03-method.Rmd

# Methodology

This section will describe the methodology used in collecting and analyzing the data used in this paper. The ramps used for analysis and the metering period will be explained, and the data collected in the field and by the detectors will also be discussed.

```{r setup, echo=FALSE, include = FALSE}
library(targets)
library(tidyverse)
library(readxl)
library(lubridate)
library(modelsummary)
library(kableExtra)
library(ggplot2)
library(ggpmisc)
library(scales)
library(DT)
library(dplyr)
library(devEMF)
library(zoo)

knitr::opts_chunk$set(echo = FALSE)
```

## Data Collection

Two on-ramps to I-15 in Davis and Salt Lake counties in Utah were chosen for data collection and analysis. These ramps include the northbound on-ramp at Layton Parkway in Davis County and the southbound on-ramp at Bangerter Highway in Salt Lake County. Data were collected during several periods, including August and September 2020, and April 2021. At Layton Parkway, 19 days of data were collected, while 5 days of data were collected at Bangerter Highway. These ramps were metered only during the PM peak period, with metering taking place between 4:00 - 6:30 PM at Layton Parkway and 3:30 - 5:45 PM at Bangerter Highway. 

As mentioned, the loop detectors at the EQ, IQ, and PQ locations collect both volume and occupancy data and are recorded in 60-second increments. In addition, the variable ramp meter rate (in units of veh/hr) for each minute is included with the detector data. The detector data used in this paper were obtained through UDOT for each data collection period.

The data collected manually was also completed in 60-second increments during the metered period and includes the number of vehicles in each lane at the EQ detector, the queue length at the ramp meter signal, and the total number of other vehicles on the ramp that have not yet reached the queue. The ramp length and the number of lanes at the ramp meter signal were also recorded. 

## Data Analysis
While beginning to analyze the data, it was discovered that the time stamps for the field and detector data were misaligned for each ramp. This significantly reduced the accuracy of the queue length estimates, but this was resolved by shifting the field data either backwards or forwards up to three minutes to best match the detector data based on the minimum RMSE found for the number of vehicles entering the ramp. 

In order to better analyze the data, rather than finding an optimum K for an entire peak period at each ramp as was done in Wu et al. (2009), the data were grouped into 15-minute bins during each day. Doing so allows for more specific optimization of K and provides additional observations that can be used to compare each K with the traffic analysis parameters. The K for each period is found by minimizing the RMSE between the queue length from the field data and that estimated by the Kalman filter equation. The optimized K, average EQ, IQ, and PQ occupancy, metering rate, density, and flow were then computed for each 15-minute period. The data were then analyzed by finding different ways in which the optimized K values were correlated to different traffic analysis parameters.