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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 maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem .
The fundamental diagram of traffic flow is a diagram that gives a relation between road traffic flux (vehicles/hour) and the traffic density (vehicles/km). A macroscopic traffic model involving traffic flux, traffic density and velocity forms the basis of the fundamental diagram. It can be used to predict the capability of a road system, or its ...
The Three-detector problem [1] is a problem in traffic flow theory. Given is a homogeneous freeway and the vehicle counts at two detector stations. We seek the vehicle counts at some intermediate location. The method can be applied to incident detection and diagnosis by comparing the observed and predicted data, so a realistic solution to this ...
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. Kerner describes three phases of traffic, while the classical theories based on the fundamental diagram of traffic ...
Braess's paradox. 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. [ 2 ]
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation [1] occurring in various areas of applied mathematics, such as fluid mechanics, [2] nonlinear acoustics, [3] gas dynamics, and traffic flow. [4] The equation was first introduced by Harry Bateman in 1915 [5][6] and ...
Minimum-cost flow problem. The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network. A typical application of this problem involves finding the best delivery route from a factory to a warehouse where the road network has some ...