# Comprehensive Review of Traffic Modeling: Towards Autonomous Vehicles
## 3 Traffic Flow and Its Characteristics
### Capacity Drop  
The concept of capacity drop refers to the sudden reduction in traffic flow from a free-flowing condition to a stop-and-go state and the subsequent difficulty in returning to the original flow rate. [PERSON] [35] introduced this concept by modifying existing traffic flow theories to account for these abrupt changes in state. This phenomenon is critical in traffic dynamics, particularly in managing and controlling traffic flow effectively. Discontinuous is introduced into the fundamental relation (Figure 6).  
The capacity drop phenomenon has been extensively studied through both empirical observations and theoretical models. For example, [PERSON] and [PERSON] [39] presented a fundamental diagram based on experimental data from the Lincoln Tunnel in New York City, highlighting the existence of a capacity drop as a gap in the diagram. This observation was further confirmed by [PERSON] and [PERSON] [40], who validated the capacity drop in various traffic scenarios.  
Numerous studies have explored the capacity drop effect across different settings. [PERSON] and [PERSON] [41], [PERSON] and [PERSON] [42], and others [43; 44; 45; 46; 47] have reported that the magnitude of the capacity drop can range between 0.5% and 35%, depending on the specific traffic conditions. This wide variation underscores the complexity of the phenomenon and the influence of various factors on traffic flow.  
Researchers have proposed several mechanisms to explain the occurrence of capacity drops. [PERSON] and [PERSON] [48] suggested that disruptions caused by lane-changing maneuvers, particularly near merging points and moving bottlenecks, can trigger capacity drops. This idea is supported by [PERSON] and [PERSON] [49], who identified two distinct types of capacity drops: one associated with the inability of the network to maintain peak traffic for extended periods and another linked to incomplete recovery after the network is reloaded.  
[PERSON] et al. [50] further contributed to this understanding by demonstrating that the queue discharge rate increases with vehicle speed within a queue, and the magnitude of the capacity drop decreases as the vehicular speed increases. This finding highlights the dynamic nature of traffic flow and its sensitivity to speed variations.  
The capacity drop phenomenon has also been explored through various simulation models. [PERSON] and [PERSON] [51] used a car-following model to simulate capacity drops, while [PERSON] et al. [52] and [PERSON] and [PERSON] [53] employed cellular automata models. [PERSON] et al. [54]  
Figure 6: Fundamental diagram with capacity drop.  
applied a geometric Brownian motion model to gain deeper insights into the underlying mechanisms of capacity drops.  
Recent studies have aimed to provide a more comprehensive understanding of capacity drops. [PERSON] et al. [55] presented an overview of different modeling approaches that capture the capacity drop phenomenon in first-order traffic flow models. Their work also introduced a new approach, validated using real data from a UK motorway network. [PERSON] et al. [56] offered a thorough review of capacity drops, examining them from both behavioral and simulation perspectives. Their findings demonstrate that capacity drops can be accurately modeled and targeted using both macroscopic and microscopic simulation tools.  
More than ten potential causes of capacity drops have been identified, including factors such as limited acceleration, differences in acceleration, variance-driven gaps, proximity to bottlenecks, the number of lanes, lane-changing behavior, and on-ramp flow. Despite significant progress in understanding capacity drops, this area remains an active field of research within traffic flow theory. Ongoing studies continue to investigate ways to mitigate capacity drops and improve traffic management strategies.