Car Density Research Articles

A New Approach to Kinematic Waves in Traffic Flow

Based on the equation of continuity, a cumulative number function of cars, ψ, which is analogous to a stream function in fluid mechanics, is defined as follows; q =∂ψ/∂ t , k =-∂ψ/∂ x , where q and k stand for the flow and the car density, respectively. Various functional assumptions between q and k , yield various fundamental equations for ψ. The analytical solutions subject to the initial or the boundary condition are given for the following cass: (i) q =4 k (1- k ) with k =κ H ( x 0 - x ) at t =0, (ii) q =4 k (1- k ) with k = ε (1+cos α x ) at t =0, (iii) q =4 k (1- k ) with q = a + b t at x =0, (iv) q =4 k (1- k )(1-β x ) with k = k 0 at t =0. It is shown that both expansion and compression shocks are possible and a few general relations for shock waves are obtained. Finally, extension to an axisymmetrical case is briefly discussed with a simple example of a constant density at the initial moment.

Simulation of traffic flows in a network

A computer simulation program which deals with traffic flows in the network of a large area is described. Each road is segmented into blocks of several ten-meter lengths and is represented by a bidirectional list in computer memory. The movement of cars, i.e. the transfer of cars from one block to the next, is expressed by a proper formula. This formula is based on the supposition that the speed of cars in a block is determined only by the density of cars in the block, and this speed-versus-density curve is empirically given the numerical values. This simulation scheme has its excellent point in that it makes it possible to trace the dynamic behavior of traffic flows in a variety of situations, some examples of which are given for an actual area of the city of Kyoto, Japan.

Traffic generation

With the growing motorization it is of increasing importance to calculate the traffic that will be generated by a new development. It is shown that the number of cars per 1000 inhabitants in a new suburb depends on the density and the income level. The number of trips per day varies in different cities from 3.2 to 12 and it is difficult to explain the difference. The number of persons pr. dwelling and their occupation seems to be of importance. The number of trips attracted by 100 m 2 of shops and offices seems to be more constant. The traffic to the central areas at least in American cities counted in persons has been decreasing since the car density reached 300 cars per 1000 inhabitants. It is suggested that the rush hour traffic from the city center should be calculated from the number of parking spaces in that area.

Equilibrium probability distributions for low density highway traffic

If on a long homogeneous highway there is no interaction between cars, then, under a wide range of conditions, an initial distribution of cars will in the course of time tend toward that of a Poisson process with statistically independent velocities for the cars in any finite interval of highway. Here we will generalize this known property to obtain the following. Suppose cars do interact in such a way as to delay a car when it passes another, but the density of cars is so low that we can neglect simultaneous interactions between three or more cars. There will again be equilibrium distributions of cars to which general classes of initial distributions will converge. These equilibrium distributions are superpositions of two statistically independent processes, one a Poisson process of single free cars with statistically independent velocities, and the other a Poisson process of interacting pairs of cars with various velocities. In the limit of zero interaction, the density of pairs vanishes leaving only the Poisson process of single cars as a special case. To the same order of approximation, including the first order effects of interactions, the headway distribution between consecutive cars will still have exponential tail outside the range of interaction.

Equilibrium probability distributions for low density highway traffic

If on a long homogeneous highway there is no interaction between cars, then, under a wide range of conditions, an initial distribution of cars will in the course of time tend toward that of a Poisson process with statistically independent velocities for the cars in any finite interval of highway. Here we will generalize this known property to obtain the following. Suppose cars do interact in such a way as to delay a car when it passes another, but the density of cars is so low that we can neglect simultaneous interactions between three or more cars. There will again be equilibrium distributions of cars to which general classes of initial distributions will converge. These equilibrium distributions are superpositions of two statistically independent processes, one a Poisson process of single free cars with statistically independent velocities, and the other a Poisson process of interacting pairs of cars with various velocities. In the limit of zero interaction, the density of pairs vanishes leaving only the Poisson process of single cars as a special case. To the same order of approximation, including the first order effects of interactions, the headway distribution between consecutive cars will still have exponential tail outside the range of interaction.

De gemiddelde bezetting van personenauto's in interlokaal verkeer*

SummaryThis paper, read in Utrecht on October 14th 1965, deals with the average occupancy of cars outside urban areas. During the years 1962 and 1963 more than 500 samples (each consisting of 150 cars) have been taken on two points of the dutch road‐system. The samples covered the different months, days (sundays, Saturdays and week‐days) and hours (except those without daylight).The average occupancy turned out to be 1.8 on week‐days (with a minimum of 1.4), 2.5 on Saturdays (with a minimum of 2.1) and 3.1 on Sundays (the over‐all average for all days being 2.1). These results seem to be representative for the whole dutch car traffic as is shown by comparison with observations on other points and other data.Comparison of the seasonal, weekly and hourly patterns of the average occupancy with those of the car traffic density enable to draw conclusions about the responsibility of different kinds of traffic (commercial and commuter traffic versus social traffic) for congestion and for the construction and maintenance cost of the road‐system.

Preliminary Investigation of Vehicular Noise Associated with Superhighways

Measurements of noise produced by freely moving vehicular traffic have been used to formulate a preliminary description of the superhighway as a noise source. The distribution of individual vehicle positions is assumed to be random at any given instant, while their relative velocities are assumed nearly constant. Under these assumptions the total acoustic power produced at locations adjoining the highway can be directly related to a statistical description of the traffic flow. The effects of flow densities of (a) passenger cars and light trucks, and (b) heavy trucks, are discussed insofar as they affect the time pattern and frequency distribution of the acoustic power produced. A description is given of the use of this characterization of traffic noise in estimating the reaction of a community to noise intrusion by the procedures outlined by Stevens, Rosenblith, and Bolt, Noise Control 1, 63 (1955).

Mathematical Models for Freely-Flowing Highway Traffic

An attempt is made to construct models for the motion of cars on a highway in a manner analogous to the way one treats the motion of molecules in a gas as described by the kinetic theory of gases. In particular the comparison is made between a traffic flow at very low volumes and the motion in a rarefied gas. From this, we are led to expect that even a very crude model of the interaction between individual cars will give a quite reasonable description of the collective behavior of large groups of cars. Some simple estimates of the dependence of average velocity on density and distribution of cars in various lanes of a multilane highway based upon very crude models seem to confirm this expectation. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.