Multiple choice

If the jam density is given as kj and the free flow speed is given as uf, the maximum flow for a linear traffic speed-density model is given by which of the following options?

  1. $\frac{1}{4} K_j \times u_f$
  2. $\frac{1}{3} K_j \times u_f$
  3. $\frac{3}{5} K_j \times u_f$
  4. $\frac{2}{3} K_j \times u_f$
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A Correct answer
Explanation

For a linear speed-density model (Greenshields model), u = u_f * (1 - k/k_j). Flow q = u * k = u_f * k * (1 - k/k_j). To maximize flow, dq/dk = 0, which gives k = k_j/2. Substituting this back, q_max = u_f * (k_j/2) * (1 - 1/2) = (1/4) * u_f * k_j.