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Traffic flow
In 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.
The foundation for modern traffic flow analysis dates back to the 1920s with Frank Knight's analysis of traffic equilibrium, further developed by Wardrop in 1952. Despite advances in computing, a universally satisfactory theory applicable to real-world conditions remains elusive. Current models blend empirical and theoretical techniques to forecast traffic and identify congestion areas, considering variables like vehicle use and land changes.
Traffic flow is influenced by the complex interactions of vehicles, displaying behaviors such as cluster formation and shock wave propagation. Key traffic stream variables include speed, flow, and density, which are interconnected. Free-flowing traffic is characterized by fewer than 12 vehicles per mile per lane, whereas higher densities can lead to unstable conditions and persistent stop-and-go traffic. Models and diagrams, such as time-space diagrams, help visualize and analyze these dynamics. Traffic flow analysis can be approached at different scales: microscopic (individual vehicle behavior), macroscopic (fluid dynamics-like models), and mesoscopic (probability functions for vehicle distributions). Empirical approaches, such as those outlined in the Highway Capacity Manual, are commonly used by engineers to model and forecast traffic flow, incorporating factors like fuel consumption and emissions.
The kinematic wave model, introduced by Lighthill and Whitham in 1955, is a cornerstone of traffic flow theory, describing the propagation of traffic waves and impact of bottlenecks. Bottlenecks, whether stationary or moving, significantly disrupt flow and reduce roadway capacity. The Federal Highway Authority attributes 40% of congestion to bottlenecks. Classical traffic flow theories include the Lighthill-Whitham-Richards model and various car-following models that describe how vehicles interact in traffic streams. An alternative theory, Kerner's three-phase traffic theory, suggests a range of capacities at bottlenecks rather than a single value. The Newell-Daganzo merge model and car-following models further refine our understanding of traffic dynamics and are instrumental in modern traffic engineering and simulation.
Attempts to produce a mathematical theory of traffic flow date back to the 1920s, when American Economist Frank Knight first produced an analysis of traffic equilibrium, which was refined into 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 theoretical techniques. These models are then developed into traffic forecasts, and take account of proposed local or major changes, such as increased vehicle use, changes in land use or changes in mode of transport (with people moving from bus to train or car, for example), and to identify areas of congestion where the network needs to be adjusted.
Traffic behaves in a complex and nonlinear way, depending on the interactions of a large number of vehicles. Due to the individual reactions of human drivers, vehicles do not interact simply following the laws of mechanics, but rather display cluster formation and shock wave propagation,[citation needed] both forward and backward, depending on vehicle density. Some mathematical models of traffic flow use a vertical queue assumption, in which the vehicles along a congested link do not spill back along the length of the link.
In a free-flowing network, traffic flow theory refers to the traffic stream variables of speed, flow, and concentration. These relationships are mainly concerned with uninterrupted traffic flow, primarily found on freeways or expressways. Flow conditions are considered "free" when less than 12 vehicles per mile per lane are on a road. "Stable" is sometimes described as 12–30 vehicles per mile per lane. As the density reaches the maximum mass flow rate (or flux) and exceeds the optimum density (above 30 vehicles per mile per lane), traffic flow becomes unstable, and even a minor incident can result in persistent stop-and-go driving conditions. A "breakdown" condition occurs when traffic becomes unstable and exceeds 67 vehicles per mile per lane. "Jam density" refers to extreme traffic density when traffic flow stops completely, usually in the range of 185–250 vehicles per mile per lane.
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Traffic flow
In 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.
The foundation for modern traffic flow analysis dates back to the 1920s with Frank Knight's analysis of traffic equilibrium, further developed by Wardrop in 1952. Despite advances in computing, a universally satisfactory theory applicable to real-world conditions remains elusive. Current models blend empirical and theoretical techniques to forecast traffic and identify congestion areas, considering variables like vehicle use and land changes.
Traffic flow is influenced by the complex interactions of vehicles, displaying behaviors such as cluster formation and shock wave propagation. Key traffic stream variables include speed, flow, and density, which are interconnected. Free-flowing traffic is characterized by fewer than 12 vehicles per mile per lane, whereas higher densities can lead to unstable conditions and persistent stop-and-go traffic. Models and diagrams, such as time-space diagrams, help visualize and analyze these dynamics. Traffic flow analysis can be approached at different scales: microscopic (individual vehicle behavior), macroscopic (fluid dynamics-like models), and mesoscopic (probability functions for vehicle distributions). Empirical approaches, such as those outlined in the Highway Capacity Manual, are commonly used by engineers to model and forecast traffic flow, incorporating factors like fuel consumption and emissions.
The kinematic wave model, introduced by Lighthill and Whitham in 1955, is a cornerstone of traffic flow theory, describing the propagation of traffic waves and impact of bottlenecks. Bottlenecks, whether stationary or moving, significantly disrupt flow and reduce roadway capacity. The Federal Highway Authority attributes 40% of congestion to bottlenecks. Classical traffic flow theories include the Lighthill-Whitham-Richards model and various car-following models that describe how vehicles interact in traffic streams. An alternative theory, Kerner's three-phase traffic theory, suggests a range of capacities at bottlenecks rather than a single value. The Newell-Daganzo merge model and car-following models further refine our understanding of traffic dynamics and are instrumental in modern traffic engineering and simulation.
Attempts to produce a mathematical theory of traffic flow date back to the 1920s, when American Economist Frank Knight first produced an analysis of traffic equilibrium, which was refined into 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 theoretical techniques. These models are then developed into traffic forecasts, and take account of proposed local or major changes, such as increased vehicle use, changes in land use or changes in mode of transport (with people moving from bus to train or car, for example), and to identify areas of congestion where the network needs to be adjusted.
Traffic behaves in a complex and nonlinear way, depending on the interactions of a large number of vehicles. Due to the individual reactions of human drivers, vehicles do not interact simply following the laws of mechanics, but rather display cluster formation and shock wave propagation,[citation needed] both forward and backward, depending on vehicle density. Some mathematical models of traffic flow use a vertical queue assumption, in which the vehicles along a congested link do not spill back along the length of the link.
In a free-flowing network, traffic flow theory refers to the traffic stream variables of speed, flow, and concentration. These relationships are mainly concerned with uninterrupted traffic flow, primarily found on freeways or expressways. Flow conditions are considered "free" when less than 12 vehicles per mile per lane are on a road. "Stable" is sometimes described as 12–30 vehicles per mile per lane. As the density reaches the maximum mass flow rate (or flux) and exceeds the optimum density (above 30 vehicles per mile per lane), traffic flow becomes unstable, and even a minor incident can result in persistent stop-and-go driving conditions. A "breakdown" condition occurs when traffic becomes unstable and exceeds 67 vehicles per mile per lane. "Jam density" refers to extreme traffic density when traffic flow stops completely, usually in the range of 185–250 vehicles per mile per lane.