Car Density Research Articles

Extreme fluctuation events in a simple high-density traffic model

We revisit a simple car-following model adapting it for simulating high-density traffic dynamics. Simulations in continuum space and discrete time are presented for the case of a single traffic lane, using periodic boundary conditions. The model parameters are fitted to empirical data for the mean car speed versus car density for densities higher than ≃ 50 vehicles / km . The time evolution of the car ensemble is studied upon application of different types of random perturbations yielding strong speed fluctuations in all cases, the latter characterized by probability distribution functions displaying fat tails. We attempt to study the phenomenon of stop-and-go along the lane in the absence of perturbations by assuming a stopping cutoff speed, and find the resulting behavior of the ensemble both in space and time.

Energy dissipation in the deterministic and nondeterministic Nagel–Schreckenberg models

In this paper, we numerically study energy dissipation per unit time per car E d in the Nagel–Schreckenberg (NS) model. Numerical results show that there is a critical density over which energy dissipation occurs, but below which no energy loss happens in the deterministic NS model. Energy dissipation depends on both the car density and initial configuration in the deterministic case. The energy dissipation rate, E d , calculated starting from a completely jammed state whose value is minimum, decreases monotonously with the increase of car density above the critical density. In the nondeterministic case, however, there is no critical density and energy dissipation happens in the whole density region, and initial configuration has no effects on energy dissipation. The dissipated energy has two different contributions: one coming from the interactions and another from the braking noise in the stochastic case. The relative contributions of the two dissipation mechanisms are presented. In the free-flow state, E d is proportional to p ( 1 − p ) where p is the stochastic braking probability. In the case of v max = 1 , E d is proportional to the mean density of “go and stop” car per time step ρ g s , which is equal to n 0 ( 1 − n 0 ) where n 0 is the fraction of stopped car. Theoretical analyses give an excellent agreement with numerical results.

Difference schemes, entropy solutions, and speedup impulse for an inhomogeneous kinematic traffic flow model

The classical Lighthill-Whitham-Richards (LWR) kinematic traffic model is extended to a unidirectional road on which the maximum density $a(x)$ represents road inhomogeneities, such as variable numbers of lanes, and is allowed to vary discontinuously. The car density $\phi = \phi(x,t)$ is then determined by the following initial value problem for a scalar conservation law with a spatially discontinuous flux: $\phi_t + (\phi v(\phi/{a(x)})_x = 0, \quad \phi(x,0)=\phi_0(x),\quad x \in \mathbb{R},\quad t\in (0,T),$ (*) where $v(z)$ is the velocity function. We adapt to (*) a new notion of entropy solutions (Burger, Karlsen, and Towers [Submitted, 2007]), which involves a Kružkov-type entropy inequality based on a specific flux connection $(A,B)$, and which we interpret in terms of traffic flow. This concept is consistent with both the driver's ride impulse and the desire of drivers to speed up. We prove that entropy solutions of type $(A,B)$ are unique. This solution concept also leads to simple, transparent, and unified convergence proofs for numerical schemes. Indeed, we adjust to (*) new variants of the Engquist-Osher (EO) scheme (Burger, Karlsen, and Towers [Submitted, 2007]), and of the Hilliges-Weidlich (HW) scheme analyzed by the authors [ J. Engrg. Math. , to appear]. It is proven that the EO and HW schemes and a related Godunov scheme converge to the unique entropy solution of type $(A,B)$ of (*). For the Godunov version, this is the first rigorous convergence and well-posedness result, since no unnecessarily restrictive regularity assumptions are imposed on the solution. Numerical experiments for first-order schemes and formally second-order MUSCL/Runge-Kutta versions are presented.

Two sides of the same coin? Private car ownership in Sweden and Norway since 1950

Norwegian private car density has lagged behind the Swedish and did not reach same national levels until the late 1980s, despite the same GDP per capita levels. Can both the time lag and the diffusion process be explained with national differences in income, institutions, infrastructure and population settlements? Or have regional differences in income and population density affected the outcome? The aim of this article is to compare car diffusion in Norway and Sweden in order to find explanations for the national and regional patterns of car diffusion. The conclusion is that car diffusion in Norway and Sweden displays two sides of same coin; the national levels converged, but the process did not follow the same regional pattern. Regional differences in income and population density have in general been a significant explanation for car density in Sweden, but not in Norway.

Processing Web-Cam Images by a Neuro-Fuzzy Approach for Vehicular Traffic Monitoring

Traffic management in an urban area is highly facilitated by the knowledge of the traffic conditions in every street or highway involved in the vehicular mobility system. Aim of the paper is to propose a neuro-fuzzy approach able to compute the main parameters of a traffic system, i.e., car density, velocity and flow, by using the images collected by the web-cams located at the crossroads of the traffic network. The performances of this approach encourage its application when the traffic system is far from the saturation. A fuzzy model is also outlined to evaluate when it is suitable to use more accurate, even if more time consuming, algorithms for measuring traffic conditions near to saturation. Keywords— Neuro-fuzzy networks, Computer vision, Fuzzy systems, Intelligent Transportation System.

The relations of “go and stop” wave to car accidents in a cellular automaton with velocity-dependent randomization

In this paper we numerically study the probability P ac of the occurrence of traffic accidents in the Nagel–Schreckenberg (NS) model with velocity-dependent randomization (VDR). Numerical results show that there is a critical density over which car accidents occur, but below which no car accidents happen. Different from the accident probability in the NS model, the accident probability in the VDR model monotonously decreases with increase of car density above the critical density. The value of the accident probability is only determined by the stochastic noise and the number of cars on road. In the stochastic VDR model with the speed limit v max = 1 , no critical density exists and car accidents happen in the whole density region. The braking probabilities of standing cars and moving cars have different influences on the accident probability. A mean-field theory reveals that the accident probability is proportional to the mean density of “go and stop” wave per time step. Theoretical analyses give excellent agreement with numerical results in the VDR model.

Application of thermodynamics to driven systems

Application of thermodynamics to driven systems is discussed. As particular examples, simple traffic flow models are considered. On a microscopic level, traffic flow is described by Bando's optimal velocity model in terms of accelerating and decelerating forces. It allows to introduce kinetic, potential, as well as total energy, which is the internal energy of the car system in view of thermodynamics. The latter is not conserved, although it has certain value in any of two possible stationary states corresponding either to fixed point or to limit cycle in the space of headways and velocities. On a mesoscopic level of description, the size n of car cluster is considered as a stochastic variable in master equation. Here n = 0 corresponds to the fixed-point solution of the microscopic model, whereas the limit cycle is represented by coexistence of a car cluster with n > 0 and free flow phase. The detailed balance holds in a stationary state just like in equilibrium liquid-gas system. It allows to define free energy of the car system and chemical potentials of the coexisting phases, as well as a relaxation to a local or global free energy minimum. In this sense the behaviour of traffic flow can be described by equilibrium thermodynamics. We find, however, that the chemical potential of the cluster phase of traffic flow depends on an outer parameter — the density of cars in the free-flow phase. It allows to distinguish between the traffic flow as a driven system and purely equilibrium systems.

Cellular automaton model for mixed traffic flow with motorcycles

A single-lane cellular automaton model is proposed to simulate mixed traffic with motorcycles. By performing numerical simulations under the periodic boundary condition, some density-flow relations and the “lane-changing” behavior of motorcycles are investigated in detail. It is found that the maximum car flow decreases because of the “lane-changing” behavior of motorcycles. The maximum total flow increases first and then decreases with increasing motorcycle density. Moreover, the transition of the total flow from the free flow to the congested flow is smooth in this model. The “lane-changing” rate of motorcycles will decrease to zero finally with the increase of the car density. But its evolutionary trend is considerably complex. Another interesting fact is that, with the increase of the motorcycle density, the “lane-changing” rate increases first and decreases later. This phenomenon is very similar to the findings in other papers on multi-lane car flows. The“lane-changing” is almost of no use in increasing the flow of motorcycles as the motorcycle density is small. But it distinctly causes the increase in the flow of motorcycles when the motorcycle density is sufficiently large, and in this density regime, the flow of motorcycles gradually decreases to the one given with the Nagel–Schreckenberg model for motorcycles with the increase of the car density. The simulation results indicate that it is necessary to set a barrier or a lane for separating the motorcycle flow from the car flow except in some special density regime.

A two-dimensional CA model for traffic flow with car origin and destination

Dynamic phase transitions in a two-dimensional traffic flow model defined on a decorated square-lattice are studied numerically. The square-lattice point and the decorated site denote intersections and roads, respectively. In the present model, a car has a finite deterministic path between the origin and the destination, which is assigned to the car from the beginning. In this new model, we found a new phase between the free-flow phase and the frozen-jam phase that is absent from previous models. The new model is characterized by the persistence of a macroscopic cluster. Furthermore, the behavior in this macroscopic cluster phase is classified into three regions characterized by the shape of the cluster. The boundary of the three regions is phenomenologically estimated. When the trip length is short and the car density is high, both ends of the belt-like cluster connect to each other through the periodic boundary with some probability. This type of cluster is classified topologically as a string on a two-dimensional torus.

A European model for the number of End-of-Life Vehicles

This paper describes a model for the projection of the number of End-of-Life Vehicles (ELVs) and presents a baseline projection. Historical data on population, the number of cars per capita (car density), GDP per capita, and the vintage distribution of cars are combined to model ELVs. The lifetime of vintages of cars is described by a Weibull distribution and the development in car density is modelled by a Gompertz function. Parameters of the distribution and function are calibrated by using historical data, mainly from Eurostat. The paper presents a baseline projection of the number of ELVs for the EU25.

Premature seizure of traffic flow due to the introduction of evolutionary games

We study the impact of evolutionary games on the flow of traffic. Since traffic participants do not always conform to the imposed rules, the introduction of games, i.e. set of strategies defining the behavioural pattern of agents on the road, appears justified. With this motivation, and the fact that individuals can change their strategy in the course of time, the evolutionary prisoner's dilemma game is introduced between neighbouring agents, enabling them to choose between cooperation and defection. Mutual cooperation enables forwarding to both agents for one step, while the defector is able to advance two steps when facing a cooperator, whereby the latter is forced to go one step backwards. Two defectors end up in a halt until the next iteration. Irrespective of their strategy, however, agents can move only if the road ahead is free. Jumps are never allowed. We show that this simple and plausible supplementation of the discrete cellular automaton Biham–Middleton–Levine (BML) model induces a traffic flow seizure by a substantially lower initial density of cars as in the absence of evolutionary games. The phenomenon is explained by studying the one-dimensional variant of the BML model with different advancement steps on the circular ring. In view of the proposed explanation, findings are generalized also to other types of games, such is the snowdrift game, and some statistical properties of gridlock formation in the presence of evolutionary rules are outlined. Our findings suggest that ‘bending the law’ results in a premature occurrence of traffic jams and thus unnecessarily burdens the transportation system.

Effects of a type of quenched randomness on car accidents in a cellular automaton model

In this paper we numerically study the probability Pac of the occurrence of car accidents in the Nagel-Schreckenberg (NS) model with a defect. In the deterministic NS model, numerical results show that there exists a critical value of car density below which no car accident happens. The critical density Pc1 is not related only to the maximum speed of cars, but also to the braking probability at the defect. The braking probability at a defect can enhance, not suppress, the occurrence of car accidents when its value is small. Only the braking probability at the defect is very large, car accidents can be reduced by the bottleneck. In the nondeterministic NS model, the probability Pac exhibits the same behaviors with that in the deterministic model except the case of vmax=1 under which the probability Pac is only reduced by the defect. The defect also induces the inhomogeneous distribution of car accidents over the whole road. Theoretical analyses give an agreement with numerical results in the deterministic NS model and in the nondeterministic NS model with vmax=1 in the case of large defect braking probability.

自動車利用とCO<sub>2</sub>排出量で評価する税制の影響

In this paper, we study the effectiveness of tax incentives and the variation in vehicle user costs on the environmental impact of private car use across cities in OECD countries and in some non-OECD countries in Asia. We present a simple model of private car stocks, vehicle kilometres travelled (VKT) per capita and per car and CO2 emission in relation to acquisition, ownership and fuel taxes, the pre-tax user cost of cars, and income per capita. In contrast with earlier studies that have tended to focus on samples of revealed or stated preference data from specific highly developed countries (or small groups of countries), we estimate our model by means of data from 68 large cities, among which 49 from OECD countries and 19 from non-OECD countries in Asia. The implications for sustainable development of the structural differences between these taxes in terms of the model outcomes are identified. Our results indicate that acquisition and ownership taxes have little impact on behavior and environmental performance, but fuel and other use-related taxes are effective.Hence our econometric analysis suggests that taxes on variable costs have a greater impact on car ownership and use than taxes on fixed costs and that the former can be an effective way to reduce CO2 emission levels, despite the rebound effect. However, given the complexity of the transport sector and the wide range of behaviour responses that can take place in any given socio-economic and institutional setting, a ‘one size fits all’ conclusion should not be drawn from the rather low-dimensional analysis conducted in this study.A very clear finding is that our results confirm the importance of the fuel tax as an effective policy instrument in transportation. The fuel tax coefficient is highly significant in our econometric model. A 1 percent increase in the fuel tax per kilometre travelled reduces car ownership density, VKT per capita and CO2 emission all by about 0.6 percent. The results are consistent with the expectation that increased fuel taxes discourage further growth in car ownership, lead to switches to other transportation modes and also lead to manufacturer and driver responses that lower CO2 emission per capita. The impact on average annual vehicle kilometres travelled per car is much less, however. The elasticity is -0.1 (significant at the 5 percent level). This low elasticity is due to the so-called rebound effect : the increasing price of fuel has led manufactures to design and sell new cars with ever-more economical engines. Consequently, the disincentive of the higher fuel price is partially offset by the greater economy, leading to a lower overall impact on average VKT travelled per car per year. While the results suggest the greatest responsiveness of private car ownership and use to the fuel tax, they do not preclude that a combination of tax instruments would be more effective than a single one.JEL classification : O57, Q51, Q56, Q58, R48

Including Human Health Damages due to Road Traffic in Life Cycle Assessment of Dwellings

DOI: http://dx.doi.org/10.1065/lca2006.04.013 Goal, Scope and background. Methodologies based on life cycle assessment have been developed to calculate the environmental impact of dwellings. Human health damages due to exposure of occupants to substances and noise emitted by road traffic are not included in these methodologies. In this study, a methodology has been developed to calculate damages to human health of occupants caused by substances and noise emitted by neighbourhood car traffic. The goal of this study is to assess the influence of the location of the dwelling on the health of the occupants, compared to the damage to human health associated with the rest of the life cycle of that dwelling. Fate, exposure and human health effects were addressed in the calculation procedure. The methodology takes into account road traffic noise and four hazardous substances emitted by cars. Chemical fate factors were calculated with an outdoor exposure model for traffic pollutants, air entrance rates and indoor intake fractions. Fate factors for noise were based on noise levels generated by traffic. Effect factors for substances were based on unit risk factors and extrapolated dose-effect relationships. Effect factors for noise were based on linear relationships between noise level changes and health effects, while taking into account threshold values for noise levels for negative impacts. Damage factors were calculated on the basis of disability adjusted life years (DALYs). Human health damage scores for changes in traffic situations have been calculated for differences in three traffic scenarios in residential areas and for the Dutch reference dwellings. For the Dutch reference dwelling and the traffic situations considered and taking into account noise, particulate matter (PM10), sulphur dioxide, benzene and benzo[ a]pyrene, communication disturbances and sleep disturbances due to noise and health effects of PM10 appear to be dominant in the total damage to human health of occupants caused by neighbourhood car traffic. A sensitivity analysis has shown that a reduction of the car and truck density and of the distance of the facade of the dwellings to the road axis has the largest positive effect on the human health of the occupants, and that a decrease of speed by traffic impediments has only a marginal or even a negative effect. Differences in overall indoor health damage due to different traffic scenarios may be 1.5 to 2 times Within the limitations of this study, damages to human health of occupants due to indoor exposure to road traffic noise and pollutants appear to be in the same order of magnitude when compared with damages associated with the life cycle of dwellings. This emphasizes the importance to include the location of dwellings in the life cycle assessment of the dwelling.

Investigation of the bottleneck in high speed traffic caused by a bridge

A cellular automaton model for the bottleneck in high speed traffic caused by a bridge is proposed. It takes the initial density apart into six regions. Based on the mean field theory and the results of definitive NS model, the relations of car density of every line are given. The simulation results show that the theoretical model is correct.

Coexisting phases and lattice dependence of a cellular automaton model for traffic flow

The Biham-Middleton-Levine traffic model is perhaps the simplest system exhibiting phase transitions and self-organization. Moreover, it is an underpinning to extensive modern studies of traffic flow. The general belief is that the system exhibits a sharp phase transition from freely flowing to fully jammed, as a function of initial density of cars. However, we discover intermediate stable phases, where jams and freely flowing traffic coexist. The geometric structure of such phases is highly regular, with bands of free flowing traffic intersecting at jammed wave fronts that propagate smoothly through the space. Instead of a phase transition as a function of density, we see bifurcation points, where intermediate phases begin coexisting with the more conventionally known phases. We show that the regular geometric structure is in part a consequence of the finite size and aspect ratio of the underlying lattice, and that for certain aspect ratios the asymptotic intermediate phase is on a periodic limit cycle (the exact microscopic configuration recurs each tau time steps). Aside from describing these intermediate states, which previously were overlooked, we derive simple equations to describe the geometric constraints, and predict their asymptotic velocities.

IMPROVING VEHICLE FLOW WITH TRAFFIC LIGHTS

A probabilistic cellular automata is used for investigating how a traffic light placed on a street intersection influences vehicle velocities. Numerical simulations reveal that above a critical density of cars, the traffic light improves the flow in both directions.

The traffic flow of two-lane system with vehicle mixing

A cellular automaton model for two-lane traffic with vehicle mixing basing on the Nagel-Schreckenberg (NaSch) model is proposed. With different parameters, we simulated the traffic flow of the two-lane system when the vehicle densities of lanes are equal or different respectively. The fundamental diagrams of the traffic flow are given. According to the analysis, the traffic state could be divided into three regions.The nonsymmetry of car density on two lanes has important influence on the traffic flow.

Why fuel prices differ

Fuel taxes differ largely between countries. This paper reviews a number of considerations from the theory of public finance that may explain these differences. Based on a multiple regression model, we find for tax competition in Europe that small countries tend to be more aggressive than large countries by charging lower fuel taxes to attract customers from neighbouring countries. There is strong evidence that fuel is just considered as one of the many sources for government expenditure: as the share of government expenditure in GDP is higher, the fuel tax tends to be higher. No support is found for the hypothesis that fuel taxes are higher in countries where externality problems are more severe (proxied by car density of the country). In this respect, the normative literature on pricing externalities has found little support in the realities of transport policy.

Phase Transitions in Traffic Models

It is suggested that the question of existence of a jamming phase transition in a broad class of single-lane cellular-automaton traffic models may be studied using a correspondence to the asymmetric chipping model. In models where such correspondence is applicable, jamming phase transition does not take place. Rather, the system exhibits a smooth crossover between free-flow and jammed states, as the car density is increased.