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$\rightarrow$F instability. Whereas the S$\rightarrow$F instability leads to a local {\it 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 {\it decrease in speed} (growing deceleration wave). We have found that the S$\rightarrow$F instability can occur only, if there is a finite time delay in driver over-acceleration. The initial speed disturbance of increase in speed (called "speed peak") that initiates the S$\rightarrow$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$\rightarrow$F instability exhibits the nucleation nature: Only when a speed peak amplitude is large enough, the S$\rightarrow$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$\rightarrow$F instability governs traffic breakdown -- a phase transition from free flow to synchronized flow (F$\rightarrow$S transition) at the bottleneck: The nucleation nature of the S$\rightarrow$F instability explains the metastability of free flow with respect to an F$\rightarrow$S Transition at the bottleneck.