Fundamental Diagram of Traffic Flow New Identification Scheme and Further Evidence from Empirical Data

This paper further investigates the specification and calibration of FDs. The purpose is to provide a consistent, systematic, and adaptive way to obtain FDs from single-loop detector measurements. In particular, the piecewise linear form is adopted for the FD, because (a) more-complex forms of the FD can be approximated by a piecewise linear form with arbitrarily many pieces, and (b) empirical evidence tends to support such a form. For example, Windover and Cassidy found that there is no dependency of wave speed on flow in either the free-flow or the congested region of traffic, implying that the flow–density relationship is locally linear (6). Meanwhile, the piecewise linear form greatly simplifies analysis and computation of the kinematic wave model of Lighthill and Whitham (7 ) and Richards (8). For example, explicit calculation is enabled in Newell’s simplified KW theory (9) and the cell transmission model (10) with the use of triangular or trapezoidal FDs.