Deadlocks and waiting times in traffic jam

Abstract

In a city of right moving and upmoving cars with hardcore constraint, traffic jam occurs in the form of bands. We show how the bands are destroyed by a small number of strictly left moving cars yielding a deadlock phase with a rough edge of left cars. We also show that the probability of waiting time at a signal for a particular tagged car has a power-law dependence on time, indicating the absence of any characteristic time scale for an emergent traffic jam. The exponent is the same for both the band and the deadlock cases. The significances of these results are discussed.