Chuck Biehl& Sheel Ganatra The Charter School of Wilmington, Wilmington , Delaware

Traffic Flow Theory and Transportation Networks

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^s applications extend to describing the motion of one car on a highway to determining the effect several cars have on each other.