Kerner developed the three-phase model to describe highway traffic in a more realistic fashion, showing how vehicles could move from free flow to synchronized flow to a jam. The model provided insights that led to solutions aimed at improving traffic flow, such as the ANCONA system, in which vehicles await their turn to enter an on-ramp based on precisely timed traffic signals. However, Kerner didn't believe his model, designed for highway traffic, was needed to describe city traffic.
"Until 2007, I believed that earlier traffic flow theories and models could explain traffic at light signals in a city network, in particular, traffic gridlock observed almost each day in large cities of the industrial world," Kerner wrote in an email to Inside Science. "I changed my mind only about four years ago."
As Kerner discovered, classic traffic models weren't predicting gridlock even at moderate levels of traffic flow. However, in his model, the same chain of events that caused highway traffic to move from free flow to synchronized flow to gridlock in city streets.
"I was surprised to learn that Kerner believes that his three-phase theory, which was developed to describe highway traffic, can be applied to traffic on city streets. Once you accept this assumption, the results of his simulations are not so surprising," commented L. Craig Davis, a former Ford Motor Company research scientist who performed traffic-physics research at University of Michigan and Michigan State University.
In the new paper, Kerner performs a simulation of a line of vehicles approaching a traffic signal. In the model, cars in free flow can travel at a maximum allowed speed of nearly 35 mph. With a small flow of traffic on a street the model shows that all vehicles at the red light can clear the intersection when the signal turns green.
"In accordance with earlier traffic theories and models, gridlock should not occur under these conditions," Kerner explained. Vehicles that pass the green light without stopping can move at free flow speed.
However, the line of vehicles can make a transition from free flow to synchronized flow "if one of these vehicles decelerates randomly," according to Kerner. Traffic in synchronized flow has a maximum speed of approximately 25 mph. "As a result, there is a decrease in the number of vehicles passing the light signal during the green light," he explained.
This effect increases the number of vehicles waiting in line at the red light of the next cycle of the light signal. Consequently, when this longer line of vehicles cannot clear during the next green light, the line begins to grow. "Traffic breakdown has occurred at the light signal," Kerner stated.
Whether a decelerating vehicle ultimately causes gridlock is random, according to the new model. In Kerner's simulations, a decelerating vehicle sometimes caused vehicles behind it to slow down to a critical speed, compelling them to make the transition to synchronized flow. This In turn guaranteed the emergence of gridlock. At other times synchronized flow, and therefore gridlock, never occurred.
"The occurrence of a critical speed for synchronized flow is a random event," Kerner wrote. "[This random occurrence] is a common feature of many other non-equilibrium systems of natural science in which phase transitions occur."
While Kerner has done extensive real-world measurements in his earlier research, it's important to note that this work is just at the stage of a simulation.