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Author: Stéphane Mollier Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Congestion in traffic networks is a common issue in big cities and has considerable economic and environmental impacts. Traffic policies and real-time network management can reduce congestion using prediction of dynamical modeling. Initially, researchers studied traffic flow on a single road and then, they extended it to a network of roads. However, large-scale networks present challenges in terms of computation time and parameters' calibration. This led the researchers to focus on aggregated models and to look for a good balance between accuracy and practicality.One of the approaches describes traffic evolution with a continuous partial differential equation on a 2D-plane. Vehicles are represented by a two-dimensional density and their propagation is described by the flow direction. The thesis aims to develop these models and devises methods for their calibration and their validation. The contributions follow three extensions of the model.First, a simple model in two-dimensional space to describe a homogeneous network with a preferred direction of flow propagation is considered. A homogeneous network has the same speed limits and a similar concentration of roads everywhere. A method for validation using GPS probes from microsimulation is provided. Then, a space-dependent extension to describe a heterogeneous network with a preferred direction of flow propagation is presented. A heterogeneous network has different speed limits and a variable concentration of roads. Such networks are of interest because they can show how bottleneck affects traffic dynamics. Finally, the case of multiple directions of flow is considered using multiple layers of density, each layer representing a different flow direction. Due to the interaction between layers, these models are not always hyperbolic which can impact their stability.
Author: Stéphane Mollier Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Congestion in traffic networks is a common issue in big cities and has considerable economic and environmental impacts. Traffic policies and real-time network management can reduce congestion using prediction of dynamical modeling. Initially, researchers studied traffic flow on a single road and then, they extended it to a network of roads. However, large-scale networks present challenges in terms of computation time and parameters' calibration. This led the researchers to focus on aggregated models and to look for a good balance between accuracy and practicality.One of the approaches describes traffic evolution with a continuous partial differential equation on a 2D-plane. Vehicles are represented by a two-dimensional density and their propagation is described by the flow direction. The thesis aims to develop these models and devises methods for their calibration and their validation. The contributions follow three extensions of the model.First, a simple model in two-dimensional space to describe a homogeneous network with a preferred direction of flow propagation is considered. A homogeneous network has the same speed limits and a similar concentration of roads everywhere. A method for validation using GPS probes from microsimulation is provided. Then, a space-dependent extension to describe a heterogeneous network with a preferred direction of flow propagation is presented. A heterogeneous network has different speed limits and a variable concentration of roads. Such networks are of interest because they can show how bottleneck affects traffic dynamics. Finally, the case of multiple directions of flow is considered using multiple layers of density, each layer representing a different flow direction. Due to the interaction between layers, these models are not always hyperbolic which can impact their stability.
Author: Gabriel Obed Fosu Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
In the past, the density-gradient term of second-order macroscopic models was replaced with a speed-gradient term to rectify the rearward movement of traffic waves. Hither, a classical speed-gradient macroscopic model is extended to account for the lateral flow dynamics on a multi-lane road. The anisotropic model is modified to capture some inherent vehicular multi-lane traffic features; lateral viscosity and velocity differentials. These variables are quantized within the scope of a two-dimensional spatial domain as opposed to the existing one-dimensional model. A detailed exemplification of acceleration and deceleration waves, stop-and-go waves, and cluster effects are presented to explain the path of information flow. All these non-linear flow properties are evident throughout the simulation.
Author: Liudmila Tumash Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This research is done in the context of European Research Council's Advanced Grant project Scale-FreeBack. The aim of Scale-FreeBack project is to develop a holistic scale-free control approach to complex systems, and to set new foundations for a theory dealing with complex physical networks with arbitrary dimension. One particular case is intelligent transportation systems that are capable to prevent the occurrence of congestions in rush hours. The contributions of the present PhD work are mainly related to traffic boundary control design and modelling on large-scale urban networks. We consider traffic from the macroscopic viewpoint describing it in terms of aggregated variables such as flow and density of vehicles, i.e., traffic is seen as a fluid whose motion is described using the concept of kinematic waves. The corresponding dynamic equation corresponds to a first-order hyperbolic partial differential equation. Within this PhD thesis, we propose control design techniques that completely rely on the intrinsic properties of the model. First of all, we solve one-dimensional (1D) boundary control problems, i.e., one road traffic. Thereby, the traffic state is driven to a space- and time-dependent desired trajectory that admits traffic regimes switching, i.e., both states can be partially congested and partially in the free-flow regime. This introduces non-linearities into the state equation, which we can handle and achieve the target by acting only from road's boundaries. Then, we extend the problem to a urban network of arbitrary size. The large-scale traffic dynamics are described by a two-dimensional (2D) conservation law model. The model parameters are defined everywhere in the continuum plane from its values on physical roads that are further interpolated as a function of distance to these roads. The traffic flow direction is determined by network's geometry (location of roads and intersections) and infrastructure parameters (speed limits, number of lanes, etc). This 2D model assumes that there exists a preferred direction of motion. For this case, we elaborate a unique method that considerably simplifies control design for traffic systems evolving in large-scale networks. In particular, we present a coordinate transformation that translates a 2D continuous traffic model into a continuous set of 1D systems equations. This enables an explicit elaboration of strategies for various control tasks to solve on large-scale networks: we design boundary control for 2D density in a mixed traffic regime, apply variable speed limit control to drive traffic to any space-dependent equilibrium, and calculate steady-states. Finally, we also present a new multi-directional two-dimensional continuous traffic model. This model is formally derived by solely using the demand-supply concept at one intersection (classical Cell Transmission Model). Our new model is called the NSWE-model, since it consists of four partial differential equations that describe the evolution of vehicle density with respect to cardinal directions: North, South, West and East. The traffic flow direction is determined by turning ratios at intersections. For this model, we design a boundary control that drives multi-directional congested traffic to a desired equilibrium vehicle density mitigating the congestion level. The effectiveness of our contributions were tested using simulated and real data. In the first case, the results are verified by using the well-known commercial traffic Aimsun, which produces microsimulations of vehicles' trajectories in a modelled network. In the second case, real data are obtained from sensors measuring traffic flow in the city of Grenoble, and collected using the Grenoble Traffic Lab.
Author: Nathan H. Gartner Publisher: Springer Science & Business Media ISBN: 3642796419 Category : Business & Economics Languages : en Pages : 376
Book Description
The problems of urban traffic in the industrially developed countries have been at the top of the priority list for a long time. While making a critical contribution to the economic well being of those countries, transportation systems in general and highway traffic in particular, also have detrimental effects which are evident in excessive congestion, high rates of accidents and severe pollution problems. Scientists from different disciplines have played an important role in the development and refinement of the tools needed for the planning, analysis, and control of urban traffic networks. In the past several years, there were particularly rapid advances in two areas that affect urban traffic: 1. Modeling of traffic flows in urban networks and the prediction of the resulting equilibrium conditions; 2. Technology for communication with the driver and the ability to guide him, by providing him with useful, relevant and updated information, to his desired destination.
Author: Thomas Jung Publisher: Fraunhofer Verlag ISBN: 9783839617083 Category : Languages : en Pages : 120
Book Description
Traffic becomes an ever more important topic in modern days, as it plays a vital role in economics, environmental issues and the daily life of most people. The simulation of traffic with mathematical models dates back to at least the 1950s. In that, microscopic models with explicit time delays, modeling the reaction times of both the driver and the car, are well known. Starting from them, we derive new macroscopic traffic models, which keep this explicit time delay. This leaves us with partial differential equations with explicit time delay, a hardly investigated type of differential equations. In this thesis we take a closer look at the analysis and especially the numerics for this models, show some properties of the equations and the numerical discretizations, and compare them to well-known, undelayed models. Finally, we will fit these models to real data and run simulations, comparing the behavior to undelayed models. Also, we compare the results to real measurements, showing that the simulations are often closer to real world traffic than undelayed simulations.
Author: Michael Herty Publisher: Logos Verlag Berlin GmbH ISBN: Category : Mathematics Languages : en Pages : 150
Book Description
Traffic flow has been a continuous source of challenging mathematical problems. The following work is dedicated to recent questions in modeling, simulation and optimization of traffic flow networks. Mathematics can help to solve traffic problems in different ways. Modelling provides fundamental understanding of traffic dynamics and behaviour. Optimization yields solutions for complex situations and helps to organize traffic flow. During the last decade there has been intensive research in different fields of and related to traffic flow. One of the primary research activities focus on the development of new and more realistic models for traffic flow on a single road. Our work's primary focus is on models for networks. We provide new ideas on modelling flow in networks and solve different optimization problems analytically and numerically. The main result is the derivation of a hierarchy of models treating different situations with suitable traffic flow models. To each level of modeling we consider the optimal control problems and present techniques to address those problems. Furthermore, we derive an adjoint calculus for scalar hyperbolic equations with nonlinear boundary controls. The derived concepts fit for general network problems as well as they do for traffic flow issues. The principles of modeling and simplification can be applied to all kinds of network flows, like fluid flow in open channels or gas networks.
Author: Stéphane Mollier
Author: Stéphane Mollier
Author: Gabriel Obed Fosu
Author: Liudmila Tumash
Author: HongSheng Qi
Author: Zhijun Qiu
Author: Nathan H. Gartner
Author: Michael Herty
Author: Avishai Ceder
Author: Thomas Jung
Author: Michael Herty