Physics of traffic gridlock in a city

TL;DR

This paper uses stochastic traffic flow simulations to analyze how traffic breakdowns and gridlock can occur unpredictably at city intersections, even under low inflow rates, due to phase transitions in traffic flow.

Contribution

It reveals the probabilistic nature of traffic breakdowns at signalized intersections caused by phase transitions, challenging the expectation of no gridlock at low inflow rates.

Findings

Traffic breakdowns can occur with some probability even at low inflow rates.

The transition from free flow to synchronized flow initiates gridlock.

Probability of breakdown increases with inflow rate and red light duration.

Abstract

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.