Car Density Research Articles

Statistical mechanical approach to Fukui-Ishibashi traffic flow models

We consider cellular automaton models for one-dimensional traffic flow problems. Starting with a microscopic relation for the updating rule describing the occupancy on each site of the road, a macroscopic evolution relation for the average speed of cars can be obtained by carrying out statistical averages. Mean field equations are obtained by considering the asymptotic form of the evolution relation. This gives the average car speed in the long time limit as a function of the car density. The evolution relation is a nonlinear mapping between the average speeds at two consecutive time steps. The mean field results can be obtained by studying the attractors of the mapping. The approach is applied to study the model recently proposed by Fukui and Ishibashi. Our calculations show that for models in which the maximum speed of each car is $M$, a decoupling scheme retaining correlations up to $M+1$ sites can be applied to the calculation of spatial correlations involving more than $M+1$ sites. Exact results are obtained using our approach for models without random delay. For models with random delay, results are in good agreement with simulation results.

Two-way traffic flow: Exactly solvable model of traffic jam

We study completely asymmetric two-channel exclusion processes in one dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars in the other lane. Particularly, we consider in detail the system with a finite density of cars on one lane and a single car on the other. When the interchannel interaction reaches a critical value, a traffic jam occurs, which turns out to be of first-order phase transition. We derive exact expressions for the average velocities, the current, the density profile and the k-point density correlation functions. We also obtain the exact probability of two cars being in one lane of distance R apart, provided there is a finite density of cars on the other lane, and show that the two cars form a weakly bound state in the jammed phase.

Strict derivation of mean field equation for one-dimensional traffic flow model

A new analysis method is presented for the study of Fukui-Ishibashi deterministic one-dimensional traffic flow cellular automaton model of high speed car on highway. By using this method, the exact mean field equation describing the fundamental diagram curve of average traffic speed versus the car density on highway can be derived strictly.

Cellular automata models of single-lane traffic

The jamming transition in the stochastic cellular automaton model (Nagel-Schreckenberg model) of highway traffic is analyzed in detail, by studying the relaxation time, a mapping to surface growth problems and the investigation of correlation functions. Three different classes of behavior can be distinguished depending on the speed limit $v_{max}$. For $v_{max} = 1$ the model is closely related to KPZ class of surface growth. For $1<v_{max} < \infty$ the relaxation time has a well defined peak at a density of cars $\rho$ somewhat lower than position of the maximum in the fundamental diagram: This density can be identified with the jamming point. At the jamming point the properties of the correlations also change significantly. In the $v_{max}=\infty $ limit the model undergoes a first order transition at $\rho \to 0$. It seems that in the relevant cases $1<v_{max} < \infty$ the jamming transition is under the influence of second order phase transition in the deterministic model and of the first order transition at $v_{max}=\infty $.

Microstructure and microdynamics of uninterrupted traffic flow

In this paper, ``uninterrupted homogeneous traffic flow'' is viewed as a dynamic system of spontaneously aggregating and breaking clusters of cars. This approach gives qualitative and quantitative descriptions of density fluctuations and dynamics of free traffic flow in terms of car clusters, and their distributions with respect to the number of cars in a cluster. The distributions have a nontrivial shape and a nonlinear dependence on the density of cars on the expressway. Their shape and evolution as a function of car density are described adequately by a model proposed here. This one-parameter model based on a modified Smoluchowski equation predicts a critical density at which a phase transition occurs from free to synchronized traffic flow for a multilane expressway: ${\ensuremath{\rho}}_{\mathrm{cr}}=16\ifmmode\pm\else\textpm\fi{}3{\mathrm{vehicles}\mathrm{}\mathrm{km}}^{\mathrm{\ensuremath{-}}1}{\mathrm{}(\mathrm{lane})}^{\mathrm{\ensuremath{-}}1},$ and that below this critical density traffic flow can be treated as a one-dimensional system. The model may also find application in the study of the low density pneumatic transport of granular and powdered materials.

Environmental exposure to gasoline and leukemia in children and young adults-an ecology study

Benzene is an established cause of leukemia in adults, especially acute non-lymphocytic leukemia (ANLL). A few studies have indicated that exposure to gasoline is a cause of childhood leukemia. The purpose of this study was to investigate if environmental exposure to benzene from gasoline and car exhaust was associated with leukemia in children and young adults. The exposure to gasoline and car exhaust was estimated by the number of cars per area. In this ecology study, data on the incidence of cancer in each municipality of Sweden during an 11-year period (1975-1985) were compared with the number of cars per area. Data on the incidence of cancer for persons aged 0-24 years at diagnosis were collected from the National Swedish Cancer Register. The following diagnoses were studied: non-Hodgkin's lymphoma, acute lymphocytic leukemia (ALL), chronic myeloid leukemia (CML), and acute myeloid leukemia (AML). We found an association between AML and car density. In municipalities with more than 20 cars/km2 the incidence of AML was 5.5 [95% confidence interval (CI) 4.4-6.8, n = 89] as compared with 3.4 (95% CI 1.9-5.7, n = 15) cases per 1 million person-years in municipalities with less than 5 cars/km2 (P = 0.05). No association was found for the other sites of cancer studied. The association between AML in young adults and car density might be attributable to exposure to benzene from gasoline vapors and exhaust gases, but further investigations are necessary before any definite conclusion can be drawn.

Car accidents and number of stopped cars due to road blockage on a one-lane highway

Within the framework of a simple model of car traffic on a one-lane highway, we study the probability of the occurrence of car accidents when drivers do not respect the safety distance between cars, and, as a result of the blockage during the time T necessary to clear the road, we determine the number of stopped cars as a function of car density. We give a simple theory in good agreement with our numerical simulations.

Gas Kinetics of Traffic Jam

The kinetics of one-dimensional traffic flow is descibed in terms of Boltzmann-like gas kinetic equation. Paveri-Fontana's gas kinetic equation is modified to take into account the desired velocity depending on the car density. A discrete version of the gas kinetic equation is derived to numerically solve the equation. The velocity distributions are calculated by a numerical method. It is found that the traffic jam is formed in the congested traffic flow when the car density is higher than the critical value. The traffic jam propagates backward, its propagation velocity increases with the accerelation and the density within the jam decreases with increasing accerelation. It is shown that the velocity distributions change significantly before and after the traffic jam.

Effect of Delay in Restarting of Stopped Cars in a One-Dimensional Traffic Model

Traffic flow in the one-dimensional cellular automaton model including cars with the delay in restarting after a stop is simulated. With the increase of the car density, a phase transition between a free moving phase and a jam phase occurs at a critical density p c =1/3. In the jam phase, according to the initial condition for the advance of the car, there appear the steady states where the mean velocity of the cars oscillates between two values, whose average is just (1- p )/2 p .

Kinetics of segregation in a two-lane highway traffic flow

A particle-hopping model is presented to simulate the segregation of cars on a two-lane highway which consists of a slow lane and a fast lane. The changing of cars between the slow and fast lanes is taken into account. When a fast (slow) car overtakes (is overtaken by) a slow (fast) car on the slow (fast) lane, the fast (slow) car shifts to the fast (slow) lane. By satisfying the demand for faster movement, a segregation of cars occurs. The car densities, velocities and currents on the slow and fast lanes are calculated by computer simulation. The velocity distributions on the two lanes are also shown. It is found that the traffic current is enhanced by the changing of cars between two lanes. The kinetics of segregation between the slow and fast lanes is described in terms of a Boltzmann-like kinetic equation. The kinetic equation is solved by a numerical method. The velocity distributions, car densities, velocities and currents obtained from the kinetic equation are compared with the simulation results.

Gas Kinetic Approach to Two-Dimensional Traffic Flow

The kinetics of cars in two-dimensional traffic flow is described in terms of Boltzmann-like gas kinetic equations. Paveri-Fontana's gas kinetic equation for one-dimensional traffic flow is extended to two-dimensional traffic. The desired velocity is taken into account in the gas kinetic equations. A discrete version of the kinetic equations is used to numerically solve the equations. The velocity distributions are calculated by a numerical method. The steady-state velocity distributions are derived numerically for different accelerations and densities. It is shown that the velocity distribution of east-bound cars deviates to the low-velocity side with increasing density of north-bound cars. It is also found that the velocity distribution deviates to the high-velocity side with increasing acceleration under the condition of constant density.

Pollution and the development of allergy: The East and West Germany story

Allergic diseases are partly genetically determined, but environmental factors have a strong influence on the expression of allergic symptoms in genetically predisposed subjects. In particular, outdoor air pollution has received widespread attention as a potential manifestation factor. The unification of Germany provided a unique opportunity to study the impact of radically different environmental and social conditions on the development of allergies in two genetically homogenous populations. A high car density and N02 exposure were typical for many West German cities. Severe pollution due to heavy industrialization and private coal burning for healing purposes were the main sources of air pollution in East German cities.

Traffic Flow in 1D Cellular Automaton Model Including Cars Moving with High Speed

Traffic flow is simulated by one-dimensional cellular automaton (CA) model including cars moving with high speed. The simulation shows a phase transition between the moving phase and the jamming phase at p =1/( m +1) ( p : density of cars, m : the maximum number of sites by which cars advance at each time step). A mean-field theory can reproduce the average velocity found by simulations.

Restructuring the East German energy system

In the former German Democratic Republic the energy systems was organized centrally with emphasis on autarky and sufficient and cheap energy for all. The use was wasteful with little regard for the environment. After unification of the two German states the East German energy system has been totally restructured. Market economic principles with competition and free pricing have been introduced. The energy industry has been privatized and new generation and transmission equipment built. The gas supply has been changed from town gas to natural gas. The old brown coal power stations are being closed down and new efficient ones built. The transition to a market economy has led to a collapse of industry to one-third of its former size and loss of three-quarters of industrial jobs. Primary energy consumption has been halved. Only road fuels have increased by 50% after car density has reached 90% of the West German level. Strict environmental legislation has resulted in large reductions in emissions and improved ambient air quality. The restructuring is estimated to cost 100 billion deutschmarks of which 50 billion has been spent. The East German energy system is set to become Europe's most modern by the year 2000.

Cellular automata model of car traffic in a two-dimensional street network

We propose a road traffic cellular automata model suitable for an urban environment. North, east, south and west car displacements are possible and road crossings are naturally implemented as rotary junctions. We consider the traffic in a Manhattan-like city and study the flow diagram and the car density profile along road segments. We observe that the length of the car queues obeys a complex dynamics and is not uniform across the network. The street length between two junctions and the turning strategies at rotaries are relevant parameters of the model. Our results are also confirmed by fully continuous traffic simulations.

Improved mean-field theory of two-dimensional traffic flow models

An improved mean-field theory is proposed for traffic-flow models in two dimensions, both in the absence and presence of faulty traffic lights. The present theory includes the effects of blockage of cars due to cars moving in the same direction, while previous theories included only the effects of cars moving in the perpendicular direction. In the absence of faulty lights, the theory gives a much better estimate of the critical car density, above which the traffic is in a jamming phase. In the presence of faulty lights, the theory captures all the essential features in published simulation data. It gives the correct behaviour of the velocity in the dilute limit of car density. The dependence of the critical car density on the fraction of faulty traffic lights is studied.

Upper Bounds for the Critical Car Densities in Traffic Flow Problems

In most models of traffic flow, the car density p is the only free parameter in determining the average car velocity . The critical car density p c , which is defined to be the car density separating the jamming phase (with =0) and the moving phase (with >0), is an important physical quantity to investigate. By means of simple statistical argument, we show that p c 2) dimensions.

Scaling behaviour in discrete traffic models

We investigate the noisy, discrete, single lane highway traffic model proposed by Nagel and Schreckenberg (1992) and demonstrate by computer simulations that, as a function of the car density, there is a dynamical transition from laminar flow to jammed traffic in the system related to the divergence of the relaxation time of average car velocity. The critical density is close to the position of the maximum in the fundamental diagram. We give estimates of the critical exponents related to this jamming transition. The critical density of the geometrical ((1+1)-dimensional percolation) transition of jammed regions can be rather far from the jamming point depending on the strength of the noise which indicates that cooperativity leading to the jamming transition can be long range in character.

Two-dimensional traffic flow problems in inhomogeneous lattices

Cellular automaton (CA) models are presented to simulate the traffic jam in a two-dimensional traffic flow. Effects of introducing inhomogeneities in the form of sites having different time scales and overpasses are studied using computer simulations. We present theoretical estimates of the critical car density and the average velocity at low car densities, and compare with numerical results. Results suggest that strategically adding these sites can help sustain a moving traffic at higher car densities.

Self-Organization in 2D Traffic Flow Model with Jam-Avoiding Drive

A stochastic cellular automaton (CA) model is presented to investigate the traffic jam by self-organization in the two-dimensional (2D) traffic flow. The CA model is the extended version of the 2D asymmetric exclusion model to take into account jam-avoiding drive. Each site contains either a car moving to the up, a car moving to the right, or is empty. A up car can shift right with probability p ja if it is blocked ahead by other cars. It is shown that the three phases (the low-density phase, the intermediate-density phase and the high-density phase) appear in the traffic flow. The intermediate-density phase is characterized by the right moving of up cars. The jamming transition to the high-density jamming phase occurs with higher density of cars than that without jam-avoiding drive. The jamming transition point p 2c increases with the shifting probability p ja . In the deterministic limit of p ja =1, it is found that a new jamming transition occurs from the low-density synchronized-shifting phase to the high-density moving phase with increasing density of cars. In the synchronized-shifting phase, all up cars do not move to the up but shift to the right by synchronizing with the move of right cars. We show that the jam-avoiding drive has an important effect on the dynamical jamming transition.