_S$

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Correct answer: (A) $k_P>k_Q>k_R>k_S$

Explanation

Greenshields gives $v=v_f(1-k/k_j)$, so density increases monotonically as speed decreases. In the plot the speeds decrease in the order S, R, Q, P.

Thus densities have the reverse order: $\mathbf{k_P>k_Q>k_R>k_S}$, **A**. At the zero-speed endpoint P, density is jam density even though flow is zero.