The workings of traffic flow theory and flow networks have long been
used to analyze and optimize traffic patterns, especially in urban areas.
While traffic flow theory associates with the properties of a vehicle or
vehicles on a road given different localized conditions, transportation
networks deal with the interrelations of many roads as a whole, taking the
length and optimum flow on a road to find optimizations on many roads.
Transportation networks are represented by weighted graphs or digraphs
in which edges are roads and vertices are intersections. To make this model
realistic in problems such as optimization, metrices are assigned to each
edge, along with a flow, which is often determined by the metric space.
Several properties associated with metric spaces are non-negative distances,
symmetry, and the triangle inequality. In transportation networks, the
symmetric property can be ignored due to one way streets, which are
represented by directed edges.
Traffic flow theory uses equations to model the properties of cars with
respect to position and time. The fundamental relation in traffic flow
theory is: Flow = Density x Speed. In other flow theories, such ones that
deal with water flow through pipes, density and speed are independent
variables. However, in traffic flow theory, density and speed are dependent
on each other, and on flow. Traffic flow theory^Òs applications extend to
describing the motion of one car on a highway to determining the effect
several cars have on each other.