Nagel-Schreckenberg Model Research Articles

Effects of Adaptive Random Deceleration on Traffic Flow

Based on the Nagel-Schreckenberg model, an improved cellular automaton traffic flow model is proposed, in which the random deceleration probability of each vehicle is no longer fixed, but is adaptively adjusted according to the local traffic density in its vision and its current velocity. The numerical simulation results show that the maximum traffic capacity of the improved model under the same parameters is greater than that of the Nagel-Schreckenberg model, and is closer to the measured data. In addition, the traffic flow and vehicle velocity under different meteorological conditions are simulated by using the improved model, and the synchronized flow phenomenon consistent with the actual traffic is reproduced. Meanwhile, the results show that under the same parameters, when the traffic density is equal to 0.3, the traffic flow of the improved model increases by about 11% compared with the original model, and when the traffic density increases to 0.6, the traffic flow increases by about 27%.

Effects of Driving Style on Energy Consumption and CO2 Emissions

The tractive force developed by energy consumption (EC) in a car engine produces its acceleration and sustains the motion against velocity dependent resistance forces. In internal combustion engines, fuel burning entails pollutant emissions (PE) released into the atmosphere. In vehicular traffic, EC and PE depend on the driving style. This paper assumed that the transition rules in a traffic cellular automata (TCA) represent a driving style, and its effect on EC and PE in TCA is studied. Extending empirical relationships, we proposed models to estimate EC and PE in TCA from the velocity and acceleration distributions, which we obtained by computer simulations for three well-known TCA. The Nagel-Schreckenberg (NS) and Fukui-Ishibashi (FI) models, and a variant (NS+FI) defined by combining the NS and FI rules, were considered. The FI driving style revealed EC and CO2 emission rates dependent on the stochastic delay (p) only for low vehicular densities. We also detected that the larger EC and CO2 emission rates were 45.4 kW and 26.7 g/s with no dependence on p. With NS and NS+FI driving styles, the larger energy consumption and CO2 emission rates occurred for small stochastic delays, 18.4 kW and 6.6 g/s and 61.1kW and 30.2 g/s for p = 0.2. On average, for NS, FI, and NS+FI models (p = 0.2), we obtained energy consumptions of 1.88, 2.60, and 2.76 MJ/km, fuel consumptions of 0.08, 0.12, and 0.13 L/km, and CO2 emissions of 0.158, 0.460, and 0.562 kgCO2/km. Our results agree with those (3.37 MJ/km and 0.235 kgCO2/km) of petrol combustion car engines at 10 km/L. This work may help in designing flow and driving style scenarios to optimize vehicular traffic EC and reduce PE.

Spatial and temporal memory effects in the Nagel-Schreckenberg model for crowdsourced traffic property determination.

We investigate the spatial and temporal memory effects of traffic density and velocity in the Nagel-Schreckenberg cellular automaton model. We show that the two-point correlation function of vehicle occupancy provides access to spatial memory effects, such as headway, and the velocity autocovariance function to temporal memory effects such as traffic relaxation time and traffic compressibility. We develop stochasticity-density plots that permit determination of traffic density and stochasticity from the isotherms of first- and second-order velocity statistics of a randomly selected vehicle. Specifically, provided ergodicity and stationarity, these stochasticity-density plots permit a direct determination of traffic properties from crowdsourced measurements of velocities of vehicles. We illustrate the predictive prowess of the approach for crowdsourced vehicle speed data collected by anonymous smartphone measurements for the state of Massachusetts, USA, as a powerful alternative to classical traffic property estimates from spatially distributed user counts.

Extreme events in Nagel–Schreckenberg model of traffic flow on complex networks

The Nagel–Schreckenberg vehicular traffic model is extended to analyse a system of vehicles moving on a scale-free network to study extreme events in them. The dependence of the free-flow and congestion states on the density of vehicles is determined. In particular, a free-flow state at low vehicular density is observed and it gradually transitions to a congested state at higher density. Using detrended fluctuation analysis, it is shown that the flux of vehicles are long range correlated in a regime of low density. At higher densities, the flux becomes uncorrelated. We study the recurrence interval distribution for extreme events and the probability for its occurrence at low and high vehicular density regimes. It is shown that the occurrence probability for extreme events is independent of the degree of the node or the threshold used for defining extreme events

Social dilemma in traffic with heterogeneous drivers

There is a “tragedy of the traffic” analogous to the “tragedy of the commons” that can be caused by overtaking. We analyze the effect of overtaking in a minimal model of vehicular traffic, the Nagel–Schreckenberg model, with two types of strategies: vehicles that overtake and vehicles that do not. We show that, under certain circumstances, overtaking is good because it maximize the flux of vehicles and minimizes the vehicle’s mean time spent on the road. However, when these conditions are not met, overtaking is harmful to all. More specifically, we found that a social dilemma emerges in the vicinity of the transition to the congested traffic if the probability of random deceleration is low, which can also happen in more realistic single-lane models. The essential mechanism creating the social dilemma is the abrupt deceleration when the overtaking vehicle returns to its lane. We analyze how the payoffs depend on the frequency of strategies in the population to conclude that the vehicles that overtake are defectors and the ones that do not are cooperators, analogous to the strategies in “tragedy of the commons” class of games.

An innovative three-dimensional approach for visibility assessment of highway signs based on the simulation of traffic flow

ABSTRACT The location of highway signs has a significant impact on timely route-finding and also on avoiding potential driver confusion. This paper proposes an approach based on three-dimensional spatial analysis to determine the best attributes for signs and traffic flow concerning the visibility of signs. The position, height and perceived area of signs; maximum speed limit; and size of cars were utilized as indicators. Traffic flow was simulated using the Nagel-Schreckenberg model, while other vehicles were considered as dynamic obstacles. The performance of the proposed approach was evaluated in a case study by designing different scenarios. The results reveal that the proposed method can be used as an appropriate tool for evaluating the visibility of existing signs along highways and for determining the optimal place and height for new signs in three-dimensional, based on several parameters such as the maximum allowable speed, traffic flow, average density, and type of vehicles.

Impact of intelligent agents on the avoidance of spontaneous traffic jams on two-lane motorways

This paper approaches the evaluation of intelligent agents for the reduction and avoidance of spontaneous traffic jams, which arise without evident reason. Individual vehicles are regarded as intelligent agents that act autonomously. The basis of this work is the Nagel-Schreckenberg (NaSch) model. Its extensions by the velocity-dependent randomization (VDR) model and multiple lanes allow us to simulate realistic traffic and congestion situations on two-lane motorways. Our concept is applied to the model and analyzed by fundamental diagrams and the average velocity, for example. The results of this paper reveal that traffic congestions are avoided when using swarm intelligence in all vehicles since human behavior, especially misbehavior, is eliminated and the velocities determined by the intelligent vehicle are directly realized. Moreover, an amount of 30% of intelligent vehicles has a significantly positive impact on traffic flow.

Generalized Anticipation Effect Models for Traffic Flow

Taking into account the startup behaviour of following vehicles in the waiting area of urban traffic signal, we propose an extended Nagel-Schreckenberg model for single-lane traffic flow, in which the dynamic behavior of each vehicle depends on not only its own headway but also the headway of the immediately preceding one. The numerical simulation of the present model reproduces some complicated nonlinear phenomena observed in real traffic such as free flow, ghostly blockage, synchronized flow and so on. For specific parameter combinations the flow-density relation of this model shows two meta-stable branches near the transition density from free flow to wide moving traffic jam. Finally, the analytical results of the model under some specific parameters are given by using the mean field theory.

Rare-event properties of the Nagel-Schreckenberg model.

We have studied the distribution of traffic flow q for the Nagel-Schreckenberg model by computer simulations. We applied a large-deviation approach, which allowed us to obtain the distribution P(q) over more than one hundred decades in probability, down to probabilities like 10^{-140}. This allowed us to characterize the flow distribution over a large range of the support and identify the characteristics of rare and even very rare traffic situations. We observe a change of the distribution shape when increasing the density of cars from the free flow to the congestion phase. Furthermore, we characterize typical and rare traffic situations by measuring correlations of q to other quantities like density of standing cars or number and size of traffic jams.

Kardar-Parisi-Zhang universality of the Nagel-Schreckenberg model.

Dynamical universality classes are distinguished by their dynamical exponent z and unique scaling functions encoding space-time asymmetry for, e.g., slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known. Only the special case v_{max}=1, where the model corresponds to the totally asymmetric simple exclusion process, is known to belong to the superdiffusive Kardar-Parisi-Zhang (KPZ) class with z=3/2. In this paper, we show that the NaSch model also belongs to the KPZ class for general maximum velocities v_{max}>1. Using nonlinear fluctuating hydrodynamics theory we calculate the nonuniversal coefficients, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents. The results of large-scale Monte Carlo simulations match the exact asymptotic KPZ solutions without any fitting parameter left. Additionally, we find that nonuniversal early-time effects or the choice of initial conditions might have a strong impact on the numerical determination of the dynamical exponent and therefore lead to inconclusive results. We also show that the universality class is not changed by extending the model to a two-lane NaSch model with lane-changing rules.

Origins of Reverse Lane Usage Using Nagel–Schreckenberg Model

On highways with two lanes, cars are requested to run on the slow lane and are allowed to run on the fast lane for overtaking. However, on real two-lane highways, we daily observe a phenomenon called "reverse lane usage", in which the flow on the fast lane exceeds that on the slow lane. The origins of the phenomenon have not been discussed clearly. In this paper, we study a two-lane extension of the Nagel-Schreckenberg model. We employ two types of lane-changing rules: a German and a Japanese type. The German type suppresses overtaking slow cars on the fast lane through the slow lane. The Japanese type, on the contrary, allows overtaking through both lanes. If two lanes allow the same maximum speed, the suppression of overtaking through the slow lane is the key for the reverse lane usage. If the maximum speed on the fast lane is faster than that on the slow lane, the reverse lane usage is observed in the Japanese type. The effects of stochasticity in lane changing, and mixing trucks and passenger cars are also discussed.

Mean-field theory for the Nagel-Schreckenberg model with overtaking strategy

Based on the Nagel-Schreckenberg (NS) model with periodic boundary conditions, a modified model considered overtaking strategy (NSOS) has been proposed [1, 2]. In this paper, we focus on the theoretical analysis of traffic flow for NSOS model by using mean-field method. In the special case of vmax = 1 where vehicles can not overtake preceding ones, the features of stationary state can be obtained exactly. However, in the case of vmax > 1 where overtaking happens, some approximative methods have to be took into account. The main results are that we find the reason why traffic flow is increased in the regime where densities exceed the maximum flow density, and the influence of traffic flow on the transition density is dominated by the braking probability p.

Continuously variable spreading exponents in the absorbing Nagel–Schreckenberg model

I study the critical behavior of a traffic model with an absorbing state. The model is a variant of the Nagel–Schreckenberg (NS) model, in which drivers do not decelerate if their speed is smaller than their headway, the number of empty sites between them and the car ahead. This makes the free-flow state (i.e. all vehicles traveling at the maximum speed, vmax, and with all headways greater than vmax) absorbing; such states are possible for densities ρ smaller than a critical value . Drivers with nonzero velocity, and with headway equal to velocity, decelerate with probability p. This absorbing Nagel–Schreckenberg (ANS) model, introduced in Iannini and Dickman (2017 Phys. Rev. E 95 022106), exhibits a line of continuous absorbing-state phase transitions in the ρ-p plane. Here I study the propagation of activity from a localized seed, and find that the active cluster is compact, as is the active region at long times, starting from uniformly distributed activity. The critical exponents δ (governing the decay of the survival probability) and η (governing the growth of activity) vary continuously along the critical curve. The exponents satisfy a hyperscaling relation associated with compact growth.

Simulation study of traffic circle intersection with traffic lights

Using the Nagel-Schreckenberg model, we investigate the flow characteristics in a traffic circle system, where the entry lanes are controlled by traffic lights operating in a fixed-time ([Formula: see text]. We considered four different strategies to control traffic coming from [Formula: see text] entry lanes. We found that depending on the strategy used, four distinct traffic phases can appear in the circulating lane of the traffic circle, namely free flow, congestion, maximum current, and gridlock. Also, we investigate the origin of the gridlock phase in both cases (i.e. with/without traffic lights). Furthermore, the lengths of queues of stopped vehicles in the entry lanes were studied. We found that the traffic flow behavior on the exit/entry lanes depends strongly on the flow characteristics at the circulating lane as well as traffic lights strategy. To improve the operation of the traffic circle system, we have studied the time delay between the traffic lights to switch where all entry lanes go red, which allowing vehicles to clear the circulating lane.

Traffic Flow Modeling on Road Networks Using Cellular Automata Theory

The paper deals with mathematical modeling of traffic flows on urban road networks. The original model is based on the cellular automata theory and presents a generalization of Nagel-Schreckenberg model to a multilane case.Numerical realization of the model is represented in a form of the program package that consists of two modules: User Interface and Visualization module (for setting initial conditions and modelling parameters and visual representation of calculations) and Computation module (for calculations).Computations are carried out for each element of the road (i.e. T or X type intersection, straight road fragment) separately and in parallel, that allows performing calculations on various complex road networks. Different kinds of average characteristics (e.g. the capacity of the crossroad) can be also obtained using the program package.

Renormalization-group study of the Nagel-Schreckenberg model.

We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) model by using the dynamically driven renormalization group (DDRG). The breaking probability p that governs the driving strategy is investigated. For the deterministic case p=0, the dynamics remain invariant in each renormalization-group (RG) transformation. Two fully attractive fixed points, ρ_{c}^{*}=0 and 1, and one unstable fixed point, ρ_{c}^{*}=1/(v_{max}+1), are obtained. The critical exponent ν which is related to the correlation length is calculated for various v_{max}. The critical exponent appears to decrease weakly with v_{max} from ν=1.62 to the asymptotical value of 1.00. For the random case p>0, the transition rules in the coarse-grained scale are found to be different from the NS specification. To have a qualitative understanding of the effect of stochasticity, the case p→0 is studied with simulation, and the RG flow in the ρ-p plane is obtained. The fixed points p=0 and 1 that govern the driving strategy of the NS model are found. A short discussion on the extension of the DDRG method to the NS model with the open-boundary condition is outlined.

An analysis on the traffic processing efficiency of a combination of serial and parallel bottlenecks

By means of the Nagel–Schreckenberg model, we have investigated into the maximum vehicular flow rate of traffic processing bottlenecks. The evaluated analytical form of this flow rate is found to give quantitative insights into the underlying physics of collective vehicular motions constrained by these bottlenecks. Our analysis shows that for large-scale expansion, a new class of processing bottleneck known as the serial bottleneck is more efficient than the conventional parallel bottleneck in the absence of human driving behavior. When characteristics such as slow-to-start is considered in the model, the consequential delay due to human reaction time not only degrade the overall efficiency, it also diminishes the efficacy of serial processing such that a serial bottleneck is no longer tenable for traffic processing. These results point to the fundamental importance of optimizing traffic efficiency, which we illustrate by elucidating the detailed mechanisms with which vehicles interact collectively in the bottlenecks. In particular, we demonstrate that by constructing combinations of serial and parallel bottlenecks, optimal efficiencies are achieved via configurations with few (many) lanes of a large (small) number of serial units when the processing time is short (long). A direct implication of these results is that autonomous self-driving vehicles could serve to improve the transportation capacity for the densely populated urban cities of the future, due to the intrinsically more efficient collective vehicular motions through these bottlenecks.

Behaviour of traffic on a link with traffic light boundaries

This paper considers a single link with traffic light boundary conditions at both ends, and investigates the traffic evolution over time with various signal and system configurations. A hydrodynamic model and a modified stochastic domain wall theory are proposed to describe the local density variation. The Nagel–Schreckenberg model (NaSch), an agent based stochastic model, is used as a benchmark. The hydrodynamic model provides good approximations over short time scales. The domain wall model is found to reproduce the time evolution of local densities, in good agreement with the NaSch simulations for both short and long time scales. A systematic investigation of the impact of network parameters, including system sizes, cycle lengths, phase splits and signal offsets, on traffic flows suggests that the stationary flow is dominated by the boundary with the smaller split. Nevertheless, the signal offset plays an important role in determining the flow. Analytical expressions of the flow in relation to those parameters are obtained for the deterministic domain wall model and match the deterministic NaSch simulations. The analytic results agree qualitatively with the general stochastic models. When the cycle is sufficiently short, the stationary state is governed by effective inflow and outflow rates, and the density profile is approximately linear and independent of time.

Traffic dynamics of carnival processions

The traffic dynamics of processions are described in this study. GPS data from participating groups in the Cologne Rose Monday processions 2014–2017 are used to analyze the kinematic characteristics. The preparation of the measured data requires an adjustment by a specially adapted algorithm for the map matching method. A higher average velocity is observed for the last participant, the Carnival Prince, than for the leading participant of the parade. Based on the results of the data analysis, for the first time a model can be established for defilading parade groups as a modified Nagel-Schreckenberg model. This model can reproduce the observed characteristics in simulations. They can be explained partly by the constantly moving vehicle driving ahead of the parade leaving the pathway and partly due to a spatial contraction of the parade during the procession.

Multilane Traffic Flow Modeling Using Cellular Automata Theory

The paper deals with the mathematical modeling of traffic flows on urban road networks using microscopic approach. The model is based on the cellular automata theory and presents a generalization of the Nagel-Schreckenberg model to a multilane case. The created program package allows to simulate traffic on various types of road fragments (T or X type intersection, strait road elements, etc.) and on road networks that consist of these elements. Besides that, it allows to predict the consequences of various decisions regarding road infrastructure changes, such as: number of lanes increasing/decreasing, putting new traffic lights into operation, building new roads, entrances/exits, road junctions.