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For a traffic stream, $v$ is the space mean speed, $k$ is the density, $q$ is the flow, $\nu_{f}$ is the free flow speed, and $k_{j}$ is the jam density. Assume that the speed decreases linearly with density.

Which of the following relation(s) is/are correct?

  1. $q = k_{j}k – \left( \frac{k_{j}}{v_{f}} \right) k^{2}$
  2. $q = v_{f}k – \left( \frac{v_{f}}{k_{j}} \right) k^{2}$
  3. $q = v_{f}v – \left( \frac{v_{f}}{k_{j}} \right) v^{2}$
  4. $q =k_{j}v – \left( \frac{k_{j}}{v_{f}} \right) v^{2}$
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