Macroscopic Models in Traffic Flow (original) (raw)
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An extended macroscopic model for traffic flow
Transportation Research Part B: Methodological, 1996
This paper presents a model of traffic on a highway based on the macroscopic description of traffic as a compressible fluid. We take the computationally efficient model of Papageorgiou and test it on field data. We extend the model to flow under the influence of traffic-obstructing incidents. In applications where the interest is in mass phenomena and real time computation, a macroscopic model is preferable over microscopic models. This model also permits systematic parameter identification, which makes it more useful for real traffic systems. The influence of incidents on the highway is included in the model and it is possible to tune its parameters for flow under incidents. This allows the model to compute the effect of incidents on flow capacity using field data.
First-Order Macroscopic Traffic Models
Advances in industrial control, 2018
All macroscopic models, both of first-order type and of higher orders, describe the evolution of aggregate quantities referred to the traffic system over time. This means that two independent variables are involved, i.e. space and time. In continuous traffic models, these independent variables are assumed to be continuous, while they are discretised in discrete traffic models. In this latter case, a freeway stretch is divided into a number of small road portions, and the time horizon is subdivided into a given number of time intervals. Let us now introduce the proper notation of macroscopic traffic models, specifically differentiated for the continuous and the discrete case. 3.1.1 The Continuous Case Referring to a generic location x (in a given road, possibly composed of several lanes) and time t, the main aggregate variables considered in continuous macroscopic traffic models are: • ρ(x, t) is the traffic density [veh/km]; • v(x, t) is the average speed [km/h]; • q(x, t) is the traffic flow [veh/h]. A first relation constituting the basis of every macroscopic model is the hydrodynamic equation, which computes the flow as the product of mean speed and density, i.e. q(x, t) = ρ(x, t)v(x, t) (3.1) A second relation is the continuity equation or conservation equation, directly derived from the conservation law of vehicle flows and expressed as
Macroscopic Analysis Of The Viscous-Diffusive Traffic Flow Model
Mathematics in Applied Sciences and Engineering
Second-order macroscopic traffic models are characterized by a continuity equation and an acceleration equation. Convection, anticipation, relaxation, diffusion, and viscosity are the predominant features of the different classes of the acceleration equation. As a unique approach, this paper presents a new macro-model that accounts for all these dynamic speed quantities. This is done to determine the collective role of these traffic quantities in macroscopic modeling. The proposed model is solved numerically to explain some phenomena of a multilane traffic flow. It also includes a linear stability analysis. Furthermore, the evolution of speed and density wave profiles are presented under the perturbation of some parameters.
Macroscopic traffic flow models are suited for large scale, network wide applications where the macrocharacteristics of the flow are of prime interest. A clear understanding of the existing macro-level traffic flow models will help in modelling of varying traffic scenarios more accurately. Existing state-of-the-art reports on traffic flow models have not considered macro-level models exclusively. This paper gives a review of macroscopic modelling approaches used for traffic networks including recent research in the past decade. The modelling of the two main components of the network i.e. links and nodes are reviewed separately in two sections and solution procedures are discussed followed by a synthesis on the advantages and disadvantages of these models. This review should encourage efficient research in this area towards network level application of these models.
MACROSCOPIC TRAFFIC FLOW MODELS HAVING SOURCE TERMS
In this paper, macroscopic traffic flow model having source terms has been presented. In maximum cases, source terms present the entrance and exit of the roads. So, to demonstrate the effect of inflow, models possessing source terms are extensively presented with their traffic predictions. These predictions are based on the real traffic data taken from the roads. These results can be used for further research in the field of traffic modeling.
Models of Traffic Flow Dynamics on Highways
Вестник КазАТК
The paper is an analytical review of the currently existing methods of traffic flows modeling. The movement of vehicles on the road can be modeled in different ways. Mathematical models as tools that allow us to study complex processes in the real world, including transport infrastructure, without capital expenditures, are a popular tool for solving many problems in various spheres of the national economy. There are several approaches to mathematical modeling of traffic flows. In microscopic models, the law of motion of each car is set, depending on its current position, speed, characteristics of the movement of neighboring cars, and other factors. Microscopic models, in turn, can be divided into models that are continuous in space and time, and into models that are discrete in space and time, the so-called cellular automata. In macroscopic models, the transport flow is considered as a fluid flow with special properties. The equations of the macroscopic model establish the relations...
A Macroscopic Traffic Model Based on the Safe Velocity at Transitions
Civil Engineering Journal
The increasing volume of vehicles on the road has had a significant impact on traffic flow. Congestion in urban areas is now a major concern. To mitigate congestion, an accurate model is required which is based on realistic traffic dynamics. A new traffic model is proposed based on the conservation law of vehicles which considers traffic dynamics at transitions. Traffic alignment to forward conditions is affected by the time and distance between vehicles. Thus, the well-known Lighthill, Whitham, and Richards (LWR) model is modified to account for traffic behavior during alignment. A model for inhomogeneous traffic flow during transitions is proposed which can be used to characterize traffic evolution. The performance of the proposed model is compared with the LWR model using the Greenshields and Underwood target velocity distributions. These models are evaluated using the Godunov technique and numerical stability is guaranteed by considering the Courant, Friedrich, and Lewy (CFL) co...
Second-order continuum traffic flow model
Physical Review E, 1996
A second-order traffic flow model is derived from microscopic equations and is compared to existing models. In order to build in different driver characteristics on the microscopic level, we exploit the idea of an additional phase-space variable, called the desired velocity originally introduced by Paveri-Fontana ͓Trans. Res. 9, 225 ͑1975͔͒. By taking the moments of Paveri-Fontana's Boltzmann-like ansatz, a hierachy of evolution equations is found. This hierarchy is closed by neglecting cumulants of third and higher order in the cumulant expansion of the distribution function, thus leading to Euler-like traffic equations. As a consequence of the desired velocity, we find dynamical quantities, which are the mean desired velocity, the variance of the desired velocity, and the covariance of actual and desired velocity. Through these quantities an alternative explanation for the onset of traffic clusters can be given, i.e., a spatial variation of the variance of the desired velocity can cause the formation of a traffic jam. Furthermore, by taking into account the finite car length, Paveri-Fontana's equation is generalized to the high-density regime eventually producing corrections to the macroscopic equations. The relevance of the present dynamic quantities is demonstrated by numerical simulations. ͓S1063-651X͑96͒05911-9͔
An energy concept for macroscopic traffic flow modelling
European Transport Research Review, 2012
Introduction The main differences between the deterministic macroscopic models are to be found in pressure expressions and representation of various phases observed experimentally. Methods In this paper, using the laws of fluid dynamics and thermodynamics to describe the traffic flow reality, a new expression of pressure is made and a second order model is proposed. Results It represents different traffic flow phases and, thus, conditions for transition between phases become clear. In addition, our approach suggests solutions to a number of problems yet to be resolved. Afterwards, simulations are presented which show some agreement with experimental data. Conclusion Finally, the proposed model highlights different types of possible actions for traffic flow control.
Macroscopic traffic models from microscopic car-following models
Physical Review E, 2001
We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of a conservation equation and a ...