Upper Bounds for the Critical Car Densities in Traffic Flow Problems
Abstract
In most models of traffic flow, the car density
p
is the only free parameter in determining the average car velocity
⟨v⟩
. The critical car density
p
c
, which is defined to be the car density separating the jamming phase (with
⟨v⟩=0
) and the moving phase (with
⟨v⟩>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
≤11/12
in 2 dimension and
p
c
≤1−
(
D−1
2D
)
D
in
D
(
D>2
) dimensions.