Self-Organized Criticality of Traffic Flow: There is Nothing Sweet about the Sweet Spot

Abstract

This paper shows that the kinematic wave model exhibits self-organized criticality when initialized with random initial conditions around the critical density. A direct consequence is that conventional traffic management strategies seeking to maximize the flow may be detrimental as they make the system more unpredictable and more prone to collapse. Other implications for traffic flow in the capacity state are discussed, such as: \item jam sizes obey a power-law distribution with exponents 1/2, implying that both its mean and variance diverge to infinity, and therefore traditional statistical methods fail for prediction and control, \item the tendency to be at the critical state is an intrinsic property of traffic flow driven by our desire to travel at the maximum possible speed, \item traffic flow in the critical region is chaotic in that it is highly sensitive to initial conditions, \item aggregate measures of performance are proportional to the area under a Brownian excursion, and therefore are given by different scalings of the Airy distribution, \item traffic in the time-space diagram forms self-affine fractals where the basic unit is a triangle, in the shape of the fundamental diagram, containing 3 traffic states: voids, capacity and jams. This fractal nature of traffic flow calls for analysis methods currently not used in our field.

Effect of the Trip-Length Distribution on Network-Level Traffic Dynamics: Exact and Statistical Results

“…also exhibit similar behavior under stochastic arrivals. As in Laval (2021), the results in section 3 strongly suggest that control can be used effectively to improve reliability simply by preventing the system to reach the critical region, e.g. by metering/perimeter control well below capacity.…”

“…Future work should verify the conjecture found here that the discrete-event simulation of the trip-based model produces critical behavior. This result is important as it is currently believed that critical behavior can emerge only in fully microscopic models (Nagatani, 2020, Laval, 2021, 2022. It would be interesting to see if other implementations (e.g. )…”