Physics of traffic gridlock in a city

Based of simulations of a stochastic three-phase traffic flow model, we reveal that at a signalized city intersection under small link inflow rates at which a vehicle queue developed during the red phase of light signal dissolves fully during the green phase, i.e., no traffic gridlock should be expected, nevertheless, traffic breakdown with the subsequent city gridlock occurs with some probability after a random time delay. This traffic breakdown is initiated by a first-order phase transition from free flow to synchronized flow occurring upstream of the vehicle queue at light signal. The probability of traffic breakdown at light signal is an increasing function of the link inflow rate and duration of the red phase of light signal.