There have been many studies for modeling vehicular traffic flow using fluid models. However, these previous approaches do not accommodate realistic models for traffic density, flow, and velocity. The existing models also fail to uncover the relationships among energy efficiency, capacity, and safety. We investigate traffic networks from a system-level perspective. In result, we provide a time-gap based mathematical traffic model for vehicular traffic flow on highways. Our model explains the widely known triangular fundamental diagram, which represents vehicular traffic systems with the three primary parameters: maximum free-flow velocity, a typical safety length of vehicles, and a mean value of the time-gap of the traffic data during congested conditions. This result is also well validated with measured traffic data using least squares matching and with previous research outcomes about the propagation velocity. In addition, we suggest two distinct analysis techniques to estimate the time-gap from the traffic data measured on highways.

This paper provides new techniques to predict electric loads using the Multiple Linear Regression (MLR) model, which adopts a statistical approach that assumes the past load and weather data have information for forecasting the target load. Since the conventional general MLR prediction performance can be degraded by seasonal effects, we propose new MLR techniques to improve the prediction performance. We have found the performance of the proposed MLR can be further improved by solving the weighted least squares problem and clustering the training set. Additionally, we compare the prediction performances of these techniques to determine the best one. Our argument will be demonstrated by two case studies with real electric and weather data.

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Abstract. Low-cost optical particle sensors have the potential to supplement existing particulate matter (PM) monitoring systems to provide high spatial and temporal resolution. However, low-cost PM sensors have often shown questionable performance under various ambient conditions. Temperature, relative humidity (RH), and particle composition have been identified as factors that directly affect the performance of low-cost PM sensors. This study investigated if NO2, which creates PM2.5 by chemical reactions in the atmosphere, can be used to improve the calibration performance of low-cost PM2.5 sensors. To this end, we evaluated the PurpleAir PA-II, called PA-II, a popular air monitoring system that utilizes two low-cost PM sensors that is frequently deployed near air quality monitoring sites of the Environmental Protection Agency (EPA). We selected a single location where 14 PA-II units have operated for more than two years since July 2017. Based on the operating periods of the PA-II units, we then chose the period of Jan. 2018 to Dec. 2019 for study. Among the 14 units, a single unit containing more than 23 months of measurement data with a high correlation between the unit's two PMS sensors was selected for analysis. Daily and hourly PM2.5 measurement data from the PA-II unit and a BAM 1020 instrument, respectively, were compared using the federal reference method (FRM), and a per-month analysis was conducted against the BAM-1020 using hourly PM2.5 data. In the per-month analysis, three key features, temperature, relative humidity (RH), and NO2, were considered. The NO2, called colocated NO2, was collected from the reliable instrument colocated with the PA-II unit. The per-month analysis showed the PA-II unit had a good correlation (coefficient of determination, R2 > 0.819) with the BAM-1020 during the months of Nov., Dec., and Jan. in both 2018 and 2019, but their correlation intensity was moderate during other months, such as July and Sep. 2018, and Aug., Sep., and Oct. 2019. NO2 was shown to be a key factor in increasing the value of R2 in the months when moderate correlation based on only PM2.5 was achieved. This study calibrated a PA-II unit using multiple linear regression (MLR) and random forest (RF) methods based on the same three features used in the analysis studies as well as their multiplicative terms. The addition of NO2 had a much larger effect than that of RH when both PM2.5 and temperature were considered for calibration in both models. When NO2, temperature, and relative humidity were considered, the MLR method achieved similar calibration performance to the RF method. Since it is practically infeasible to colocate a reliable NO2 instrument colocation with high accuracy at low-cost PM sensors, we investigated the effectiveness of using NO2 data (which we call distant NO2), collected from monitoring sites deployed at locations far from the considered low-cost PM sensor for calibration performance enhancement. It was shown that the use of distant NO2 enhances the calibration performance compared to calibration without NO2 when it is highly correlated with colocated NO2. Overall, PA-II units have good agreement with PM2.5 monitoring systems of high quality. Moreover, the calibration performance can be improved by using machine learning algorithms and by considering temperature, RH, and especially NO2.