A model of irreversible jam formation in dense traffic

Here we extend the results for the stationary properties of the MP+CF phase, by deriving exact expressions for the local density at the first site of the chain and the probability P(1) of a completely jammed configuration. The unusual phase transition, characterized by jumps in both the bulk density and the current (in the thermodynamic limit), as α crosses the boundary α=p from the MP to the CF phase, is explained by the finite-size behavior of P(1). By using a random walk theory, we find that, when α approaches from below the boundary α=p, three different regimes appear, as the size L→∞: (i) the lifetime of the gap between the rightmost clusters is of the order O(L) in the MP phase; (ii) small jams, separated by gaps with lifetime O(1), exist in the MP+CF phase close to the left chain boundary; and (iii) when β=p, the jams are divided by gaps with lifetime of the order O(L1∕2). These results are supported by extensive Monte Carlo calculations.