Microscopic theory of traffic-flow instability governing traffic breakdown at highway bottlenecks: Growing wave of increase in speed in synchronized flow

Abstract

We have revealed a growing local speed wave of increase in speed that can randomly occur in synchronized flow (S) at a highway bottleneck. The development of such a traffic flow instability leads to free flow (F) at the bottleneck; therefore, we call this instability as an S→F instability. Whereas the S→F instability leads to a local increase in speed (growing acceleration wave), in contrast, the classical traffic flow instability introduced in 50s-60s and incorporated later in a huge number of traffic flow models leads to a growing wave of a local decrease in speed (growing deceleration wave). We have found that the S→F instability can occur only, if there is a finite time delay in driver overacceleration. The initial speed disturbance of increase in speed (called "speed peak") that initiates the S→F instability occurs usually at the downstream front of synchronized flow at the bottleneck. There can be many speed peaks with random amplitudes that occur randomly over time. It has been found that the S→F instability exhibits the nucleation nature: Only when a speed peak amplitude is large enough, the S→F instability occurs; in contrast, speed peaks of smaller amplitudes cause dissolving speed waves of a local increase in speed (dissolving acceleration waves) in synchronized flow. We have found that the S→F instability governs traffic breakdown -a phase transition from free flow to synchronized flow (F→S transition) at the bottleneck: The nucleation nature of the S→F instability explains the metastability of free flow with respect to an F→S transition at the bottleneck.

Analysis of speed disturbances in empirical single vehicle probe data before traffic breakdown

“…In accordance with the three‐phase theory, Kerner's S→F instability should govern traffic breakdown (F→S transition) at freeway bottlenecks [27]. In the theory of the S→F instability it has also been found that before the traffic breakdown (F→S transition) occurs with the resulting congested pattern formation, there can be a series of random F→S transitions that are all followed by S→F transitions caused by the S→F instability.…”

“…Simulations of classic traffic flow instability of Herman et al [9] and Gazis et al [10] in free flow in a traffic flow model (a) GM model class (b, c) S→F instability in synchronised flow introduced in Kerner's three‐phase theory (adapted from [27])…”

“…Recently, Kerner has developed a microscopic theory of the S→F instability [27]. It turns out that the S→F instability governs the nucleation nature of traffic breakdown (F→S transition) at a highway bottleneck.…”

Defining Highway Node Acceptance Capacity (HNAC): Theoretical Analysis and Data Simulation

“…is statement is related to the phenomenon observed in Section 1. However, unfortunately, in Kerner's abovementioned and following works [4][5][6], clear de nition of HNAC and explicit formulas were not provided, either in other followers' works [7,8].…”

Traffic and granular flow: the role of data and technology in the understanding of particle dynamics

“…In D€ ulgar et al 2019, the authors were motivated by the lack of empirical characterization of traffic "breakdown" as a two-way transition between different traffic states. The authors adopt the classification of Kerner (2015) that divides the traffic fundamental diagram into three regions. The traffic breakdown is then seen as a transition between a Free-flow Region (designated by F) and a Synchronized Region (designated by S): the "nucleation" in the F-S transition leads to a traffic breakdown that is governed in its turn by the S-F "instability."…”