EE$3012$B Assignment $1$

Consider a highway segment with $m$ lanes $($lane #$1,$ lane #$2,$cdots, lane #$m),$ as illustrated in

Figure $1.$ The traffic on each lane $i$ is uniform $($i$.$e$.,$ on each lane, all vehicles travel at the same

speed and have a same headway$).$ The flow, density and speed on lane #i are denoted as $q_i,k_i$

and $v_i,$ respectively. The overall flow, overall density and space$-$mean speed on the highway

segment are denoted as $q,k$ and $v,$ respectively. Based on the definition of flow, density and

space$-$mean speed, show that $q,k$ and $v$ satisfy the conservation law $q=kv.$

Figure $1.$ The highway segment with $m$ lanes