Fundamental Diagram of Traffic Flow

A systematic approach is developed to identify the bivariate relation of two fundamental traffic variables, traffic volume and density, from single-loop detector data. The approach is motivated by the observation of a peculiar feature of traffic fluctuations. That is, in a short time, traffic usually experiences fluctuations without a significant change in speed. This fact is used to define equilibrium in a new manner, and a mixed integer programming approach is proposed for constructing a piecewise linear fundamental diagram (FD) accordingly. By construction, the proposed method is data adaptive and optimal in the sense of least absolute deviation. This method is used to perform a case study with data from one section of a multilane freeway. The results indicate that both capacity drop and concave–convex FD shapes abound in practice. Differences in traffic behavior across freeway lanes and along freeway sections revealed through the FD are discussed.