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A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow. A network can be used to model traffic in a computer network, circulation with demands, fluids in pipes, currents in an electrical circuit, or ...
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.
Three-phase traffic theory is a theory of traffic flow developed by Boris Kerner between 1996 and 2002. [1] [2] [3] It focuses mainly on the explanation of the physics of traffic breakdown and resulting congested traffic on highways.
Braess's paradox is the observation that adding one or more roads to a road network can slow down overall traffic flow through it. The paradox was first discovered by Arthur Pigou in 1920, [1] and later named after the German mathematician Dietrich Braess in 1968.
A transport network, or transportation network, is a network or graph in geographic space, describing an infrastructure that permits and constrains movement or flow. [1] Examples include but are not limited to road networks , railways , air routes , pipelines , aqueducts , and power lines .
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).
The first mathematical model of traffic flow in the framework of Kerner's three-phase traffic theory that mathematical simulations can show and explain traffic breakdown by an F → S phase transition in the metastable free flow at the bottleneck was the Kerner-Klenov stochastic microscopic traffic flow model introduced in 2002. [46]
In the study of traffic flow theory, the flow-density diagram is used to determine the traffic state of a roadway. Currently, there are two types of flow density graphs: parabolic and triangular. Academia views the triangular flow-density curve as more the accurate representation of real world events. The triangular curve consists of two vectors.