Comparison of Machine Learning and Statistical Approaches for Predicting Travel Times in the Oklahoma Highway System

Traffic management systems play a vital role in supporting the smooth flow of traffic in road networks. By accurately predicting travel time, a traffic condition parameter that is extensively used in such systems, we can significantly improve the efficiency of these systems, decision-makers, and travelers. In this work, we use a dataset from the Oklahoma Department of Transportation to compare the accuracy of statistical and machine learning approaches to predicting travel time. We establish baseline accuracy by constructing a traditional statistical model using the seasonal autoregressive integrated moving average (SARIMA) approach. We compare this baseline to two machine learning models: one-dimensional convolutional neural networks (1-D CNNs) and long short-term memory (LSTM) networks. Our results show that our 1-D CNN and LSTM models have better performance than the statistical model. As an example, in a 4-step architecture (a model structure that simultaneously predicts travel time four periods ahead), the median root means squared relative error (RMSRE) scores for our LSTM and 1-D CNN models are 0.060 and 0.063, respectively. These compare to the median RMSRE score of 0.12 for the corresponding 4-step SARIMA model. The results also indicate that the machine learning approaches have significantly lower computation time compared to SARIMA. In addition, the 1-D CNN model has the least error variance across all architectures and among all modeling methods. Finally, the 1-D CNN approach is more consistent in terms of prediction error across the experimented architectures compared to the LSTM appraoch. Therefore, based on the results, we highly recommend using machine learning approaches, specifically, 1-D CNNs, for estimating travel time in roadway systems and for other similar time-series prediction problems

Space-time modeling of traffic flow

A key concern in transportation planning and traffic management is the ability to forecast traffic flows on a street network. Traffic flows forecasts can be transformed to obtain travel time estimates and then use these as input to travel demand models, dynamic route guidance and congestion management procedures. A variety of mathematical techniques have been proposed for modeling traffic flow on a street network. Briefly, the most widely used theories are: -Kinetic models based on partial differential equations that describe waves of different traffic densities, -deterministic models that use nonlinear equations for the estimation of different car routes, -large scale simulation models such as cellular automata and, -stochastic modeling of traffic density at distinct points in space. One problem with these approaches is that the traffic flow process is characterized by nonstationarities that cannot be taken into account by the vast majority of modeling strategies. However, recent advances in statistical modeling in fields such as econometrics or environmetrics enable us to overcome this problem. The aim of this work is to present how two statistical techniques, namely, vector autoregressive modeling and dynamic space-time modeling can be used to develop efficient and reliable forecasts of traffic flow. The former approach is encountered in the econometrics literature, whereas the later is mostly used in environmetrics. Recent advances in statistical methodology provide powerful tools for traffic flow description and forecasting. For a purely statistical approach to travel time prediction one may consult Rice and van Zwet (2002). In this work, the authors employ a time varying coefficients regression technique that can be easily implemented computationally, but is sensitive to nonstationarities and does not take into account traffic flow information from neighboring points in the network that can significantly improve forecasts. According to our approach, traffic flow measurements, that is count of vehicles and road occupancy obtained at constants time intervals through loop detectors located at various distinct points of a road network, form a multiple time series set. This set can be described by a vector autoregressive process that models each series as a linear combination of past observations of some (optimally selected) components of the vector; in our case the vector is comprised by the different measurement points of traffic flow. For a thorough technical discussion on vector autoregressive processes we refer to Lutkerpohl (1987), whereas a number of applications can be found in Ooms (1994). Nowadays, these models are easily implemented in commercial software like SAS or MATLAB; see for example LeSage (1999). The spatial distribution of the measurement locations and their neighboring relations cannot be incorporated in a vector autoregressive model. However, accounting for this information may optimize model fitting and provide insight into spatial correlation structures that evolve through time. This can be accomplished by applying space-time modeling techniques. The main difference of space-time models encountered in literature with the vector autoregressive ones lies in the inclusion of a weight matrix that defines the neighboring relations and places the appropriate restrictions. For some early references on space-time models, one could consult Pfeifer and Deutsch (1980 a,b); for a Bayesian approach, insensitive to nonstationarities we refer to Wikle, Berliner and Cressie (1998). In this work, we discuss how the space-time methodology can be implemented to traffic flow modeling. The aforementioned modeling strategies are applied in a subset of traffic flow measurements collected every 15 minutes through loop detectors at 74 locations in the city of Athens. A comparative study in terms of model fitting and forecasting accuracy is performed. Univariate time series models are also fitted in each measurement location in order to investigate the relation between a model's dimension and performance. References: LeSage J. P. (1999). Applied Econometrics using MATLAB. Manuscript, Dept. of Economics, University of Toronto Lutkerpohl H. (1987). Forecasting Aggregated Vector ARMA Processes. Lecture Notes in Economics and Mathematical Systems. Springer Verlag Berlin Heidelberg Ooms M. (1994). Empirical Vector Autoregressive Modeling. Springer Verlag Berlin Heidelberg Pfeifer P. E., and Deutsch S. J. (1980a). A three-stage iterative procedure for Space-Time Modeling. Technometrics, 22, 35-47 Pfeifer P. E., and Deutsch S. J. (1980b). Identification and Interpretation of First-Order Space-Time ARMA models. Technometrics, 22, 397-408 Rice J., and van Zwet E. (2002). A simple and effective method for predicting travel times on freeways. Manuscript, Dept. of Statistics, University of California at Berkeley Wikle C. K., Berliner L. M. and Cressie N. (1998). Hierarchical Bayesian space-time models. Environmental and Ecological Statistics, 5, 117-154

Forecasting airport passenger traffic: the case of Hong Kong International Airport

Hong Kong International Airport is one of the main gateways to Mainland China and the major aviation hub in Asia. An accurate airport traffic demand forecast allows for short and long-term planning and decision making regarding airport facilities and flight networks. This paper employs the Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) methodology to build and estimate the univariate seasonal ARIMA model and the ARIMX model with explanatory variables for forecasting airport passenger traffic for Hong Kong, and projecting its future growth trend from 2011to 2015. Both fitted models are found to have the lower Mean Absolute Percentage Error (MAPE) figures, and then the models are used to obtain ex-post forecasts with accurate forecasting results. More importantly, both ARIMA models predict a growth in future airport passenger traffic at Hong Kong

Predicting respiratory motion for real-time tumour tracking in radiotherapy

Purpose. Radiation therapy is a local treatment aimed at cells in and around a tumor. The goal of this study is to develop an algorithmic solution for predicting the position of a target in 3D in real time, aiming for the short fixed calibration time for each patient at the beginning of the procedure. Accurate predictions of lung tumor motion are expected to improve the precision of radiation treatment by controlling the position of a couch or a beam in order to compensate for respiratory motion during radiation treatment. Methods. For developing the algorithmic solution, data mining techniques are used. A model form from the family of exponential smoothing is assumed, and the model parameters are fitted by minimizing the absolute disposition error, and the fluctuations of the prediction signal (jitter). The predictive performance is evaluated retrospectively on clinical datasets capturing different behavior (being quiet, talking, laughing), and validated in real-time on a prototype system with respiratory motion imitation. Results. An algorithmic solution for respiratory motion prediction (called ExSmi) is designed. ExSmi achieves good accuracy of prediction (error $4-9$ mm/s) with acceptable jitter values (5-7 mm/s), as tested on out-of-sample data. The datasets, the code for algorithms and the experiments are openly available for research purposes on a dedicated website. Conclusions. The developed algorithmic solution performs well to be prototyped and deployed in applications of radiotherapy

Bus arrival time prediction using stochastic time series and Markov chains

Public transit agencies rely on disseminating accurate and reliable information to transit users to achieve higher service quality and attract more users. With the development of new technologies, the concept of providing users with reliable information about bus arrival times at bus stops has become increasingly attractive. Due to the fact that bus operation parameters and variables are highly stochastic, modeling prediction of bus travel and arrival times has become one of the many challenging tasks. Stochastic time series and delay propagation models to predict bus arrival times using historical information were developed. Markov models were developed to predict propagation of bus delay to downstream bus stops based on heterogeneous conditions. The bus arrival times were predicted using a Markov model only and performance measures were obtained and a combined arrival time prediction model consisting of delay propagation and full autoregressive model was also developed. The inclusion of bus delay propagation into the bus arrival time prediction algorithm is an important contribution to the research efforts to predict bus arrival times. The research showed that Markov models can provide accurate bus arrival time predictions without increasing the need for a large number of bus operation variables, simulations and high polling frequency of the geographical bus location as used by other modeling approaches

Time Series Forecasts of International Tourism Demand for Australia,

This paper examines stationary and nonstationary time series by formally testing for the presence of unit roots and seasonal unit roots prior to estimation, model selection and forecasting. Various Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) models are estimated over the period 1975(1)-1989(4) for tourist arrivals to Australia from Hong Kong, Malaysia and Singapore. The mean absolute percentage error (MAPE) and root mean squared error (RMSE) are used as measures of forecast accuracy. As the best fitting ARIMA model is found to have the lowest RMSE, it is used to obtain post-sample forecasts. Tourist arrivals data for 1990(1) to 1996(4) are compared with the forecast performance of the ARIMA model for each origin market. The fitted ARIMA model forecasts tourist arrivals from Singapore between 1990(1)-1996(4) very well. Although the ARIMA model outperforms the seasonal ARIMA models for Hong Kong and Malaysia, the forecast of tourist arrivals is not as accurate as in the case of Singapore.