  In most models of traffic flow, the car density $p$ is the only free
parameter in determining the average car velocity $\langle v \rangle$. The
critical car density $p_c$, which is defined to be the car density separating
the jamming phase (with $\langle v \rangle = 0$) and the moving phase (with
$\langle v \rangle > 0$), is an important physical quantity to investigate. By
means of simple statistical argument, we show that $p_c < 1$ for the
Biham-Middleton-Levine model of traffic flow in two or higher spatial
dimensions. In particular, we show that $p_{c} \leq 11/12$ in 2 dimension and
$p_{c} \leq 1 - \left( \frac{D-1}{2D} \right)^D$ in $D$ ($D > 2$) dimensions.

Adaptation, Noise, and Self-Organizing Systems;Condensed Matter;Adaptation and Self-Organizing Systems