# Comprehensive Review of Traffic Modeling: Towards Autonomous Vehicles
## 3 Traffic Flow and Its Characteristics
### Other Phenomena  
In the study of traffic flow, several phenomena beyond the basic principles have been observed and analyzed. These phenomena provide a deeper understanding of the complexities involved in traffic dynamics.  
The relaxation phenomenon, first identified by [PERSON] [79], occurs when vehicles involved in a lane-changing maneuver initially accept short spacings but gradually transition to more comfortable spacings over 20 to 30 s. This behavior has been incorporated into various car-following models and lane-change decision processes, as explored by [PERSON] [80], [PERSON] et al. [81], [PERSON] [82], and others [83; 84; 85; 86; 87]. The phenomenon highlights the dynamic nature of driver behavior during lane changes, which must be considered in accurate traffic modeling.  
Density oscillations between lanes, initially studied by [PERSON] et al. [88], represent another important aspect of traffic flow. These oscillations, which occur particularly in queuing situations, were first described in detail by [PERSON] and [PERSON] [89]. They noted that such oscillations stabilize as they propagate upstream, with distinct periodicity. Subsequent studies by [PERSON] and [PERSON] [90] and others have investigated how network geometry influences these oscillations, using both microscopic and macroscopic models. [PERSON] and [PERSON] [91] extended this research by proposing a self-organization approach to traffic light control, which helps manage oscillations at intersections.  
[PERSON] and [PERSON] [92] proposed a mechanism to explain the formation and propagation of stop-and-go waves, a common occurrence in congested highway traffic. Their theory describes how oscillations spontaneously appear and transform into these waves, often exacerbated by merging and divergent maneuvers near ramps. [PERSON] et al. [93] further explored how these oscillations change in amplitude as they propagate along highways, providing a comprehensive theory on their dynamics. These insights are crucial for developing strategies to mitigate the impact of such oscillations on traffic flow.  
The concept of phase transitions in traffic flow, which refers to shifts between different states of traffic (e.g., from free flow to congested flow), is a significant area of study. [PERSON] [94; 95; 96] applied deterministic cellular automaton models to simulate these transitions, analyzing the impact of various factors on traffic flow. This work has been expanded by [PERSON] and [PERSON] [97] and [PERSON] and [PERSON] [98], who investigated the transitions between moving and jammed phases. Understanding these transitions is critical for predicting and managing congestion in real-time traffic scenarios.  
Recent studies have continued to explore these phenomena, applying advanced modeling techniques such as recurrent neural networks ([PERSON] et al. [99]) and mechanical vibrations ([PERSON] et al. [100]) to analyze traffic oscillations. These efforts aim to develop new control strategies that can dampen oscillations and improve overall traffic flow efficiency. Additionally, ongoing research into phase transitions, such as those by [PERSON] et al. [101] and others, continues to provide valuable insights into the dynamic nature of traffic flow, with implications for future traffic management systems.