The GATE Grind

GATE 2022 CE (CE2) – Question 28

Traffic Engineering and Transportation Planning · Fundamental relationships of traffic flow · 1 mark · Multiple select

For a traffic stream, v is the space mean speed, k is the density, q is the flow, vf is the free flow speed, and kj is the jam density. Assume that the speed decreases linearly with density. Which of the following relation(s) is/are correct?

  1. $q=k_jk-(k_j/v_f)k^2$
  2. $q=v_fk-(v_f/k_j)k^2$
  3. $q=v_fv-(v_f/k_j)v^2$
  4. $q=k_jv-(k_j/v_f)v^2$

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Correct answer: (B) $q=v_fk-(v_f/k_j)k^2$; (D) $q=k_jv-(k_j/v_f)v^2$

Explanation

Greenshields gives $v=v_f(1-k/k_j)$. Multiplying by k gives $q=v_fk-(v_f/k_j)k^2$, which is B.

Solve for $k=k_j(1-v/v_f)$ and multiply by v to obtain $q=k_jv-(k_j/v_f)v^2$, which is D. **Answer: B and D**.