# Tunnel Traffic Evolution during Capacity Drop Based on High-Resolution Vehicle Trajectory Data
## 2 Literature Review  
Researchers observed the phenomenon of the capacity drop in early studies. Initially, the concept of the \"capacity drop\" first appeared in the 1960s when [PERSON] [7] and [PERSON] [8] obtained two significantly different areas by drawing the flow-density point diagram of the Lincoln Tunnel in the United States. There are free flow and congested flow. It has a significant flow difference at the regional junction of two areas, the \"capacity drop\" phenomenon. [PERSON] draws the \"reverse-\(\lambda\)\" shape of the flow-density point diagram and the discontinuity of the change from free flow to congested flow to explain the capacity drop [9]. He believed that the driver in congested traffic flow is more inclined to have a more considerable car-following distance, but this comment lacks corresponding data support. The range of 5%-30% drop in the maximum discharge flow at the bottleneck has been widely observed, bringing excessive travel delays and safety concerns [10; 11; 12].  
Previous research has investigated the cause of capacity drop using aggregated traffic data from loop detectors. [PERSON] proposed the \"three-phase traffic\" theory and the concept of \"phase transition\" [13; 14; 15] and believed that the \"phase transition\" process of traffic flow caused the \"breakdown phenomenon\" of a sudden decrease in vehicle speed, resulting in capacity drop. Studies have observed capacity drop in areas where lane changing often occurs, near weaving segments [16; 17], merging [18; 19; 20], diverging [21], and lane-drop [22] bottlenecks. Some researchers found that the magnitude of the capacity drop is associated with the density [23; 24], the demand of ramp flows [25], the speed at the bottleneck [26], and the number of lanes [27].  
Recent studies explored the capacity drop from the human behavior perspective. Based on [PERSON]'s hyperbolic theory [28], [PERSON] conducted statistical analysis by intercepting part of the vehicle trajectory data in Next Generation Simulation (NGSIM) [29]. He elaborated and explained the asymmetric driving behavior theory [30] and effectively connected the capacity drop phenomenon with this theory. It is believed that after experiencing congestion, drivers tend to adopt a more considerable headway distance during acceleration. The shock wave formed by the disturbance during the driving process has a more noticeable impact on capacity drop [31; 32]. The macroscopic node model and kinematic wave theory are proposed to predict the causes of the capacity drop [33; 34].  
Some researchers believe that car-following behaviors are the cause of the capacity drop. For example, [PERSON] established a behavior model of first-order capacity drop at the continuous bottleneck based on the LWR model [35; 36], taking the limited acceleration of the vehicle as an additional constraint of the optimal model of traffic flow at the bottleneck. More recently, [PERSON] et al. revealed that combining different acceleration rates and desired driving behavior speeds induced voids and reduced capacity [37]. Through research and analysis of NGSIM data, [PERSON] quantified the traffic flow generated by stop-and-go waves and lane changing downstream of the bottleneck [38]. On the other hand, [PERSON] et al. considered the lane changer's insertion speed as a factor in AIMSUM, a traffic simulation software. They found that lane-changing vehicles with a high insertion speed could offset the capacity drop [39].