  Analytical investigation is made on the two-dimensional traffic-flow model
with alternative movement and exclude-volume effect between right and up arrows
[Phys. Rev. {\bf A} 46 R6124 (1992)]. Several exact results are obtained,
including the upper critical density above which there are only jamming
configurations, and the lower critical density below which there are only
moving configurations. The observed jamming transition takes place at another
critical density $p_{c}(N)$, which is in the intermidiate region between the
lower and upper critical densities. It is derived that
$p_{c}(N)\,=\,CN^{\alpha}$, where $C$ and $\alpha$ are determined to be
respectively $0.76$ and $-0.14$ from previous numerical simulation. This
transition is suggested to be a second-order phase transition, the order
parameter is found. The nature of self-organization, ergodicity breaking and
synchronization are discussed, Comparison with the sandpile model is made.
