Self-organization of traffic jams in cities: Effects of stochastic dynamics and signal periods

We propose a cellular automata model for vehicular traffic in cities by combining (and appropriately modifying) ideas borrowed from the Biham-Middleton-Levine (BML) model of city traffic and the Nagel-Schreckenberg (NS) model of highway traffic. We demonstrate a phase transition from the ``free-flowing'' dynamical phase to the completely ``jammed'' phase at a vehicle density which depends on the time periods of the synchronized signals and the separation between them. The intrinsic stochasticity of the dynamics, which triggers the onset of jamming, is similar to that in the NS model, while the phenomenon of complete jamming through self-organization as well as the final jammed configurations are similar to those in the BML model. Using our model, we have made an investigation of the time dependence of the average speeds of the cars in the ``free-flowing'' phase as well as the dependence of flux and jamming on the time period of the signals.