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.

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

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

Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods

A variety of nonlinear follow-the-leader models of traffic flow are discussed in the light of available observational and experimental data. Emphasis is placed on steady-state flow equations. Some trends regarding the advantages of certain follow-the-leader functionals over others are established. However, it is found from extensive correlation studies that more data are needed before one can establish the unequivocal superiority of one particular model. A discussion is given of some ideas concerning the possible reasons for the existence of a bimodal flow versus concentration curve especially for multilane highways.

Nonlinear Follow-the-Leader Models of Traffic Flow

The equations of motion governing the two-dimensional flow of pedestrians are derived for flows of both single and multiple pedestrian types. Two regimes of flow, a high-density (subcritical) and a low-density (supercritical) flow regimes, are possible, rather than two flow regimes for each type of pedestrian. A subcritical flow always fills the space available. However, a supercritical flow may either fill the space available or be self-confining for each type of pedestrian, depending on the boundary location. Although, the equations governing these flows are simultaneous, time-dependent, non-linear, partial differential equations, remarkably they may be made conformally mappable. The solution of these equations becomes trivial in many situations. Free streamline calculations, utilizing this property, reveal both upstream and downstream separation of the flow of pedestrians around an obstacle. Such analysis tells much about the nature of the assumptions used in various models for the flow of pedestrians. The present theory is designed for the development of general techniques to understand the motion of large crowds. However, it is also useful as a predictive tool. The behavior predicted by these equations of motion is compared with aerial observations for the Jamarat Bridge near Mecca, Saudi Arabia. It is shown that, for this important case, pedestrians, that is pilgrims, aim at achieving each immediate goal in minimum time rather than achieving all goals in overall minimum time. Typical of many examples, this case illustrated the strong dependence of path on the psychological state of the pedestrians involved. It is proposed that the flow of pedestrians over the Jamarat Bridge be improved by appropriate barrier placement, that force an effective global view of the goals.

A continuum theory for the flow of pedestrians

The results of a traffic capacity study started in june 1934 by the traffic bureau of the ohio state highway department are presented. The data were collected by the photographic method described in volume 13 of the PROCEEDINGS OF THE HIGHWAY RESEARCH BOARD. After a brief description of the method of collecting and tabulating the information, certain selected data are analyzed to secure a measure of the working capacity of a two-lane roadway and the amount of vehicle time lost under varying degrees of congestion. The study of 1180 groups of 100 vehicles each, including not over 10 percent trucks, reveals the average free moving speed to be about 43 miles per hour on either a two or three lane road. When the number of vehicles exceeds 400 to 600 per hour, the average speed decreases and the effect of a few slow-moving vehicles is more pronounced. The mean speed of 859 light trucks was 41.0 miles per hour, and of 225 heavy trucks, 32.4 miles per hour. for 18 buses, the average was 41.6 miles per hour. In the discussion, Mr. Bibbins discusses the method of obtaining over-all speeds over a stretch of highway by recording the tag number of the vehicle entering the stretch and checking the same tag number on leaving. Mr. Canning describes a method of obtaining average running speed. Mr. Miller discusses measurement of traffic delay by traffic counts and the progress of an automobile in traffic. The record of progress is obtained by means of an instrument attached to the automobile which marks a graduated ribbon indicating the speed of the vehicle and the time loss due to cross traffic, stop lights, slow moving traffic, congestion, road conditions, etc. In Pennsylvania, a number of touring cars were equipped with Recordographs that indicate the speed of a car graphically on a ribbon. The Recordograph traffic analysis was found to be an accurate method of determining the traffic capacity of highways and valuable aid in determining traffic conditions.

H.h. Miller

Papers

A study of traffic capacity