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Macroscopic Traffic Flow Model
A Macroscopic traffic flow model is a mathematical traffic model that formulates the relationships among traffic flow characteristics like density, flow, mean speed of a traffic stream, etc.. Such models are conventionally arrived at by integrating microscopic traffic flow models and converting the single-entity level characteristics to comparable system level characteristics. An example is the Two-fluid model. The method of modeling traffic flow at macroscopic level originated under an assumption that traffic streams as a whole are comparable to fluid streams. The first major step in macroscopic modeling of traffic was taken by Lighthill and Whitham in 1955, when they indexed the comparability of ‘traffic flow on long crowded roads’ with ‘flood movements in long rivers’. A year later, Richards (1956) complemented the idea with the introduction of ‘shock-wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that move ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Traffic Model
A traffic model is a mathematical model of real-world traffic, usually, but not restricted to, road traffic. Traffic modeling draws heavily on theoretical foundations like network theory and certain theories from physics like the kinematic wave model. The interesting quantity being modeled and measured is the traffic flow, i.e. the throughput of mobile units (e.g. vehicles) per time and transportation medium capacity (e.g. road or lane width). Models can teach researchers and engineers how to ensure an optimal flow with a minimum number of traffic jams. Traffic models often are the basis of a traffic simulation. Types ;Microscopic traffic flow model: Traffic flow is assumed to depend on individual mobile units, i.e. cars, which are explicitly modeled ; Macroscopic traffic flow model: Only the mass action or the statistical properties of a large number of units is analyzed Examples * Biham–Middleton–Levine traffic model * Traffic generation model * History of network traffic m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Traffic Flow
In mathematics and transportation engineering, traffic flow is the study of interactions between travellers (including pedestrians, cyclists, drivers, and their vehicles) and infrastructure (including highways, signage, and traffic control devices), with the aim of understanding and developing an optimal transport network with efficient movement of traffic and minimal traffic congestion problems. History Attempts to produce a mathematical theory of traffic flow date back to the 1920s, when Frank Knight first produced an analysis of traffic equilibrium, which was refined into John Glen Wardrop, Wardrop's first and second principles of equilibrium in 1952. Nonetheless, even with the advent of significant computer processing power, to date there has been no satisfactory general theory that can be consistently applied to real flow conditions. Current traffic models use a mixture of empirical and Deductive reasoning, theoretical techniques. These models are then developed into Trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure. To simplify comparisons of density across different s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Traffic Flow
In mathematics and transportation engineering, traffic flow is the study of interactions between travellers (including pedestrians, cyclists, drivers, and their vehicles) and infrastructure (including highways, signage, and traffic control devices), with the aim of understanding and developing an optimal transport network with efficient movement of traffic and minimal traffic congestion problems. History Attempts to produce a mathematical theory of traffic flow date back to the 1920s, when Frank Knight first produced an analysis of traffic equilibrium, which was refined into John Glen Wardrop, Wardrop's first and second principles of equilibrium in 1952. Nonetheless, even with the advent of significant computer processing power, to date there has been no satisfactory general theory that can be consistently applied to real flow conditions. Current traffic models use a mixture of empirical and Deductive reasoning, theoretical techniques. These models are then developed into Trans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microscopic Traffic Flow Models
Microscopic traffic flow models are a class of scientific models of vehicular traffic dynamics. In contrast, to macroscopic models, microscopic traffic flow models simulate single vehicle-driver units, so the dynamic variables of the models represent microscopic properties like the position and velocity of single vehicles. Car-following models Also known as ''time-continuous models'', all car-following models have in common that they are defined by ordinary differential equations describing the complete dynamics of the vehicles' positions x_\alpha and velocities v_\alpha. It is assumed that the input stimuli of the drivers are restricted to their own velocity v_\alpha, the net distance (bumper-to-bumper distance) s_\alpha = x_ - x_\alpha - \ell_ to the leading vehicle \alpha-1 (where \ell_ denotes the vehicle length), and the velocity v_ of the leading vehicle. The equation of motion of each vehicle is characterized by an acceleration function that depends on those input stimuli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-fluid Model
Two-fluid model is a macroscopic traffic flow model to represent traffic in a town/city or metropolitan area, put forward in the 1970s by Ilya Prigogine and Robert Herman. There is also a two-fluid model which helps explain the behavior of superfluid helium. This model states that there will be two components in liquid helium below its lambda point The lambda point is the temperature at which normal fluid helium (helium I) makes the transition to superfluid helium II (approximately 2.17 K at 1 atmosphere). The lowest pressure at which He-I and He-II can coexist is the vapor−He-I−He-II t ... (the temperature where superfluid forms). These components are a normal fluid and a superfluid component. Each liquid has a different density and together their sum makes the total density, which remains constant. The ratio of superfluid density to the total density increases as the temperature approaches absolute zero. External links Two Fluid Model of Superfluid Helium References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Flow
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shock-wave
In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density of the medium. For the purpose of comparison, in supersonic flows, additional increased expansion may be achieved through an expansion fan, also known as a Prandtl–Meyer expansion fan. The accompanying expansion wave may approach and eventually collide and recombine with the shock wave, creating a process of destructive interference. The sonic boom associated with the passage of a supersonic aircraft is a type of sound wave produced by constructive interference. Unlike solitons (another kind of nonlinear wave), the energy and speed of a shock wave alone dissipates relatively quickly with distance. When a shock wave passes through m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Road Traffic Management
: ''For the road traffic science, see various articles under Road traffic management.'' Road traffic control involves directing vehicular and pedestrian traffic around a construction zone, accident or other road disruption, thus ensuring the safety of emergency response teams, construction workers and the general public. Traffic control also includes the use of CCTV and other means of monitoring traffic by local or state roadways authorities to manage traffic flows and providing advice concerning traffic congestion. Traffic Control Technicians (TCT's) or Traffic Control Supervisors (TCS's) are often known as "lollipop men" (usually this name only applies to TCT's working near schools to aid pupils in road crossing) from the appearance of their ''Stop/Slow'' signs, known as "Stop bats". Overview Road Traffic control is an outdoors occupation, night or day for long hours in all weathers, and is considered a dangerous occupation due to the high risk of being struck by passing vehicl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Modeling
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statistical m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
