Traffic flow theory

Traffic flow theory describes how vehicles move along a road as a stream. Three variables are central: flow q (vehicles per hour passing a point), density k (vehicles per kilometre) and space mean speed v (km/h). They are related by q = k v. As density rises from zero, speed falls; flow first increases, reaches a maximum, the capacity, at the critical density, and then falls as the road jams.

Greenshields' simple model assumes speed falls linearly with density, from free-flow speed at zero density to zero at jam density. This produces a parabolic flow-density curve with capacity at half the jam density and half the free speed. Better models fit real data more closely, but the shape of the fundamental diagram, rising, peaking and then falling, is universal. Indian roads have mixed traffic, from two-wheelers to trucks, so flows are expressed in passenger car units (PCU), with equivalence factors for each class that depend on traffic mix and road type.

Capacity and level of service guide design. Level of service grades conditions from free flow to forced flow by density, speed or delay. Shock waves form where flow states meet, for example at a bottleneck or a signal, and travel back through traffic at a speed given by the change in flow over the change in density. Queueing models predict delays at toll plazas and signals. Microscopic models, such as car-following, and simulation tools are used for complex networks.