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

Dynamic spatial weight matrix and localised STARIMA for network modelling

Various statistical model specifications for describing spatiotemporal processes have been proposed over the years, including the space–time autoregressive integrated moving average (STARIMA) and its various extensions. These model specifications assume that the correlation in data can be adequately described by parameters that are globally fixed spatially and/or temporally. They are inadequate for cases in which the correlations among data are dynamic and heterogeneous, such as network data. The aim of this article is to describe autocorrelation in network data with a dynamic spatial weight matrix and a localized STARIMA model that captures the autocorrelation locally (heterogeneity) and dynamically (nonstationarity). The specification is tested with traffic data collected for central London. The result shows that the performance of estimation and prediction is improved compared with standard STARIMA models that are widely used for space–time modeling. En los últimos años, se han propuesto diversas especificaciones de modelado estadístico para describir procesos espacio-temporales. Esto incluye el modelo espacio-temporal autorregresivo integrado de media móvil (STARIMA) y sus varios derivados. Estas especificaciones de modelo asumen que la correlación de los datos puede ser adecuadamente descrita por parámetros que se fijan a nivel global en el espacio y/o tiempo. Dichos parámetros son inadecuados para los casos en los que las correlaciones entre los datos son dinámicas y heterogéneas, como en el contexto de los datos de la red. El objetivo de este artículo es describir la autocorrelación en los datos de red con una matriz de ponderación espacial dinámica y un modelo STARIMA localizado (LSTARIMA) que captura la autocorrelación local (heterogeneidad) de forma dinámica (no estacionariedad). La especificación del modelo es evaluada con datos de tráfico recolectados en el centro de Londres. Los resultados demuestran que los rendimientos de estimación y predicción mejoran con el método propuesto en comparación con los modelos STARIMA estándar que son ampliamente utilizados para el modelado de espacio-temporal

Modeling, Analysis and Application of Big Traffic Data for Intelligent Transportation Systems

University of Technology Sydney. Faculty of Engineering and Information Technology.Intelligent Transportation System (ITS), an integrated system of people, roads, and vehicles by utilizing information and communications technology, has emerged as an efficient way of improving the performance of transportation systems, enhancing travel security, and providing more choice to travelers. Recently, it has been seen that the big data era for ITS is coming due to the wide use of traffic detectors like traffic cameras and GPSs. These traffic detectors can collect various types of traffic data that significantly contribute to the development of ITS, which has the benefit of the public with convenient and safe travel. With big traffic data, data-driven methods provide powerful and theoretical support for data modeling, analysis, and applications. However, existing methods still suffer from some shortcomings. First, traffic predictors usually use black-box methods to capture the spatiotemporal correlation between traffic. As a result, it reduces the flexibility of predictors due to the time-varying spatial-temporal correlation caused by frequent variation of road conditions. Second, it is impossible to cover all urban areas with traffic detectors. Thus, data absence and data sparsity have an essential impact on the reliability of travel state monitoring in a large road network. Lastly, most big data applications are based on the centralized method for processing and analyzing data, which consume more time and computational resources, optimal decision making. These make research on big traffic data in ITS become both exciting and essential. In this thesis, a physically intuitive approach is developed for short-term traffic flow prediction that captures the time-varying spatiotemporal correlation between traffic, mainly attributed to the road network topology, travel speed, and trip distribution. Experimental results demonstrate its superior accuracy and lower computational complexity compared with its counterparts. After that, a novel methodology is presented to estimate link travel time distributions (TTDs) using end-to-end (E2E) measurements detected by the limited traffic detectors. The experimental results show that the estimated results are in excellent agreement with the empirical distributions. Lastly, a distributed scheme is proposed for taxi cruising route recommendations based on taxi demands predicted by the proposed Graph Convolutional Network (GCN) based method. Experiment and simulation are both implemented. Experimental results validate the accuracy of the proposed taxi demand predictor. Simulation results indicate that our proposed taxi recommendation scheme is better than its counterparts in the aspects of minimizing the number of vacant taxis and maximizing the global revenue of taxi drivers

Spatio-temporal forecasting of network data

In the digital age, data are collected in unprecedented volumes on a plethora of networks. These data provide opportunities to develop our understanding of network processes by allowing data to drive method, revealing new and often unexpected insights. To date, there has been extensive research into the structure and function of complex networks, but there is scope for improvement in modelling the spatio-temporal evolution of network processes in order to forecast future conditions. This thesis focusses on forecasting using data collected on road networks. Road traffic congestion is a serious and persistent problem in most major cities around the world, and it is the task of researchers and traffic engineers to make use of voluminous traffic data to help alleviate congestion. Recently, spatio-temporal models have been applied to traffic data, showing improvements over time series methods. Although progress has been made, challenges remain. Firstly, most existing methods perform well under typical conditions, but less well under atypical conditions. Secondly, existing spatio-temporal models have been applied to traffic data with high spatial resolution, and there has been little research into how to incorporate spatial information on spatially sparse sensor networks, where the dependency relationships between locations are uncertain. Thirdly, traffic data is characterised by high missing rates, and existing methods are generally poorly equipped to deal with this in a real time setting. In this thesis, a local online kernel ridge regression model is developed that addresses these three issues, with application to forecasting of travel times collected by automatic number plate recognition on London’s road network. The model parameters can vary spatially and temporally, allowing it to better model the time varying characteristics of traffic data, and to deal with abnormal traffic situations. Methods are defined for linking the spatially sparse sensor network to the physical road network, providing an improved representation of the spatial relationship between sensor locations. The incorporation of the spatio-temporal neighbourhood enables the model to forecast effectively under missing data. The proposed model outperforms a range of benchmark models at forecasting under normal conditions, and under various missing data scenarios

A visual analytics framework for spatio-temporal analysis and modelling

To support analysis and modelling of large amounts of spatio-temporal data having the form of spatially referenced time series (TS) of numeric values, we combine interactive visual techniques with computational methods from machine learning and statistics. Clustering methods and interactive techniques are used to group TS by similarity. Statistical methods for TS modelling are then applied to representative TS derived from the groups of similar TS. The framework includes interactive visual interfaces to a library of modelling methods supporting the selection of a suitable method, adjustment of model parameters, and evaluation of the models obtained. The models can be externally stored, communicated, and used for prediction and in further computational analyses. From the visual analytics perspective, the framework suggests a way to externalize spatio-temporal patterns emerging in the mind of the analyst as a result of interactive visual analysis: the patterns are represented in the form of computer-processable and reusable models. From the statistical analysis perspective, the framework demonstrates how TS analysis and modelling can be supported by interactive visual interfaces, particularly, in a case of numerous TS that are hard to analyse individually. From the application perspective, the framework suggests a way to analyse large numbers of spatial TS with the use of well-established statistical methods for TS analysis

Understanding and Modeling Taxi Demand Using Time Series Models

The spatio-temporal variations in demand for transportation, particularly taxis, are impacted by various factors such as commuting, weather, road work and closures, disruption in transit services, etc. Identifying the factors that influence taxi demand and understanding its dynamic provide planners with the information necessary to improve the transportation systems and also help drivers to reduce their vacant time. This dissertation focuses on important factors affecting the demand. In the beginning, the impact of price changes on the demand is studied. Chapter One discusses how the seasonal effects and trends are removed from the demand, and then price elasticity for demand is calculated as a measure to quantify the impact of each factor. Furthermore, the first chapter provides elasticity values for the New York City and each of the five boroughs, and studies the relationship between these values and some socio-economic characteristics. The second part of this dissertation studies the demand of taxi and how it is affected by other public transportation modes and weather. This demand modeling technique utilizes a combination of time series and linear regression models. The proposed method is then applied to yellow cab data in New York City. The pick-up points of yellow cab data in April, May, and June of 2014 are considered and aggregated every hour. The results show a significant correlation between taxi demand and demand for other transportation modes, as well as weather conditions. It is shown that combining time series models with linear regression will improve the performance of the model. This study then follows by working on the time series models and considering the spatial variation of the demand. To understand the user demand for taxis through space and time, a generalized spatio-temporal autoregressive (STAR) model is proposed. In order to deal with the high dimensionality of the model, LASSO-type penalized methods are proposed to tackle the parameter estimation. The forecasting performance of the proposed models is measured using the out-of-sample mean squared prediction error (MSPE), and it is found that the proposed models outperform other alternative models such as vector autoregressive (VAR) models. The proposed modeling framework has an easily interpretable parameter structure and can feasibly be applied by taxi operators. The efficiency of the proposed model shows advantages for model estimation in real-time applications. Furthermore, this dissertation studies the demand for e-hailing services which are growing rapidly especially in large cities. Similar to taxi demand, Uber demand is not distributed uniformly, either spatially or temporally, and this study proposes using spatio-temporal models to predict Uber demand as well. Moreover, the prediction performances of several statistical models are compared with each other: a) one temporal model (vector autoregressive (VAR)), b) two proposed spatio-temporal models (spatial-temporal autoregressive (STAR), c) least absolute shrinkage and selection operator applied on STAR (LASSO-STAR)). They are compared in different scenarios (based on the number of time and space lags), and for both peak and off-peak periods (rush hours and non-rush hours). This section additionally proposes different weighting matrices to improve the performance of the model. The results show the need to consider spatial models for e-hailing services and demonstrate significant improvement in the prediction of demand using the two proposed models

Modelling and inference for the travel times in vehicle routing problems

Every day delivery companies need to select routes to deliver goods to their customers. A common method for the formulation and for finding the best route is the vehicle routing problem (VRP). One of the key assumptions when solving a VRP is that the input values are correct. In the case of travel time along a section of road, these values must be predicted in advance. Hence selecting the optimal solution requires accurate predictions. This thesis focuses upon the prediction of travel time along links, such that the predictions will be used in the defined VRP. The road network is split into links, which are connected together to form routes in the VRP. Travel time predictions are generated for each link. We predict the general behaviour of the travel times for each link, using time series forecasting models. These are tested both empirically, against the observed travel time, and theoretically, against the ideal characteristics of a VRP travel time input, including the resulting prediction uncertainty in the VRP. Small input variations are likely to have little impact upon the optimal solution. In contrast, infrequent and unpredicted large delays, e.g., from accidents, which occur outside the general travel time behaviour can change optimal routes. We study the delay behaviour and suggest a novel model consisting of three parts: the delay occurrence rate, length and size. We then suggest ways to input both the delay and the general travel time models to the VRP, which results in an optimal solution that is more robust to delays. Traffic moves from one link into the network, so if one link is busier then the same traffic will flow to the connecting links. We extend the single link model to incorporate information from the surrounding links using a network model. This produces better predictions than the single link models and hence better inputs for the VRP