Nagel Schreckenberg Research Articles

Improvement of driving safety in road traffic system

A road traffic system is a complex system in which humans participate directly. In this system, human factors play a very important role. In this paper, a kind of control signal is designated at a given site (i.e., signal point) of the road. Under the effect of the control signal, the drivers will decrease their velocities when their vehicles pass the signal point. Our aim is to transit the traffic flow states from disorder to order and then improve the traffic safety. We have tested this technique for the two-lane traffic model that is based on the deterministic Nagel–Schreckenberg (NaSch) traffic model. The simulation results indicate that the traffic flow states can be transited from disorder to order. Different order states can be observed in the system and these states are safer.

A Modified Sensitive Driving Cellular AutomatonModel

A modified cellular automaton model for traffic flow onhighway is proposed with a novel concept about the variable security gap.The concept is first introduced into the original Nagel–Schreckenberg model,which is called the non-sensitive driving cellular automaton model. And then it is incorporated with a sensitive driving NaSch model, in which therandomization brake is arranged before the deterministic deceleration. Aparameter related to the variable security gap is determined throughsimulation. Comparison of the simulation results indicates that the variablesecurity gap has different influence on the two models. The fundamentaldiagram obtained by simulation with the modified sensitive driving NaSchmodel shows that the maximum flow are in good agreement with the observeddata, indicating that the presented model ismore reasonable and realistic.

Impacts of different types of ramps on the traffic flow

The impact of the on- and off-ramps in a cellular automaton model for the traffic flow is studied. We include to the model the effect of spacing between the on- and the off-ramps on a same periodic road at a intersection (interchange) with another road. First, we use the Nagel–Schreckenberg (NaSch) model (J. Phys. I 2 (1992) 2221) without modifications to extract the basic phenomena of traffic flow, and in the following step we focus our investigation on the NaSch model with velocity-dependent randomization (VDR model) (Eur. Phys. J. B 5 (1998) 793) to examine the other system behaviors. Our results provide evidence that the metastable states and the phase separation can occur in the same way like in the models with local site defects.

Effects of quenched randomness induced by car accidents on traffic flow in a cellular automata model

In this paper we numerically study the impact of quenched disorder induced by car accidents on traffic flow in the Nagel-Schreckenberg (NS) model. Car accidents occur when the necessary conditions proposed by [J. Phys. A 30, 3329 (1997)]] are satisfied. Two realistic situations of cars involved in car accidents have been considered. Model A is presented to consider that the accident cars become temporarily stuck. Our studies exhibit the "inverse- lambda form" or the metastable state for traffic flow in the fundamental diagram and wide-moving waves of jams in the space-time pattern. Model B is proposed to take into account that the "wrecked" cars stay there forever and the cars behind will pass through the sites occupied by the "wrecked" cars with a transmission rate. Four-stage transitions from a maximum flow through a sharp decrease phase and a density-independent phase to a high-density jamming phase for traffic flow have been observed. The density profiles and the effects of transmission rate and probability of the occurrence of car accidents in model B are also discussed.

Dyck paths, Motzkin paths and traffic jams

It has recently been observed that the normalization of a one-dimensional out-of-equilibriummodel, the asymmetric exclusion process (ASEP) with random sequential dynamics, isexactly equivalent to the partition function of a two-dimensional lattice path model ofone-transit walks, or equivalently Dyck paths. This explains the applicabilityof the Lee–Yang theory of partition function zeros to the ASEP normalization.In this paper we consider the exact solution of the parallel-update ASEP, a special case ofthe Nagel–Schreckenberg model for traffic flow, in which the ASEP phase transitions can beinterpreted as jamming transitions, and find that Lee–Yang theory still applies. We showthat the parallel-update ASEP normalization can be expressed as one of severalequivalent two-dimensional lattice path problems involving weighted Dyck or Motzkinpaths. We introduce the notion of thermodynamic equivalence for such paths andshow that the robustness of the general form of the ASEP phase diagram undervarious update dynamics is a consequence of this thermodynamic equivalence.

CAR-ORIENTED MEAN-FIELD THEORY REVISITED

We study the Car-Oriented Mean-Field approximation (COMF) to the Nagel–Schreckenberg model in the case of v max =3. The self-consistent equations are obtained. The solution is reached by the method of iteration. When the stochastic noise is small, the numerical simulations can be well described by the mean-field theory. When the stochastic noise is large, the flux around critical density is overestimated. The overshooting of the free flow can be attributed to the collective effect of the stochastic noise.

Dangerous situations in the velocity effect model

This paper investigates the occurrence of dangerous situations (DS) in the velocity effect (VE) model. The VE model is different from the Nagel-Schreckenberg (NS) model and the Fukui-Ishibashi model in that it is based on a non-exclusion process. Two different types of DS-DS caused by stopped cars and DS caused by non-stopped cars-are studied. The results are compared with those from the NS model. It is shown that in the deterministic case, DS caused by stopped cars in the VE model are as likely as those in the NS model provided that one starts from the same random initial conditions. In the non-deterministic case, DS caused by stopped cars in the VE model are qualitatively similar to those in the NS model but quantitatively different. As regards DS caused by non-stopped cars in the VE model, there are none in the deterministic case and there are none when the density is large and positive for small density in the non-deterministic case.

TWO-LANE TRAFFIC WITH PLACES OF OBSTRUCTION TO TRAFFIC

As the Nagel–Schreckenberg model (NaSch model) became known as a realistic approach to describe traffic flow on single-lane streets, this model was extended to two-lane traffic by several groups. On the base of our two-lane model, we will now investigate the impact of a place of obstruction, e.g., because of road works, on partial fractions, densities and mean velocities.

Boundary effects on car accidents in a cellular automaton model

In this paper we numerically study the probability Pac of occurrence of car accidents in the Nagel–Schreckenberg (NS) model with open boundary condition. In the deterministic NS model, numerical results show that there exists a critical value of extinction rate β above which no car accidents occur, and below which the probability Pac is independent of the speed limit vmax and the injection rate α, but only determined by the extinction rate β. In the non-deterministic NS model, the probability Pac is a non-monotonic function of β in the region of low β value, while it is independent of β in the region of high β value. The stochastic braking not only reduces the occurrence of car accidents, but splits degenerate effects of vmax on the probability Pac. Theoretical analyses give an agreement with numerical results in the deterministic NS model and in the non-deterministic NS model with vmax = 1 in the case of low β value region. Qualitative differences between open and periodic systems in the relations of Pac to the bulk density ρ imply that various correlations may exist between the two systems.

CELLULAR AUTOMATA MODELS FOR TRAFFIC FLOW WITH "SLOW-TO-START" RULE: EFFECT OF RANDOMIZATION

In this paper, we study the effect of randomization probability p on the fundamental diagrams of the Nagel–Schreckenberg model (NS) with "slow-to-start" rule introduced by Benjamin, Johnson and Hui (BJH). It is shown that this model exhibits metastable states (which leads to the occurrence of hysteresis) only for very low values of the randomization probability (p≤0.08). Here we propose a simple generalization of the BJH model by introducing a distance-dependent randomization. With such simple generalization, the hysteresis effect and phase separation exist for all values of randomization probability. The new fundamental diagrams are analyzed within the framework of the distributions of time and distance headways.

Wavelet analysis in a traffic model

Wavelet analysis is applied to the study of vehicular fluctuations in highway traffic. The traffic flow on a single lane highway is simulated by the Nagel–Schreckenberg traffic model. Both the usual correlation functions as well as the wavelet-transformed functions are calculated and compared. Off-diagonal correlations are effectively suppressed by the wavelets, and correlations from different scales are nearly decoupled. The signature of traffic jams is identified in the wavelet-spectrum. Wavelet analysis provides a useful tool to explore the self-similarity in traffic fluctuations.

The "Takeover" of a One-Lane Traffic Model

Within a varied Nagel–Schreckenberg model of traffic flow on one-lane highways, we study the probability of "takeover" and its effect on traffic flow. In the paper, we define the probability of takeover, and compare the results derived partially from the equation estimated accordingly with those completely obtained from the computer simulations. The probability of driver-oriented takeover is also considered.

Dangerous situations within the framework of the Nagel Schreckenberg model

This paper investigates the occurrence of dangerous situations (DS) within the framework of the Nagel–Schreckenberg model. The conditions of the DS are modified. It is shown that when vmax = 1, there will be no DS in both deterministic and non-deterministic cases. The situation is different for vmax > 1. We show that in the deterministic case, the probability of DS covers a two-dimensional region, which depends on both the density and the initial configuration. As for the non-deterministic case, our results are qualitatively the same as previous ones, but are quantitatively different.

The influence of tollbooths on highway traffic

We study the effects of tollbooths on the traffic flow. The highway traffic is simulated by the Nagel–Schreckenberg model. Various types of toll collection are examined, which can be characterized either by a waiting time or a reduced speed. A first-order phase transition is observed. The phase separation results a saturated flow, which is observed as a plateau region in the fundamental diagram. The effects of lane expansion near the tollbooth are examined. The full capacity of a highway can be restored. The emergence of vehicle queuing is studied. Besides the numerical results, we also obtain analytical expressions for various quantities. The numerical simulations can be well described by the analytical formulas. We also discuss the influence on the travel time and its variance. The tollbooth increases the travel time but decreases its variance. The differences between long- and short-distance travelers are also discussed.

CAR ACCIDENTS IN THE DETERMINISTIC AND NONDETERMINISTIC NAGEL–SCHRECKENBERG MODELS

In this paper, we study further the probability for the occurrence of car accidents in the Nagel–Schreckenberg model. By considering the braking probability, the conditions for car accidents to occur are modified to obtain accurate results. A universal phenomenological theory will also be presented to describe the probability for car accidents to occur in the deterministic and nondeterministic models, respectively.

A VARIED FORM OF THE NAGEL–SCHRECKENBERG MODEL

By making slight changes of the Nagel–Schreckenberg model, we propose a varied model for a realistic description of the traffic flow on single-lane highways. While the NaSch model fails to cover the "takeover", this realistic situation gets a good description in our model. Moreover, from the fundamental diagrams achieved in our model, we can divide the forms of traffic flow into five different modes, which are obviously observed in their corresponding time-space diagrams. We also make a comparison of the results of a simple kind of mean-field approximation and the cellular automaton approach.

SIMULATING TRAFFIC ON GERMAN HIGHWAYS BASED ON THE NAGEL–SCHRECKENBERG-MODEL

The Nagel–Schreckenberg model (NaSch model) proved to be a realistic approach to describe traffic flow on single-lane streets. In this paper, we add some lane changing rules for two-lane traffic and discuss the influence of the variation on the mean velocity and the flow.

Random walk theory of jamming in a cellular automaton model for traffic flow

The jamming behavior of a single lane traffic model based on a cellular automaton approach is studied. Our investigations concentrate on the so-called VDR model which is a simple generalization of the well-known Nagel–Schreckenberg model. In the VDR model one finds a separation between a free flow phase and jammed vehicles. This phase separation allows to use random walk like arguments to predict the resolving probabilities and lifetimes of jam clusters or disturbances. These predictions are in good agreement with the results of computer simulations and even become exact for a special case of the model. Our findings allow a deeper insight into the dynamics of wide jams occuring in the model.

EFFECTS OF ON- AND OFF-RAMPS IN CELLULAR AUTOMATA MODELS FOR TRAFFIC FLOW

We present results on the modeling of on- and off-ramps in cellular automata for traffic flow, especially the Nagel–Schreckenberg model. We study two different types of on-ramps that cause qualitatively the same effects. In a certain density regime ρ low < ρ < ρ high one observes plateau formation in the fundamental diagram. The plateau value depends on the input-rate of cars at the on-ramp. The on-ramp acts as a local perturbation that separates the system into two regimes: A regime of free flow and another one where only jammed states exist. This phase separation is the reason for the plateau formation and implies a behavior analogous to that of stationary defects. This analogy allows to perform very fast simulations of complex traffic networks with a large number of on- and off-ramps because one can parametrise on-ramps in an exceedingly easy way.

The asymptotic steady states of deterministic one-dimensional traffic flow models

The asymptotic steady state of deterministic Nagel–Schreckenberg (NS) traffic flow cellular automaton (CA) model for high-velocity cars ( v max =M>1 ) is studied. It is shown that the fundamental diagram, i.e., the relationship between the average car velocity and the car density, of the NS model in which the velocity of a car may increase by at most one unit per time step is exactly the same as that of the Fukui–Ishibashi (FI) traffic flow CA model in which a car may increase its velocity abruptly from zero to M or the maximum velocity allowed by the empty spacings ahead in one time step. This implies that for both gradual and abrupt accelerations, the self-organization of cars gives the same asymptotic behavior in one-dimensional traffic flow models.