Simultaneous estimation of states and parameters in Newell’s simplified kinematic wave model with Eulerian and Lagrangian traffic data (original) (raw)

A shockwave profile model for traffic flow on congested urban arterials

2011

In this paper a new traffic flow model for congested arterial networks, named shockwave profile model (SPM), is presented. Taking advantage of the fact that traffic states within a congested link can be simplified as free-flow, saturated, and jammed conditions, SPM simulates traffic dynamics by analytically deriving the trajectories of four major shockwaves: queuing, discharge, departure, and compression waves. Unlike conventional macroscopic models, in which space is often discretized into small cells for numerical solutions, SPM treats each homogeneous road segment with constant capacity as a section; and the queuing dynamics within each section are described by tracing the shockwave fronts. SPM is particularly suitable for simulating traffic flow on congested signalized arterials especially with queue spillover problems, where the steady-state periodic pattern of queue build-up and dissipation process may break down. Depending on when and where spillover occurs along a signalized arterial, a large number of queuing patterns may be possible. Therefore it becomes difficult to apply the conventional approach directly to track shockwave fronts. To overcome this difficulty, a novel approach is proposed as part of the SPM, in which queue spillover is treated as either extending a red phase or creating new smaller cycles, so that the analytical solutions for tracing the shockwave fronts can be easily applied. Since only the essential features of arterial traffic flow, i.e., queue build-up and dissipation, are considered, SPM significantly reduces the computational load and improves the numerical efficiency. We further validated SPM using real-world traffic signal data collected from a major arterial in the Twin Cities. The results clearly demonstrate the effectiveness and accuracy of the model. We expect that in the future this model can be applied in a number of real-time applications such as arterial performance prediction and signal optimization.

A simple explicit model approximating the relationship between speed and density of vehicular traffic on urban roads

International Journal of Critical Infrastructures, 2012

With the increase in simulation of urban environments for the purpose of planning, modelling vehicular traffic has become important. Since empirical evidence on traffic flow is relatively sparse, models are being increasingly used for planning urban roads and environments. In this paper, a simple, explicit model is proposed to approximate the speed versus density of vehicular traffic flow. The model, which uses two parameters derived from simple measurements of real-time traffic data, allows for a prediction of the approximate relationship for congested as well as uncongested vehicular traffic flow. The proposed model is especially useful in conditions where available data is sparse and can be invaluable for the modelling and simulation of urban environments.

A review of the mathematical models for traffic flow

International Journal of Advances in Engineering Sciences and Applied Mathematics, 2009

In this paper, we critically review mathematical models for the flow of traffic that treat traffic as a continuum and provide a discussion of their shortcomings. We also review a spatially discrete traffic flow model that does not suffer from such shortcomings and provide recently collected, corroborating data for a trip-time estimation scheme based on the spatially discrete model. Keywords Traffic models • Spatially discrete traffic model • Large-scale systems • String stability • Limit of dynamical systems.

Vehicular traffic models for speed-density-flow relationship

Journal of Mathematical Modelling, 2020

The relationship among vehicles on the road is modeled using fundamental traffic equations. In traffic modeling, a particular speed-density equation usually fits a peculiar dataset. The study seeks to parameterize some existing fundamental models so that a given equation could match different dataset. The new equations are surmisal offshoots from existing equations. The parameterized equations are used in the LWR model and solved using the Lax-Friedrichs differencing scheme. The simulation results illustrate different scenarios of acceleration and deceleration traffic wave profiles. The proposed models appropriately explain the varying transitions of different traffic regimes.

On kinematic waves II. A theory of traffic flow on long crowded roads

is studied before and after some change in road conditions, and statistical technique is used to find out whether the change significantly reduces journey times or accidents. Extensive researches on similar lines are carried out in the U.S.A., notably by the Division of Highway Transport Research, and by certain university departments such as the Post-graduate School of Highway Engineering at Yale.

Lagrangian traffic state estimation for freeway networks

2011

Recent studies show that the classic kinematic wave model can be formulated and solved more efficiently and accurately in Lagrangian (vehicle numbertime) coordinates compared in Eulerian (spacetime) coordinates. In this paper we present a state estimator formulated in Lagrangian coordinates for freeway networks. It is based on the extended Kalman filtering technique, in which the discretized Lagrangian kinematic wave model is used as the process equation. Meanwhile, the node models in Lagrangian coordinates are developed to complete the network modeling. This Lagrangian state estimator is validated and compared to an Eulerian counterpart in a microscopic simulation environment. The results demonstrate that a networkwide Lagrangian state estimation become available and indicate the Lagrangian estimator outperforms the Eulerian approach.

Incorporation of Lagrangian measurements in freeway traffic state estimation

Transportation Research Part B: Methodological, 2010

Cell-phones equipped with a global positioning system (GPS) provide new opportunities for location-based services and traffic estimation. When traveling on-board vehicles, these phones can be used to accurately provide position and velocity of the vehicle as probe traffic sensors. This article presents a new technique to incorporate mobile probe measurements into highway traffic flow models, and compares it to a Kalman filtering approach. These two techniques are both used to reconstruct traffic density. The first technique modifies the Lighthill-Whitham-Richards partial differential equation (PDE) to incorporate a correction term which reduces the discrepancy between the measurements (from the probe vehicles) and the estimated state (from the model). This technique, called Newtonian relaxation, ''nudges" the model to the measurements. The second technique is based on Kalman filtering and the framework of hybrid systems, which implements an observer equation into a linearized flow model. Both techniques assume the knowledge of the fundamental diagram and the conditions at both boundaries of the section of interest. The techniques are designed in a way in which does not require the knowledge of on-and off-ramp detector counts, which in practice are rarely available. The differences between both techniques are assessed in the context of the Next Generation Simulation program (NGSIM), which is used as a benchmark data set to compare both methods. They are finally tested with data from the Mobile Century experiment obtained from 100 Nokia N95 mobile phones on I-880 in California on February 8, 2008. The results are promising, showing that the proposed methods successfully incorporate the GPS data in the estimation of traffic.

Freeway traffic state estimation using extended Kalman filter for first-order traffic model in Lagrangian coordinates

2011 International Conference on Networking, Sensing and Control, ICNSC 2011, 2011

Freeway traffic state estimation is one of the central components in real-time traffic management and information applications. Recent studies show that the classic kinematic wave model can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number-time) coordinates. This paper investigates the opportunities of the Lagrangian form for state estimation. The main advantage for state estimation is that in Lagrangian coordinates, the numerical solution scheme is reduced to an upwind scheme. We propose a new model-based extended Kalman filter (EKF) state estimator where the discretized Lagrangian model is used as the model equation. This state estimator is applied to freeway traffic state estimation and validated using synthetic data. Different filter design specifications with respect to measurement aspects are considered. The achieved results are very promising for subsequent studies.

Reproducible Features of Congested Highway Traffic

2000

Observation of a four-mile long, inhomogeneous, congested traffic stream revealed that vehicle accumulations between detectors vary with flow in a predictable way, and that a macroscopic kinematic wave with a reproducible speed exists in queues despite unusual traffic behavior. As a result, time-dependent vehicle trip times and accumulations inside long queues (and the queue length itself) can be predicted from readily available data without using any "degrees of freedom" to fit the parameters of a model. Experimental vehicle counts were within 20 vehicles of the predictions for over two hours. (~)