Upper Bounds for the Critical Car Densities in Traffic Flow Problems

Details Upper Bounds for the Critical Car Densities in Traffic Flow Problems Upper Bounds for the Critical Car Densities in Traffic Flow Problems

1995-02-10

arxiv.org/abs/adap-org/9502002v2

Physics

Condensed Matter

REVTEX 3.0, 5 pages with 1 figure appended at the back, Minor revision, to be published in the Sept issue of J.Phys.Soc.Japan

Scientific paper

10.1143/JPSJ.64.3570

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.

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