Microscopic Theory of Traffic Flow Instability Governing Traffic Breakdown at Highway Bottlenecks: Growing Wave of Increase in Speed in Synchronized Flow

摘要

We have revealed a growing local speed wave of increase in speed that canrandomly occur in synchronized flow (S) at a highway bottleneck. Thedevelopment of such a traffic flow instability leads to free flow (F) at thebottleneck; therefore, we call this instability as an S$\rightarrow$Finstability. Whereas the S$\rightarrow$F instability leads to a local {\itincrease in speed} (growing acceleration wave), in contrast, the classicaltraffic flow instability introduced in 50s--60s and incorporated later in ahuge number of traffic flow models leads to a growing wave of a local {\itdecrease in speed} (growing deceleration wave). We have found that theS$\rightarrow$F instability can occur only, if there is a finite time delay indriver over-acceleration. The initial speed disturbance of increase in speed(called "speed peak") that initiates the S$\rightarrow$F instability occursusually at the downstream front of synchronized flow at the bottleneck. Therecan be many speed peaks with random amplitudes that occur randomly over time.It has been found that the S$\rightarrow$F instability exhibits the nucleationnature: Only when a speed peak amplitude is large enough, the S$\rightarrow$Finstability occurs; in contrast, speed peaks of smaller amplitudes causedissolving speed waves of a local increase in speed(dissolving accelerationwaves) in synchronized flow. We have found that the S$\rightarrow$F instabilitygoverns traffic breakdown -- a phase transition from free flow to synchronizedflow (F$\rightarrow$S transition) at the bottleneck: The nucleation nature ofthe S$\rightarrow$F instability explains the metastability of free flow withrespect to an F$\rightarrow$S Transition at the bottleneck.