A Tracking Algorithm for Car Paths on Road Networks (original) (raw)

Traffic Flow on a Road Network

SIAM Journal on Mathematical Analysis, 2005

This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem.

Travelling Waves in Traffic

Travelling Waves in Traffic, 2018

The LWR is a continuous density model. In this paper, we present a meaningful way of representing traffic density as a collection of box- functions in motion. Each box will have a length L and a headway D with associated speed. The function easily lends itself useful in simulating traffic and the backpropagation of density which appears as congestion.

Conservation law models for traffic flow on a network of roads

Networks and Heterogeneous Media, 2015

The paper develops a model of traffic flow near an intersection, where drivers seeking to enter a congested road wait in a buffer of limited capacity. Initial data comprise the vehicle density on each road, together with the percentage of drivers approaching the intersection who wish to turn into each of the outgoing roads.

Source-Destination Flow on a Road Network

Communications in Mathematical Sciences, 2005

We construct a model of traffic flow with sources and destinations on a roads network. The model is based on a conservation law for the density of traffic and on semilinear equations for traffic-type functions, i.e. functions describing paths for cars.

Numerical algorithms for simulations of a traffic model on road networks

2007

We introduce a simulation algorithm based on a fluid-dynamic model for traffic flows on road networks, which are considered as graphs composed by arcs that meet at some junctions. The approximation of scalar conservation laws along arcs is made by three velocities Kinetic schemes with suitable boundary conditions at junctions. Here we describe the algorithm and we give an example.

A Fluid-Dynamic Traffic Model on Road Networks

Archives of Computational Methods in Engineering, 2007

We consider a mathematical model for fluiddynamic flows on networks which is based on conservation laws. Road networks are studied as graphs composed by arcs that meet at some nodes, corresponding to junctions, which play a key-role. Indeed interactions occur at junctions and there the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which processes each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.

Numerical Modelling of Traffic Induced Vibrations

Meccanica, 2001

A solution procedure is presented to compute free field vibrations induced by train or road traffic, the excitation being either deterministic or stochastic. The full interaction between the vehicle, the track or road and the soil is accounted for, using a substructure approach that takes advantage of the fact that the properties of the track or road and the soil do not change along the longitudinal direction. A time-frequency approach is proposed to characterize the free field radiated in the soil. The examples show the importance of guided waves along the track for understanding the dynamic behavior of the track or the road.

The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory

Transportation Research Part B: Methodological, 1994

This paper presents a simple representation of traffic on a highway with a single entrance and exit. The representation can be used to predict traffic's evolution over time and space, including transient phenomena such as the building, propagation, and dissipation of queues. The easy-to-solve difference equations used to predict traffic's evolution are shown to be the discrete analog of the differential equations arising from a special case of the hydrodynamic model of traffic flow. The proposed method automatically generates appropriate changes in density at locations where the hydrodynamic theory would call for a shockwave; i.e., a jump in density such as those typically seen at the end of every queue. The complex side calculations required by classical methods to keep track of shockwaves are thus eliminated. The paper also shows how the equations can mimic the real-life development of stop-and-go traffic within moving queues.

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

Transportation Research Part B: Methodological, 2017

The traffic state estimation process estimates various traffic states from available data in a road network and provides valuable information for travelers and decision makers to improve both travel experience and system performance. In many existing methods, model parameters and initial states have to be given in order to estimate traffic states, which limits the accuracy of the results as well as their transferability to different locations and times. In this paper, we propose a new framework to simultaneously estimate model parameters and traffic states for a congested road segment based on Newell's simplified kinematic wave model (Newell, 1993). Given both Eulerian traffic count data and Lagrangian vehicle reidentification data, we formulate a single optimization problem in terms of the initial number of vehicles and model parameters. Then we decouple the optimization problem such that the initial number of vehicles can be analytically solved with a closed-form formula, and the model parameters, including the jam density and the shock wave speed in congested traffic, can be computed with the Gauss-Newton method. Based on Newell's model, we can calculate individual vehicles' trajectories as well as the average densities, speeds, and flow-rates inside the road segment. We also theoretically show that the optimization problem can have multiple solutions under absolutely steady traffic conditions. We apply the proposed method to the NGSIM datasets, verifying the validity of the method and showing that this method yields better results in the estimation of average densities than existing methods.