Mechanism of the jamming transition in the two-dimensional traffic networks

The mechanism of the jamming transition in two-dimensional traffic networks is discussed on the basis of several models, where the update rule is deterministic, though the initial car configuration is random. It has turned out that the introduced concept of the occupation probability, which depends upon time and the site, is useful. The fluctuation in the local   car density plays an important role to give rise to small initial clusters of the cars. To examine the growth of such clusters a time-dependent function C$C$ is introduced, which is the number of the neighboring car pairs, and C$C$ increases to a certain maximum value, correlated with the total jamming. The critical car density in the symmetric two-dimensional N×N/N×N$N\times N/N\times N$ system is found to be 0.22–0.23 for each of the east-bound (x)$\left(x\right)$ and the north-bound (y)$\left(y\right)$ cars.