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GATE 2019 CE (CE2) – Question 29

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

A highway’s speed–density relationship follows Greenshields’ model, with free speed $v_f$ and jam density $k_j$. Find maximum flow.

  1. $v_fk_j$
  2. $v_fk_j/2$
  3. $v_fk_j/4$
  4. $v_fk_j/8$

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Correct answer: (C) $v_fk_j/4$

Explanation

Greenshields gives $q=v_fk(1-k/k_j)$. Setting $dq/dk=v_f(1-2k/k_j)=0$ gives $k=k_j/2$ and speed $v_f/2$. Thus maximum flow is **vfkj/4, C**.