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 Traffic comprises pedestrians, vehicles, ridden or herded animals, trains, and other conveyances that use public ways (roads) for travel and transportation. Traffic laws govern and regulate traffic, while rules of the road include traffi ...

and minimal

traffic congestion Traffic congestion is a condition in transport that is characterized by slower speeds, longer trip times, and increased vehicular queueing. Traffic congestion on urban road networks has increased substantially since the 1950s. When traffic d ...

problems.

History

Attempts to produce a mathematical theory of traffic flow date back to the 1920s, when

Frank Knight Frank Hyneman Knight (November 7, 1885 – April 15, 1972) was an American economist who spent most of his career at the University of Chicago, where he became one of the founders of the Chicago School. Nobel laureates Milton Friedman, Georg ...

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 Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...

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 Land use involves the management and modification of natural environment or wilderness into built environment such as settlements and semi-natural habitats such as arable fields, pastures, and managed woods. Land use by humans has a long his ...

or changes in