On kinematic waves II. A theory of traffic flow on long crowded roads

TLDR

Traffic flow on crowded arterial roads is characterized by a flow‑concentration relationship that has been postulated and experimentally supported, and introductory material is provided for readers unfamiliar with quantitative traffic studies. The paper develops a theory of how changes in traffic distribution propagate along crowded roads, applies it to the motion of a concentration hump and its interaction with bottlenecks, and derives methods to estimate the resulting hold‑up extent and duration. Using the kinematic wave method from part I, the authors model the propagation of a concentration hump along a crowded main road and its behavior when encountering a bottleneck, providing analytical tools for estimating its dynamics. The theory predicts that a concentration hump moves slightly slower than the mean vehicle speed, causes sudden speed reductions at entry and gradual acceleration at exit, spreads over time, and that the model is mainly applicable to long road stretches while offering insights into flow near junctions and controlled junction start flow.

Abstract

This paper uses the method of kinematic waves, developed in part I, but may be read independently. A functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing (§2). From this a theory of the propagation of changes in traffic distribution along these roads may be deduced (§§2, 3). The theory is applied (§4) to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road. It is suggested that it will move slightly slower than the mean vehicle speed, and that vehicles passing through it will have to reduce speed rather suddenly (at a ‘shock wave’) on entering it, but can increase speed again only very gradually as they leave it. The hump gradually spreads out along the road, and the time scale of this process is estimated. The behaviour of such a hump on entering a bottleneck, which is too narrow to admit the increased flow, is studied (§5), and methods are obtained for estimating the extent and duration of the resulting hold-up. The theory is applicable principally to traffic behaviour over a long stretch of road, but the paper concludes (§6) with a discussion of its relevance to problems of flow near junctions, including a discussion of the starting flow at a controlled junction. In the introductory sections 1 and 2, we have included some elementary material on the quantitative study of traffic flow for the benefit of scientific readers unfamiliar with the subject.