Microscopic and macroscopic traffic flow models including random accidents

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.

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.

The priority-based traffic light controlling system at an intersection dedicates right-of-way to the highest priority direction. The system is applied for urban traffic system in Vietnam, where various types of vehicles run in close proximity to one another, needs a traffic model suitable to determine the priority of directions going through intersection. The paper has studied current traffic models, microscopic and macroscopic traffic flow models as well as three-phase traffic model, to propose spatio-temporal traffic statistics model. The paper considers red light as a traffic obstacle causing moving jam behind traffic light. The proposed spatio-temporal traffic statistics model studies traffic flow on a road segment bounded by two intersections, where various types of vehicles travel. The spatio-temporal traffic statistics model represents the road surface area occupied by vehicles at locations and over time as spatio-temporal histograms. The expectation of histogram is a factor determining the priority of direction going through intersection.

Macroscopic traffic flow models play a significant role in the Intelligent Transportation Systems (ITS), especially for the urban traffic control and the dynamic traffic assignment. Two main problems limit the application of the existing traffic models. One is the traffic dynamics described by the complex nonlinear equations which are difficult to resolve in real time, and the other is that some model parameters need to be calibrated in prior. This paper presents a hybrid macroscopic and microscopic (macro-microscopic) traffic flow model of freeway traffic by extending the cell transmission model (CTM) with the real time speed dynamics. Simple supplying and demanding functions are defined to represent the traffic propagation between the upstream and downstream cell boundaries. A microscopic car-following model is integrated to specify the dynamics of the average speed in each cell. Simulation results with specific traffic data set collected from a 4-kilometre long urban freeway show the performance of the model compared to the well-known METANET model.

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 chapter is devoted to the detailed study of the relation between a microscopic cellular automation and a macroscopic partial differential equation model for the movement of pedestrians. We describe the mathematical tools allowing to derive the macroscopic from the microscopic model. Such a connection between discrete, particle based and continuous, density based models can help to improve the understanding of basic properties of human crowds. We exemplify this by applying our results to typical cases. The first one is the formation of lanes in bi-directional flow. The second is the analysis of the fundamental diagram. Our analysis provides (at least qualitatively) a connection between these phenomena and model parameters. We conclude by pointing out a number of possible directions of future research.

In various areas of science, technology, environment protection, construction, it is very important to study processes of porous materials interaction with different substances in different aggregation states. From the point of view of ecology and environmental protection it is particularly actual to investigate processes of porous materials interaction with water in liquid and gaseous phases. Since one mole of water contains $6,022140857\cdot 10^{23}$ molecules of $\mathtt{H_2O}$, macroscopic approaches considering the water vapor as continuum media in the framework of classical aerodynamics are mainly used to describe properties, for example properties of water vapor in the pore. In this paper we construct and use for simulation the macroscopic two-dimensional diffusion model describing the behavior of water vapor inside the isolated pore. Together with the macroscopic model it is proposed microscopic model of the behavior of water vapor inside the isolated pores. This microscopic model is built within the molecular dynamics approach. In the microscopic model a description of each water molecule motion is based on Newton classical mechanics considering interactions with other molecules and pore walls. Time evolution of water vapor - pore system is explored. Depending on the external to the pore conditions the system evolves to various states of equilibrium, characterized by different values of the macroscopic characteristics such as temperature, density, pressure. Comparisons of results of molecular dynamic simulations with the results of calculations based on the macroscopic diffusion model and experimental data allow to conclude that the combination of macroscopic and microscopic approach could produce more adequate and more accurate description of processes of water vapor interaction with porous materials.

Macroscopic pedestrian models are theoretically simpler than microscopic models, and they can potentially be solved faster while producing reasonable predictions of crowd dynamics. Therefore, they can be very useful for applications such as large-scale simulation, real-time state estimation and crowd management. However, the numerical methods presently used to solve macroscopic pedestrian models, which are mostly grid-based, have some shortcomings that limit their applicability. More specifically, they usually include complex procedures for grid generation and remeshing, and they produce simulation results that may not be sufficiently accurate (for example, because of unclear boundaries between flow states). Smoothed Particle Hydrodynamics (SPH) constitutes an alternative numerical method that could potentially overcome these limitations. SPH is a meshfree method where a crowd is represented by a set of particles that possess material properties and move according to macroscopic laws. Relevant state variables at each particle are approximated using information about the material properties of the neighboring particles and a smoothing function. This paper puts forward for the first time a generic SPH framework for solving macroscopic pedestrian models; in addition, it demonstrates that an SPH-based simulation model can produce meaningful and accurate results by means of three case studies. The first case study shows that the proposed numerical method can approximate well the analytical solution of a simple macroscopic model applied to a queue-discharge scenario. The second case study demonstrates that the proposed numerical method can potentially reproduce density dispersion (a phenomenon observed in real crowds) more accurately than grid-based methods, due to its meshfree, Lagrangian, and particle-based nature. The third case study highlights the need to reformulate the acceleration equation of the basic macroscopic model in order to reproduce lane formation in bi-directional flows (also an observed phenomenon) using the proposed SPH framework, and this paper presents a solution to do so.

This paper presents the estimation of travel time on highways based on macroscopic modelling. The focus is on real-time values as compared to average or static values. The macroscopic models are used for distributed and time/space lumped settings and corresponding travel time estimation functions and algorithms are developed. The implications of these algorithms for the implementation of various incident management and traffic control strategies are also discussed.

Cooperative ligand-binding curves may often appear deceptively featureless, yet the underlying microscopic models may be rather complex, and the connection between them is not intuitive. To address some of these issues, we have extended the framework of the decoupled sites representation (DSR), previously developed in the context of pH titration, to include cooperative ligand binding as well as multiple conformations and multiple ligands. The extended framework is based on general thermodynamic arguments and is applicable to both anti-cooperative and cooperative binding. It can be used to elucidate the connection between the experimentally observed binding curves and parameters of underlying microscopic models. It is demonstrated that any binding curve can be decomposed into simple standard components that permit a model-independent physical interpretation in terms of noninteracting (quasi) groups. A simple mathematical form of the DSR is proposed, that is well-suited for use in least-squares fitting of experimental binding curves; the fitting procedure produces an integer parameter indicative of the degrees of cooperativity possible in the system. A two-site example is worked out in detail. We demonstrate that the same macroscopic binding behavior observed experimentally can have qualitatively different origins at the level of the underlying microscopic mechanism. We also show that, in the absence of the microscopic model, it is not possible to draw a meaningful distinction between non-cooperative and anti-cooperative scenarios. We define a new measure of cooperativity and show that it is in many cases more adequate than the Hill coefficient when used to characterize complex binding curves. The extended DSR is applied to experimental data sets on oxygen binding to carp hemoglobin at different pHs, where the framework is used to interpret the degree of cooperativity in the system and provides an indication as to whether specific microscopic models are applicable.

Limitations of current traffic models and strategies to address them

In this paper, we adopt the coarse graining method proposed by Lee H K et al. to develop a macroscopic model from the microscopic traffic model-GOVM. The proposed model inherits the parameter p which considers the influence of next-nearest car introduced in the GOVM model. The simulation results show that the new model is strictly consistent with the former microscopic model. Using this macroscopic model, we can avoid considering the details of each traffic on the road, and build more complex models such as road network model easily in the future.

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.

Mathematical models that predict performance can aid in the understanding and development of solid oxide fuel cells (SOFCs). Of course, various modeling approaches exist involving different length scales. In particular, very significant advances are now taking place using microscopic models to understand the complex composite structures of electrodes and three-phase boundaries. Ultimately these advances should lead to predictions of cell behavior, which at present are measured empirically and inserted into macroscopic cell models. In order to achieve this ambitious goal, simulation tools based on these macroscopic models must be redesigned by matching them to the complex microscopic phenomena, which take place at the pore scale level. As a matter of fact, the macroscopic continuum approach essentially consists of applying some type of homogenization technique, which properly averages the underlying microscopic phenomena for producing measurable quantities. Unfortunately, these quantities in the porous electrodes of fuel cells are sometimes measurable only in principle. For this reason, this type of approach introduces additional uncertainties into the macroscopic models, which can significantly affect the numerical results, particularly their generality. This paper is part of an ongoing effort to address the problem by following an alternative approach. The key idea is to numerically simulate the underlying microscopic phenomena in an effort to bring the mathematical description nearer to actual reality. In particular, some recently developed mesoscopic tools appear to be very promising since the microscopic approach is, in this particular case, partially included in the numerical method itself. In particular, the models based on the lattice Boltzmann method (LBM) treat the problem by reproducing the collisions among particles of the same type, among particles belonging to different species, and finally among the species and the solid obstructions. Recently, a model developed by the authors was proposed which, based on LBM, models the fluid flow of reactive mixtures in randomly generated porous media by simulating the actual coupling interaction among the species. A parallel three–dimensional numerical code was developed in order to implement this model and to simulate the actual microscopic structures of SOFC porous electrodes. In this paper, a thin anode (50 micron) of Ni-metal / YSZ-electrolyte cermet for a high–temperature electrolyte supported SOFC was considered in the numerical simulations. The three–dimensional anode structure was derived by a regression analysis based on the granulometry law applied to some microscopic pictures obtained with an electron microscope. The numerical simulations show the spatial distribution of the mass fluxes for the reactants and the products of the electrochemical reactions. The described technique will allow one to design new improved materials and structures in order to statistically optimize these fluid paths.

We analyze the relationship between the macroscopic and microscopic descriptions of two-state systems, in particular the regime in which the microscopic one shows sustained ‘stochastic oscillations’ while the macroscopic tends to a fixed point. We propose a quantification of the oscillatory appearance of the fluctuating populations, and show that good stochastic oscillations are present if a parameter of the macroscopic model is small, and that no microscopic model will show oscillations if that parameter is large. The transition between these two regimes is smooth. In other words, given a macroscopic deterministic model, one can know whether any microscopic stochastic model that has it as a limit, will display good sustained stochastic oscillations.