# Comprehensive Review of Traffic Modeling: Towards Autonomous Vehicles
## 3 Traffic Flow and Its Characteristics
### Three-Phase Traffic Flow Models  
In traffic flow theory, a phase is defined as a state that exists in both space and time. Traditional fundamental diagrams, as discussed earlier, typically classify traffic into two phases: free flow and congested flow. However, [PERSON] and [PERSON] [77] introduced a more nuanced model called the three-phase traffic theory. This theory expands upon the conventional understanding by introducing an additional phase, thereby providing a more comprehensive explanation of traffic behavior. The three-phase traffic theory is grounded in the concept of synchronized flow and postulates that the steady states of synchronized traffic cover a two-dimensional (2D) region in the flow-density plane, which contrasts with the traditional one-dimensional approach. This theory challenges the idea that a single fundamental diagram can fully capture the dynamics of traffic flow. Instead, it suggests that traffic congestion can be divided into three distinct phases: free flow (F), synchronized flow (S), and wide moving jam (J) (Figure 8). In the first phase of free traffic flow, empirical data have a positive correlation between the flow rate (\(q\)) and vehicle density (\(k\)). This relationship ends at the maximum free flow (\(q_{\text{max}}\)) with a corresponding critical density (\(k_{\text{crit}}\)). There are the same phases as in the two-phase models presented in previous sections. The average speed of the vehicle in the phase of a wide moving jam is much lower than the average speed of the free flow. On the downstream front, vehicles accelerate at the speed of the free flow. On the upstream jam front, vehicles come from the free flow or synchronous flow and must reduce their speed. In the synchronized flow phase, both the flow rate and vehicle speed may vary. The downstream front of the synchronized flow is often spatially fixed, usually at a bottleneck at a certain location on the road. The flow rate in this phase could remain similar to that in free flow, even if vehicle speeds are greatly reduced.  
[PERSON] and [PERSON] developed the first-order phase-transition model to explain the onset of synchronized flow from free flow, which led to the continuum version of the three-phase theory. This was further extended by [PERSON] et al. [78], who proposed a cellular automata approach consistent with the three-phase theory. Their work provided empirical validation for the theory, showing that traditional two-phase models could not fully explain certain traffic phenomena, such as the persistence of synchronized flow and the spontaneous formation of wide moving jams.  
Overall, the three-phase traffic theory offers a more detailed understanding of traffic dynamics by recognizing that traffic flow is not simply a matter of free flow versus congestion. Instead, it acknowledges the complex and transitional nature of traffic, where phases like synchronized flow play a critical role in how congestion develops and dissipates on roadways.  
Figure 8: Three traffic phases: F—free flow; S—synchronized flow; J—wide moving jams.