Multi-phase Time Series Models for Motorway Flow Forecasting Mohsen Davarynejad, Yubin Wang, Jos Vrancken and Jan van den Berg Abstract— In this study, a multi-phase time series prediction approaches is proposed for solving the motorway flow fore- casting problem. The schemes presented here is based on an extensive study of flow patterns that were collected from a densely used ring road of Amsterdam, The Netherlands. The new prediction approach proposed here is based on a multi- phase information extraction whose ultimate goal is to forecast traffic states at the boundary points of a network. With its sim- ple architecture that makes the proposed approach of interest of practical application, a significant improvement is achieved in comparison with existing models. In its general form, the proposed approach could handle the curse of dimensionality,a common problem associated with the number of dimensions of input space. Index Terms— Demand Forecasting, Multi-phase Time Series Prediction, Kalman Filter, Adaptive Prediction, Support Vector Machine. I. I NTRODUCTION In advanced traffic management and control (which aims to reduce traffic congestions, improve mobility, influence traffic behaviors, improve traffic safety, etc), the prediction of road traffic states is an important requirement, specially when it comes to making available real-time information on travel demand. As a matter of fact, demand can be estimated using a simple calculation on volumes that are measured by detectors. Having this information enables to make short-term and long-term predictions of the traffic circulating. Prediction, in this content, concerns the ability to make predictions of traffic flows for several minutes using real-time data. Continues prediction and updating of traffic states are fundamental requirements for a proper traffic control [3], [6]. Proactive transportation management needs an ability to anticipate traffic conditions in advanced traffic management systems (ATMSs), in which without it, intelligent transportation systems (ITS) will provide services in a reactive manner, meaning analyzing the situation and finding a solution when a set of problems occurred. The ideal traffic state (that could be traffic flow, speed, travel time, and queue length) prediction is a networked- based model which simulates the movement of traffic through M. Davarynejad and J. Vrancken are with the Faculty of Technol- ogy, Policy and Management, Systems Engineering Group, Delft Univer- sity of Technology, the Netherlands, m.davarynejad@ieee.org, j.l.m.vrancken@tudelft.nl Y. Wang is with the Trinit´ e Automation B.V., Postbus 189, 1420 AD Uithoorn, y.wang@trinite.nl J. van den Berg is with the Faculty of Technology, Policy and Management, Section of Information and Communication Technologies, Delft University of Technology, the Netherlands, j.vandenberg@tudelft.nl a network (that could be deterministic vs. stochastic, con- tinuous vs. discrete and microscopic vs. macroscopic rep- resentation) and takes advantage of spatial and temporal information along with traffic flow dynamics. However, at the boundaries of every network, with the assumption that no upstream detector is available to be used for state prediction, the situation is different, since to predict the demand for travel through the network, the only available data describes past conditions. The prediction of states of boundaries of the network can be formulated as a time series problem as following. Given a collection of discrete-time past states measured in regular intervals at the boundaries of the network, x = {x 1 , x 2 ,..., x k ,..., x n } defined in some finite space, where dim(x k )= 1, we are interested in de- termining  x =  x n+1 ,  x n+2 ,...,  x n+q ,...,  x n+p in such a way that e n+1 , e n+2 ,..., e n+q ,..., e n+p is minimal, where e n+q =  x n+q − x n+q . A description of the contents of the paper by section follows. The next section contains a brief overview of past studies. Section III describes data used to conduct this research. Section IV presents the generic structure of the system along with the specific models used here. Section V illustrates the performance of the algorithm on real traffic data. Concluding remarks are stated in Section VI. II. MODELING APPROACHES A wide range of modeling approaches has been applied to traffic forecasting, including the multivariable time-series model [29], Kalman filtering method [19], spacetime autore- gressive integrated moving average (STARIMA) that incor- porates both the historical traffic data and the spatial features of a road network [9] and etc. Traditional parametric Box- Jenkins time series models have been used in [28] for single point traffic flow forecasting where a theoretical foundation for using seasonal ARIMA forecast models is established. In nonparameter regression (NPR) models, where no rigid assumptions about the data is required, the only requirement to describe the underlying process is the availability of suffi- cient historic data [7]. It concerns searching neighbors in the historical database. Three challenging steps when implement- ing an NPR methods are: 1) A right and appropriate state space, 2) An appropriate distance metric as a fundamental tool to determinate nearness of historical observations to the current conditions, 3) Selection of a forecast function which estimates the future state of the system. A Comparison of seasonal ARIMA (as a parametric model) and nonparametric models for traffic flow forecasting is available at [21] with the 2011 14th International IEEE Conference on Intelligent Transportation Systems Washington, DC, USA. October 5-7, 2011 978-1-4577-2197-7/11/$26.00 ©2011 IEEE 2033