Spontaneous phase transition from free flow to synchronized flow in traffic on a single-lane highway

Traffic flow complexity comes from the car-following and lane-changing behavior. Based on empirical data for individual vehicle speeds and time headways measured on a single-lane highway section, we have studied the traffic flow properties induced by pure car-following behavior. We have found that a spontaneous sudden drop in velocity could happen in a platoon of vehicles when the velocity of the leading vehicle is quite high (∼70 km/h). In contrast, when the velocity of the leading vehicle in a platoon slows down, such a spontaneous sudden drop of velocity has not been observed. Our finding indicates that traffic breakdown on a single-lane road might be a phase transition from free flow to synchronized flow ($F\to S$ transition). We have found that the flow rate within the emergent synchronized flow can be either smaller or larger than the flow rate in the free flow within which the synchronized flow propagates. Our empirical findings support Kerner's three-phase theory in which traffic breakdown is associated with an $F\to S$ transition.

Figure 1

(a) Sketch of part of the Nanjing Airport Highway and locations of the cameras. The notation KX+Y is widely used in transportation engineering in China and it means that the camera is 1000X+Y m away from the highway end. (b) A snapshot of the video from camera K18+128, which shows the lane closing.

Figure 2

Time series of (a) individual vehicle velocities and (b) time headways at camera K19+248. (c) Probability distribution of time headways based on 379 data points. In (a), the horizontal dashed line shows the average velocity of 70 km/h. The data were obtained in the afternoon of August 6th, 2010.

Figure 3

Typical time series of individual vehicle velocities and time headways corresponding to the two velocity drops shown by the arrows in Fig. 2a.

Figure 4

Two snapshots in the time period in Fig. 3b.

Figure 5

Time series of individual vehicle velocities and time headways at camera K20+237. The data were obtained in the afternoon of August 6th, 2010.

Figure 6

Typical time series of individual vehicle velocities and time headways at camera K18+128, in which no spontaneous transition occurs. The leading vehicle moves with velocity 42 km/h at the camera location, but it might increase its velocity afterwards so that the velocities of the following vehicles in the platoon increase to ∼55 km/h (shown by the horizontal dotted line). The data were obtained in the afternoon of August 6th, 2010.

Figure 7

Velocity of vehicles in platoon of 50 vehicles. A three-phase traffic model is used in the simulation. Maximum velocity of vehicles is set as 82.8 km/h (23 m/s). Some other parameters are AD $=$ -6, α $=$ 0.4, $p=0.1$. For details of the model and other parameters used, one may refer to Refs. [41, 42, 43]. In the two platoons, $v_l=72$ km/h (20 m/s) and 54 km/h (15 m/s), respectively (AD is anticipated deceleration, α is acceleration threshold parameter, $p$ is randomization parameter).

Figure 8

Vehicle velocity in platoon of 50 vehicles. The FVD model is used in the simulation. The parameters used are (a) λ $=$ 0.5 s ${}^{-1}$, κ $=$ 0.4 s ${}^{-1}$; (b) λ $=$ 0.4 s ${}^{-1}$, κ $=$ 0.3 s ${}^{-1}$; (c) λ $=$ 0.3 s ${}^{-1}$, κ $=$ 0.2 s ${}^{-1}$. In each panel, $v_l=70$,60,50 km/h, respectively.