# Prediction of Freeway Traffic Breakdown Using Artificial Neural Networks
## 2 Related Work  
Previous studies have shown that the occurrence of traffic breakdowns is stochastic in nature [3; 4; 5; 6; 7]. Furthermore, a breakdown event can occur at different flow levels rather than at a predetermined threshold value (i.e., capacity). In particular, the probability of a breakdown occurrence follows an 'S' shape as a function of traffic flow [7]. Parametric [5; 8] and nonparametric [9; 10] methods have been adopted to represent the survival rate based on pre-breakdown flow rates. Due to the diversity in traffic design and traffic characteristics specific to each location, several methods have been used to identify breakdowns in previous research. First, a speed threshold was used to identify breakdown events in [6]. The threshold is determined for each study site based on geometric and traffic conditions. [PERSON] and [PERSON] [5] defined the threshold speed as 10 mph below the free flow speed. [PERSON] and [PERSON] [11] used a 20% threshold below the prevailing free flow speed. Second, traffic breakdowns were identified by sudden speed drops. For example, ref. [6] proposed using a speed drop of 6 miles per hour and below 45 miles per hour in consecutive time intervals of 5 min as a threshold to detect a breakdown event. The third method, known as the volume-occupancy correlation method, identifies breakdowns by requiring a correlation between traffic volume and occupancy that satisfies a minimum threshold over a sustainable period of time [12]. Once researchers have selected the breakdown identification method and gained access to additional data, they initiated the search for factors other than traffic volume that influence the occurrence of traffic breakdowns and found that in addition to flow rates, other factors, such as adverse weather conditions [13], incident [14] and merging behavior [15] have been found to influence probabilities of traffic breakdown. [PERSON] et al. [13] investigated the relationship between weather, traffic density and capacity, and they found that in adverse weather conditions, drivers tend to increase their following distances and decrease their driving speeds, resulting in a decrease in throughput. This has also been supported in the research of [PERSON] and [PERSON] [16]. They highlighted the direct impact of vehicle spacing on speed by simulation. Specifically, when time headway increases from 1 s to 4 s, the average travel time will experience a 35.6% increase. By constructing a probability model of traffic breakdown, they found that, at the same levels of traffic flow, the probability of breakdown occurring on a rainy day is significantly higher than on a sunny day [4]. The other factor that has been shown to have an impact on breakdown events is incident. [PERSON] et al. [14] analyzed the impact of traffic incidents on travel time reliability on freeways using historical incident data. The analysis revealed that an incident on the shoulders increases the probability of traffic breakdowns because they reduce the capacity of a freeway segment and generate a temporary bottleneck. Furthermore, in the merge segments of the freeways, the traffic condition is influenced by ramp traffic. Therefore, the merging behavior and the flow rate on the ramp can affect the characteristics of traffic breakdown such as the critical flow rate and the phenomenon of congestion [15]. Because the occurrence of traffic breakdown can be attributed to various factors, researchers have included multiple features in building breakdown prediction models. For example, speed and occupancy were used to construct a bivariate Weibull distribution to model the probability of breakdown [17]. In recent years, machine learning algorithms have been used to predict the occurrence of breakdowns and have achieved high accuracy [11; 18]. In particular, [PERSON] and [PERSON] [11] proposed a machine learning algorithm to predict the occurrence of traffic breakdowns considering spatial and temporal correlations in traffic data.