Real-time travel time estimation using macroscopic traffic flow models

The development of synchronized flow has been a challenge in traffic flow studies, and so far the approaches based on macroscopic models have yet to provide a good level of understanding. In this work we present a continuum model which considers two vehicle classes, based on kinetic traffic flow theory for aggressive drivers. The numerical solutions show that the transition F → S occurs under specific conditions, qualitatively in agreement with Kerner's three-phase theory.

Real-time travel-time prediction method applying multiple traffic observations

Macroscopic traffic flow modelling of large-scale freeway networks with field data verification: State-of-the-art review, benchmarking framework, and case studies using METANET

We propose a Bayesian approach for parameter uncertainty quantification in macroscopic traffic flow models from cross-sectional data. We consider both a simple first order model consisting in the mass conservation equation and its second order version including a speed evolution equation. A bias term is introduced and modeled as a Gaussian process to account for the traffic flow models limitations. We validate the results comparing the error in the macroscopic variables (flow, speed, density) for both models, showing that second order models globally perform better in reconstructing traffic quantities of interest.

Environmentally friendly traffic control strategy - A case study in Xi’an city

We introduce microscopic and macroscopic stochastic traffic models including traffic accidents. The microscopic model is based on a Follow-the-Leader approach whereas the macroscopic model is described by a scalar conservation law with space dependent flux function. Accidents are introduced as interruptions of a deterministic evolution and are directly linked to the traffic situation. Based on a Lax-Friedrichs discretization convergence of the microscopic model to the macroscopic model is shown. Numerical simulations are presented to compare the above models and show their convergence behaviour.

The state of the art of macroscopic vehicle traffic flow models is discussed and the traffic flow stability of these models is analyzed. A nonlinear traffic flow stability criterion is investigated using the wavefront expansion technique. Qualitative relationships between traffic flow stability and model parameters are derived for an entire class of second-order macroscopic traffic flow models. Numerical results axe obtained using the CLAWPACK package for the well-known Payne-Whitham model, in order to illustrate the stability criterion. The newly derived stability results are consistent with previous reported results obtained using both microscopic models and approximate linearization methods. Moreover, the stability criteria derived in the paper can provide more refined information regarding the propagation of traffic flow perturbations and shock waves in second-order models than previously established methodologies.

An integrated macroscopic traffic model is proposed, which integrates a macroscopic urban traffic flow model with a microscopic traffic emission model for individual vehicles. As a macroscopic model, the integrated model is fast enough for on-line control purposes. Nevertheless, the model can still capture the traffic emissions for vehicles in different states compared with using a macroscopic traffic emission model, because of the accuracy of the microscopic traffic emission model. Model Predictive Control is applied to control urban traffic areas based on the integrated traffic model, aiming at reducing both travel delays and traffic emissions.

Traffic congestion and delays at signalized intersections remain a challenge in urban mobility. To minimize congestion, adaptive traffic signal control systems have been adopted across the United States. However, for these systems to function at their best, systems require an accurate estimation of traffic states, such as traffic density and queue length. This paper implements a relatively novel method, Physics-Informed Neural Networks (PINNs), for real-time traffic density estimation to enhance adaptive intersection signal control. The methodology leverages PINNs, which integrate both data-driven learning and physical constraints imposed by the Lighthill-Whitham-Richards (LWR) macroscopic traffic flow model. A simulation of a four-way intersection was used to generate realistic spatio-temporal traffic data to evaluate the performance of the model. Separate PINNs models, one trained for each incoming approach using simulation-based spatio-temporal density data, provide segment-level density predictions. These real-time density estimates are then employed within an adaptive traffic signal control algorithm designed to adjust green light phasing based on detected demand. The proposed PINNs control strategy was evaluated through simulation, comparing its performance against the Webster traffic timing method using key metrics such as average vehicle delay at the intersection and average vehicle travel time. The findings show an approximate 18% decrease in average vehicle delay and more than a 6% reduction in average travel time when utilizing adaptive traffic control based on the PINNs method for determining density values. These findings highlight the potential of leveraging PINNs for accurate, real-time traffic state estimation, which can effectively inform and improve the performance of adaptive traffic signal control systems, leading to reduced congestion and enhanced mobility at intersections.

We consider a macroscopic traffic flow model tagged on a closure nonlinear density-velocity relationship yielding a quasi-linear first order (hyperbolic) partial differential equation (PDE) as an initial boundary value problem (IBVP). We present the analytic solution of the PDE which is in implicit form. We describe the derivation of a finite difference scheme of the IBVP which is a first order explicit upwind difference scheme. We establish the well-posed-ness and stability condition of the finite difference scheme. To implement the numerical scheme we develop computer program using MATLAB programming language in order to verify some qualitative behaviors for various traffic parameters. DOI: http://dx.doi.org/10.3329/bjsir.v47i3.13070 Bangladesh J. Sci. Ind. Res. 47(3), 339-346 2012

In this work, we propose an algorithm performing short-term predictions of the flow and speed of vehicles on a stretch of road, using past measurements of these quantities. This algorithm is based on a physics-aware recurrent neural network. A discretization of a macroscopic traffic flow model (using the so-called Traffic Reaction Model) is embedded in the architecture of the network and yields traffic state estimations and predictions for the flow and speed of vehicles, which are physically-constrained by the macroscopic traffic flow model and based on estimated and predicted space–time dependent traffic parameters. These parameters are themselves obtained using a succession of LSTM recurrent neural networks. The algorithm is tested on raw flow measurements obtained from loop detectors.

Positively Conservative Scheme for Macroscopic Traffic Flow Models

An Automated Calibration Procedure for Macroscopic Traffic Flow Models

Today, the issue of video data processing is very urgent. For example, determining the purpose of human behavior, analyzing economic networks, identifying and eliminating traffic jams on the streets, etc. Nowadays, the increase in the number of vehicles moving on the roads creates traffic jams on the city streets. This makes it urgent to eliminate traffic jams, especially in tourist cities. First of all, the causes of traffic congestion should be identified, traffic congestion can have various causes, such as insufficient capacity, unrestricted demand, traffic light delays, pedestrians crossing the roads at the wrong place , wrong location of sidewalks and etc. Therefore, there is a need to simulate and optimize traffic control to better meet this growing demand. In this research paper, microscopic and macroscopic traffic flow models are reviewed and their properties are discussed to determine which one is suitable for use in this study.

This paper presents a real-time freeway network traffic surveillance tool RENAISSANCE. Based on a stochastic macroscopic freeway network traffic flow model and the extended Kalman filter, RENAISSANCE is fed with a limited amount of real-time traffic measurements to enable a number of freeway network traffic surveillance tasks, including traffic state estimation and prediction, travel time estimation and prediction, queue tail/head/length estimation and prediction (queue tracking), and incident alarm. The paper first introduces the stochastic macroscopic freeway network traffic flow model and a real-time traffic measurement model, upon which a complete dynamic system model for freeway network traffic is established, with a special attention to the handling of some important model parameters. The addressed traffic surveillance tasks are described along with the functional architecture of RENAISSANCE. A simulation test was conducted for the tool with respect to a hypothetical freeway network example, while the traffic state estimator of RENAISSANCE was also tested with real traffic measurement data collected from a Bavarian freeway.