Traffic Incident Detection and Modelling using Quantum Frequency Algorithm and AutoRegressive Integrated Moving Average Models Jeanelle E. Abanto, Charmailene C. Reyes Jasmine A. Malinao, Henry N. Adorna Department of Computer Science, Algorithms and Complexity Laboratory, University of the Philippines, Diliman, Quezon City 1101 Philippines Email: {jeabanto, ccreyes2}@up.edu.ph, {jamalinao, hnadorna} @dcs.upd.edu.ph Abstract—In this study, we used AutoRegressive Integrated Moving Average (ARIMA) to effectively represent expected normal traffic behavior of those weeks identified to be ab- normal in the previous literature. Using the 2006 North Luzon Expressway North Bound (NLEX NB) Balintawak (Blk) segment’s hourly traffic volume and time mean speed data sets provided by the National Center for Transportation Studies (NCTS), we processed the data to generate time series plots of the weekly densities, the normal range of traffic density, and the abnormal. We obtained these through Quantum Frequency Algorithm (QFA). We fit the ARIMA model to some weeks of Blk which have evident occurrences of incidents as detected and crosschecked with the incidents data provided by NCTS. We performed a forecast of the fit and generated a time series plot of the superimposed plots of the actual data and the forecast for each of the top incidents generated in the previous literature. These plots provided a simplistic time-domain 2D visualizations that successfully exposed the abnormal points where incidents happened. These also provided an estimate of the expected traffic density behavior if incidents did not happen. Keywords-Incident; Normal; Abnormal; Normal Traffic Pat- tern; Quantum Frequency Algorithm; AutoRegressive Inte- grated Moving Average; I. I NTRODUCTION Various studies in traffic behavior had been done to determine the behavior of the traffic flow in expressways. In [1], it was shown that data signature-based density analysis and space mean speed can provide an efficient and effective representation of traffic behavior. In the results, outliers and potential outliers were determined by using data visualiza- tion (data images and Non-Metric Multidimensional Scaling (nMDS)) and confidence measures, providing a glimpse of interesting areas in some segments of the expressway. Close inspection and validation of their time-domain behavior pinpoint to those days of a week with abnormal traffic flow behavior (i.e. prolonged very low or high traffic volume, abrupt spikes or troughs brought about by various traffic disruptions). The literature still lacks an effective estimate of the expected traffic behavior not affected by incidents. Thus, this is established in this paper. The range of normal traffic behavior estimated from [15] used data which includes occurrences of incidents. The study aims to show that ARIMA is effective in forecasting the expected traffic be- havior of North Luzon Expressway (NLEX) using the time- series traffic density data set. To more accurately estimate the expected normal traffic behavior, we search for the best AutoRegressive Integrated Moving Average (ARIMA) model that will fit our data set before forecasting. Since the data set recorded and provided by the National Center for Transportation Studies (NCTS) is in time mean speed, it will be preprocessed similar to [1] for each data set in the year 2006 in order to analyze the results and identify the potential outliers. With the densities and clusters produced by the model in [1], we compute for the normal traffic behavior of each cluster. Analysis to these clusters were done in [15] in order to identify the abnormal weeks and their corresponding incidents in the 2006 incidents data set provided by the NCTS. In this paper, we fit the ARIMA model to some of the weeks of Blk’s cluster 0, where examples of occurrences of incidents are evident. We also provide time-series plots of the forecasts calculated from the fitted ARIMA model superimposed with the actual data. These forecasts model the expected traffic density behavior of Blk if incidents did not happen. Our goal is to produce an effective estimate of the normal traffic behavior of Blk, that could provide domain experts a simplistic representation of the overall traffic behavior of the expressway. The rest of the paper is organized as follows: Section II defines the concepts, and notations used. We present steps on how to perform a density-based clustering model based data analysis in Section III. Section IV discusses details of the results we obtained. Finally, we formulate conclusions and recommendations in Section V. II. BASIC DEFINITIONS AND NOTATIONS A. Data Set The data sets provided by NCTS in this study on the NLEX North Bound segments in the year 2006 are periodic. The data sets used in the study consist of the hourly time mean speed and mean volume of the Balintawak (BLK), and