Parameter estimation for stochastic hybrid model applied to urban traffic flow estimation

This study proposes a novel data-based approach for estimating the parameters of a stochastic hybrid model describing the traffic flow in an urban traffic network with signalized intersections. The model represents the evolution of the traffic flow rate, measuring the number of vehicles passing a given location per time unit. This traffic flow rate is described using a mode-dependent first-order autoregressive (AR) stochastic process. The parameters of the AR process take different values depending on the mode of traffic operation – free flowing, congested or faulty – making this a hybrid stochastic process. Mode switching occurs according to a first-order Markov chain. This study proposes an expectation-maximization (EM) technique for estimating the transition matrix of this Markovian mode process and the parameters of the AR models for each mode. The technique is applied to actual traffic flow data from the city of Jakarta, Indonesia. The model thus obtained is validated by using the smoothed inference algorithms and an online particle filter. The authors also develop an EM parameter estimation that, in combination with a time-window shift technique, can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator

Freeway Origin Destination Matrices: Not as Simple as They Seem

Travel demand can be elegantly represented using an Origin-Destination (OD) matrix. The link counts observed on the network are produced by the underlying travel demand. One could use these counts to reconstruct the OD matrix. An offline approach to estimate a static OD matrix over the peak period for freeway sections using these counts is proposed in this research. Almost all the offline methods use linear models to approximate the relationship between the on-ramp and off-ramp counts. Previous work indicates that the use of a traffic flow model embedded in a search routine performs better than these linear models. In this research that approach is enhanced using a microscopic traffic simulator, AIMSUN, and a gradient based optimization routine, MINOS, interfaced to estimate an OD matrix. This approach is an application of the Prediction Error Minimization (PEM) method. The problem is non-linear and non-smooth, and the optimization routine finds multiple local minima, but cannot guarantee a global minima. However, with a number of starting seed matrices, an OD matrix with a good fit in terms of reproducing traffic counts can be estimated. The dominance of the mainline counts in the OD estimation and an identifiability issue is indicated from the experiments. The quality of the estimates improves as the specification error, introduced due to the discrepancy between the traffic flow model and the real world process that generates the on-ramp and off-ramp counts, reduces.travel demand, OD estimation, simulation, optimization

Development of dynamic recursive models for freeway travel time predictions

Traffic congestion has been a major problem in metropolitan areas, which is caused by either insufficient roadway capacity or unforesceable incidents. In order to promote the efficiency of the existing roadway networks and mitigate the impact of traffic congestion, the development of a sound prediction model for travel times is desirable. A comprehensive literature review about existing prediction models was conducted by investigating the advantages, disadvantages, and limitations of each model. Based on the features and properties of previous models, the base models including exponential smoothing model (ESM), moving average model (MAM), and Kalman filtering model (KFM) are developed to capture stochastic properties of traffic behavior for travel time prediction. By incorporating KFM into ESM and MAM, three dynamic recursive prediction models including dynamic exponential smoothing model (DESM), improved dynamic exponential smoothing model (JDESM), and dynamic moving average model (DMAM) are developed, in which the time-varying weight parameters are optimized based on the most recent observation. Model evaluation has been conducted to analyze prediction accuracy under various traffic conditions (e.g., free-flow condition, recurrent and non-recurrent congested traffic conditions). Results show that the IDESM in general outperforms other models developed in this study in prediction accuracy and stability. In addition, the feature and logic of the IDESM lead to its high transferability and adaptability, which could enable the prediction model to perform well at multiple locations and deal with complicated traffic conditions. Besides the proficient capability, the IDESM is easy to implement in the real world transportation network. Thus, the IDESM is proven an appealing approach for short-time travel time prediction under various traffic conditions. The application scope of the IDESM is identified, while the optimal prediction intervals are also suggested in this study

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

Proactive Assessment of Accident Risk to Improve Safety on a System of Freeways, Research Report 11-15

This report describes the development and evaluation of real-time crash risk-assessment models for four freeway corridors: U.S. Route 101 NB (northbound) and SB (southbound) and Interstate 880 NB and SB. Crash data for these freeway segments for the 16-month period from January 2010 through April 2011 are used to link historical crash occurrences with real-time traffic patterns observed through loop-detector data. \u27The crash risk-assessment models are based on a binary classification approach (crash and non-crash outcomes), with traffic parameters measured at surrounding vehicle detection station (VDS) locations as the independent variables. The analysis techniques used in this study are logistic regression and classification trees. Prior to developing the models, some data-related issues such as data cleaning and aggregation were addressed. The modeling efforts revealed that the turbulence resulting from speed variation is significantly associated with crash risk on the U.S. 101 NB corridor. The models estimated with data from U.S. 101 NB were evaluated on the basis of their classification performance, not only on U.S. 101 NB, but also on the other three freeway segments for transferability assessment. It was found that the predictive model derived from one freeway can be readily applied to other freeways, although the classification performance decreases. The models that transfer best to other roadways were determined to be those that use the least number of VDSs–that is, those that use one upstream or downstream station rather than two or three.\ The classification accuracy of the models is discussed in terms of how the models can be used for real-time crash risk assessment. The models can be applied to developing and testing variable speed limits (VSLs) and ramp-metering strategies that proactively attempt to reduce crash risk