## 2 Literature Review
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Researcher** & **Traffic Data** & **Findings** & **Weather Condition** \\ \hline [PERSON] [3] & 23 days in June 1989 (only nine days were used in the analysis) & One of the first papers to show the capacity drop phenomenon wherein bottleneck capacities start to decrease when queues near the on-ramp form. & \\ \hline [PERSON] and [PERSON] [30] & Five days of 16 November-3 December 1998 & Further proof of the capacity drop that occurs sequentially in time and space. They used slanted cumulative curves to show the change in flow. & Not mentioned \\ \hline [PERSON] and [PERSON] [12] & Five days across different years (one in 2000, two in 2001, and two in 2008) & Showed empirical evidence of the capacity drop phenomenon using a new methodology known as phase diagrams. & Not mentioned \\ \hline [PERSON] and [PERSON] [11] & 203 cases of data from 16 study sections (dates not mentioned) & Showed that the capacity drop and the number of lanes have a negative relationship. They also used a systematic methodology of detecting the capacity drop using downstream and upstream speed comparisons. & \\ \hline [PERSON] and [PERSON] [6] & Six days between 1995–1997 & Concluded that bottlenecks occur at a fixed reproducible location. They also described the discharge flows as nearly constant that only vary slightly with a fixed rate. & Only used data during clear skies and no measurable precipitation. \\ \hline [PERSON] and [PERSON] [8] & 20–23 March 2000 (4 days) & Showed that the bottleneck is activated because of drivers slowing down as they enter the shoulder lane. & Dry and sunny except on 23 March 2000, when a light rain was experienced and was considered negligible. \\ \hline [PERSON], [PERSON], and [PERSON] [10] & 12 morning rush periods in 2002–2004 & They showed that the capacity drop has a relationship with vehicle densities. They were the first ones to also extend the capacity drop observations to other bottleneck types: merge bottleneck, reduction on travel lanes, and horizontal curve. They also observed a difference in the capacity drop when there is inclement weather but did not explain it further. & One day was marked with inclement weather (light rain). \\ \hline [PERSON], [PERSON], and [PERSON] [13] & Six days across different years (two in 2009, three in 2011, and one in 2012) & They showed that the capacity drops and the speed in congestion have a linear relationship. They also showed that weather may have an effect on the capacity drop but it was inconclusive since they only have one observation. & Gathered data on a rainy day (18 March 2011) but was not used in the linear fit between the speed in congestion and queue discharge rate. \\ \hline Our work & Twenty-one days from January to December 2022. & This paper shows that the critical density significantly decreases during any weather condition (clear, light, medium, and heavy rain). Previous studies also prove that the capacity drop is a function of the speed in congestion but that this might not be true during inclement weather. The findings of this research show otherwise. The queue discharge rate is highly correlated to the speed of congestion in any weather condition. It is also shown for the first time that as the speed in congestion increases, the percentage in the capacity drop between the pre-queue capacity and the queue discharge rate decreases. & Included 21 data points representing different weather conditions (clear, light, medium, and heavy rain). \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Weather consideration in previous studies. Another research that included rainfall data in their analysis is in [PERSON], [PERSON], and [PERSON] [13]. They discussed that prediction of the capacity drop could be improved by relating it to the speed of congestion. They plotted the speed in congestion against the queue discharge rate and fitted a linear function. The correlation coefficient is 0.9819. As the speed in congestion increases, the queue discharge rate also increases.