Nagel Schreckenberg Research Articles

Optimal safe driving dynamics for autonomous interacting vehicles

We consider the car following problem for a set of autonomous vehicles following each other on either an infinite or circular road. The behavior of each car is specified by its "speed regulator", a device that decides to increase or decrease the speed of the car as a function of the head-tail distance to its predecessor and the speed of both cars. A collective behavior emerges that corresponds to previously proposed cellular automata traffic models. We further analyze the traffic patterns of the system in the long term, as governed by the speed regulator and we study under which conditions traffic patterns of maximum flow can or cannot be reach. We show the existence of suboptimal flow conditions that require external coordination mechanisms (that we do not consider in this paper) in order to reach the optimal flow achievable with the given density. In contrast with other approaches, we do not try to reproduce observed or measured traffic patterns. We analyze a deterministic speed regulator in order to decipher the emergent dynamics, and to ponder what maneuvers can be safely performed. Here, we restrict our attention to the car following problem. By comparing our speed regulator with classical models, auch as the Nagel–Schreckenberg and KKW models, we observe that although our regulator is formulated in simple terms, its dynamics share similarities with these models. In particular, the KKW model is designed to reproduce the observed behavior that a trailing car in the synchronization range of the leading car tends to regulate its speed to maintain a constant distance. this same behavior is adopted by our speed regulator, showing that this is a safe way of driving.

Hybrid characteristics of heterogeneous traffic flow mixed with electric vehicles considering the amplitude of acceleration and deceleration

In order to explore the influence of electric vehicles on the traffic flow characteristics of traditional fuel vehicles, this paper proposes an improved cellular automata model considering the physical properties of vehicles, such as, the acceleration and deceleration amplitude, relative speed and safety distance etc. Based on the sensitivity analysis of the randomization probability, combined with the actual data, the model parameters are quantified to simulate the electric-fuel vehicle mixed traffic flow. Through numerical simulation, the results show that compared with NS (Nagel–Schreckenberg) model and VE(Velocity Effect) model, the improved model can reproduce rich traffic phenomena and is closer to the measured data. With the increase of electric vehicle permeability, the flow rate and speed are increased, the congestion near the critical density is reduced and the traffic safety is improved. At high density, the congestion shows a trend of decreasing first, then increasing and then decreasing again, and the safety is lower than that of homogeneous traffic flow. The speed fluctuation of fuel vehicles is enlarged, and the speed of the overall traffic flow shows an upward trend. In addition, it is found that the TIT curve can identify the state change of traffic flow, and electric vehicles in high-density mixed flow cause greater disturbance to the speed of traffic flow and reduces traffic safety. The results of this paper can provide a basis for further research of electric-fuel vehicle hybrid traffic flow.

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.

Effect of pedestrian traffic light on traffic flow accompany with pedestrian crossing

In reality, vehicles and pedestrians are delayed for their interference with each other at the crosswalk, or by the unreasonable allocation of traffic light time. Especially under the popular rule of vehicles yield to pedestrians in front of the crosswalk, traffic flow are seriously affected. In this paper, the effects of pedestrian traffic light and the related parameters on traffic flow are studied. On the road, the Nagel–Schreckenberg (NaSch) model is conducted to simulate the scenario with and without pedestrian traffic light. Results show that, vehicle traffic flow can be effectively improved with pedestrian traffic light. Moreover, the optimization of pedestrian waiting time with different vehicle and pedestrian arrival rates are obtained from comprehensive simulations. Finally, effects of some other parameters are briefly discussed.

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

МОДЕЛИРОВАНИЕ ТРАНСПОРТНЫХ ПОТОКОВ С УЧАСТКАМИ ДОРОГИ, НЕДОСТУПНЫМИ ДЛЯ ПРОЕЗДА

Computerized traffic modeling makes it possible to find out the modification needs to assess the traffic flow on the roads and detect likely problem areas in order to take timely measures to eliminate them. Competent preparation of a road network formation plan based on the acquired information makes it possible to reduce the load on the road transport line, avoid traffic jams, and also reduce the average time spent by drivers on the roads. The macroscopic and microscopic models of the cars flow were analyzed by authors to implement the computer model. The article considered the model of the cellular automata by Nagel–Schreckenberg, with the author’s addition that takes into account the presence of the road sections inaccessible for driving in. The need to modify the lane change algorithm was implemented: the condition of the need to change the lane when car is meeting an inaccessible road section was added. And also the “polite” drivers algorithm for bypassing inaccessible areas with a high density of the traffic flows was proposed. Such a model is realized on Python programming language. An analysis of vehicles behavior with different traffic density and location of inaccessible road sections for two- and three-lane roads was carried out based on that model modification.

Car accident in synchronized traffic flow: A stochastic cellular automaton model

In this paper, we study the probability of car accidents in the modified Nagel–Schreckenberg (mNaSch) under the periodic boundary condition. In order to understand the quality of interaction between vehicles in each phase of the mNaSch, the velocity correlation coefficients were investigated. The effect of the evacuation of damaged vehicles was also studied. The fundamental diagram of the system is constructed in both cases with and without the evacuation. We found that the synchronized phases in the mNaSch are manifested into two aspects. In the first phase, the velocity correlation coefficients are zero where all vehicles move at the same speed. Hence, in the other phase, the speed of vehicles shows a synchronization as the form of clusters of moving vehicles where two speeds predominate simultaneously and the velocity correlation coefficients are higher. In addition, the car accidents in the modified mNaSch depend strongly on the initial configuration especially, if we consider those car accidents really happening in the system. The evacuation of damaged vehicles enhances the traffic situation and qualitatively changes the traffic phases in the mNaSch.

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.

Crossover transitions in a bus–car mixed-traffic cellular automata model

We modify the Nagel–Schreckenberg (NaSch) cellular automata model to study mixed-traffic dynamics. We focus on the interplay between passenger availability and bus-stopping constraints. Buses stop next to occupied cells of a discretized sidewalk model. By parametrizing the spacing distance between designated stops, our simulation covers the range of load-anywhere behavior to that of well-spaced stops. The interplay of passenger arrival rates and bus densities drives crossover transitions from platooning to non-platooned (free-flow and congested) states. We show that platoons can be dissolved by either decreasing the passenger arrival rate or increasing the bus density. The critical passenger arrival rate at which platoons are dissolved is an exponential function of vehicle density. We also find that at low densities, spacing stops close together induces platooned states, which reduces system speeds and increases waiting times of passengers.

The research of traffic flow in LaoTieshan channel based on AIS data

In order to study the ship traffic flow in LaoTieshan channel, this paper rewrites the rules of NS (Nagel-Schreckenberg) model of Cellular Automata (CA) based on AIS（Automatic Identification System） data. By referring to the idea of synchronous flow in three-phase traffic flow theory and introducing the speed adaptation mechanism into the simulation, the new model reproduces the traffic flow of LaoTieshan channel and gets the relevant fundamental diagrams. Compared with the actual flow-density diagram drawn from AIS data, it is found that the simulated flow generated by the improved model is more in line with the actual condition, and also conforms to the phase transition of traffic flow in LaoTieshan channel. The method and idea of the simulation are helpful to explain and investigate some complex situations in LaoTieshan channel.

Spatiotemporal evolution characteristics and phase diagrams of traffic dynamics at a crossroads

This paper studies the spatiotemporal evolution characteristics of traffic dynamics at a crossroads which consists of two perpendicular one-lane roads, employing alternating update rules and periodic boundary conditions. Unlike in previous studies, the deterministic Nagel–Schreckenberg traffic flow model is adopted in this work. Based on a close observation of the evolution near the upstream and downstream traffic flow at the crossing point, we have found typical periodically recurring sequences of vehicle motion configurations, and their specific characteristics depend on the value of the maximum velocity of vehicles and the vehicle densities on both roads. We have presented phase diagrams which consist of five basic regions. The flow formulas in these regions have been analyzed or derived. The results of theoretical analysis are in good agreement with the simulation results.

AN EFFICIENT INTELLIGENT TRAFFIC LIGHT CONTROL AND DEVIATION SYSTEM FOR TRAFFIC CONGESTION AVOIDANCE USING MULTI-AGENT SYSTEM

An efficient and intelligent road traffic management system is the corner stone for every smart cities. Vehicular Ad-hoc NETworks (VANETs) applies the principles of mobile ad hoc networks in a wireless network for Vehicle-to-vehicle data exchange communication. VANETs supports in providing an efficient Intelligent Transportation System (ITS) for smart cities. Road traffic congestion is a most common problem faced by many of the metropolitan cities all over the world. Traffic on the road networks are widely increasing at a larger rate and the current traffic management systems is unable to tackle this impediment. In this paper, we propose an Efficient Intelligent Traffic Light Control and Deviation (EITLCD) system, which is based on multi-agent system. This proposed system overcomes the difficulties of the existing traffic management systems and avoids the traffic congestion problem compare to the prior scenario. The proposed system is composed of two systems: Traffic Light Controller (TLC) system and Traffic Light Deviation (TLD) system. The TLC system uses three agents to supervise and control the traffic parameters. TLD system deviate the vehicles before entering into congested road. Traffic and travel related information from several sensors are collected through a VANET environment to be processed by the proposed technique. The proposed structure comprises of TLC system and makes use of vehicle measurement, which is feed as input to the TLD system in a wireless network. For route pattern identification, any traditional city map can be converted to planar graph using Euler’s path approach. The proposed system is validated using Nagel–Schreckenberg model and the performance of the proposed system is proved to be better than the existing systems in terms of its time, cost, expense, maintenance and performance.

The Impact of Traffic Crashes on Urban Network Traffic Flow

This paper aims to investigate the impact of occasional traffic crashes on the urban traffic network flow. Toward this purpose, an extended model of coupled Nagel–Schreckenberg (NaSch) and Biham–Middleton–Levine (BML) models is presented. This extended model not only improves the initial conditions of the coupled models, but also gives the definition of traffic crashes and their spatial/time distribution. Further, we simulated the impact of the number of traffic crashes, their time distribution, and their spatial distribution on urban network traffic flow. This research contributes to the comprehensive understanding of the operational state of urban network traffic flow after traffic crashes, towards mastering the causes and propagation rules of traffic congestion. This work also a theoretical guidance value for the optimization of urban traffic network flow and the prevention and release of traffic crashes.

Segment travel time route guidance strategy in advanced traveler information systems

In this paper, a segment travel time route guidance strategy was proposed in advanced traveler information systems. The route guidance information provided to the vehicles is the sum of travel time on equally divided segments. To evaluate its performance, the new strategy was compared with three other strategies in three different two-route scenarios based on the Nagel–Schreckenberg cellular automaton model. First, four strategies were applied to a symmetrical two-route scenario. The simulation results show that the smaller the segment length is, the greater the average flow will be. The more vehicles that choose roads based on the new strategy, the shorter the average travel time will be. There exists a optimal segment length for each the ratio of dynamic vehicles Sdyn which makes the travel time shortest. Second, in a symmetrical two-route scenario with a permanent bottleneck, results show that zero state and oscillation state were observed. When the bottleneck length more than 1000 cells, the oscillation state disappears. Finally, in a symmetrical two-route scenario with a temporary bottleneck, results show that when the inflow is high, the traffic network with Sdyn=0.5 is better than the one with Sdyn=0. When inflow is low, the situation is just opposite.

Vehicular traffic modeling with greedy lane-changing and inordinate waiting

Lane changing and vehicular slowdowns are known to impact traffic flow. Using a modified Nagel–Schreckenberg cellular automata model for two vehicle types: blocking (e.g. cars) and non-blocking (e.g. motorcycles), we determined the thresholds at which the interplay of lane changing, random and non-random slowdowns strongly impact vehicle speeds. Lane changing improves speed with diminishing returns as vehicles opt to change lanes. At the same time, lane changing is detrimental to the overall speed when lane straddling occurs. Increasing random slowdowns beyond a critical value (in the case of motorcycles, slowdown values of pslow≈[0.2,0.3,0.4] for densities ρ=[0.20,0.15,0.10] respectively) can force crossover from free flowing traffic into a state where interactions between vehicles reduce the average speed.

Uncertainty Quantification of Load Effects under Stochastic Traffic Flows

Load effect characterization under traffic flow has received tremendous attention in bridge engineering, and uncertainty quantification (UQ) of load effect is critical in the inference process. Bayesian probabilistic approach is developed to overcome the unreliable issue caused by negligence of uncertainty of parametric and modeling aspects. Stochastic traffic load simulation is conducted by embedding the random inflow component into the Nagel–Schreckenberg (NS) model, and load effects are calculated by stochastic traffic load samples and influence lines. Two levels of UQ are performed for traffic load effect characterization: at parametric level of UQ, not only the optimal parameter values but also the associated uncertainties are identified; at model level of UQ, rather than using a single prescribed probability model for load effects, a set of probability distribution model candidates is proposed, and model probability of each candidate is evaluated for selecting the most suitable/plausible probability distribution model. Analytic work was done to give closed-form solutions for the expression involved in both parametric and model UQ. In the simulated examples, the efficiency and robustness of the proposed approach are firstly validated, and UQ are performed to different load effect data achieved by varying the structural span length under the changing total traffic volume. It turns out that the uncertainties of load effects are traffic-specific and response-specific, so it is important to conduct UQ of load effects under different traffic scenarios by using the developed approach.

Impact of traffic lights on car accidents at intersections

Using the cellular automata Nagel–Schreckenberg (NaSch) model, we numerically study the impact of traffic lights on the probability of car accidents ([Formula: see text]) at the intersection of two roads. It is found that, the probability [Formula: see text] is more stable with variation of the green light ([Formula: see text]) when the symmetric lights are adopted. Moreover, simulation results show the existence of a critical time [Formula: see text], below which ([Formula: see text]) [Formula: see text] increases as the injection rate ([Formula: see text]) increases, however, above which ([Formula: see text]) the growing of [Formula: see text] has for effect the decrease of [Formula: see text]. Furthermore, the decrease of [Formula: see text] is almost always accompanied by a loss of the flux, especially with asymmetrical lights. To overcome this problem, we proposed a strategy that can greatly increase the flux and keep the probability [Formula: see text] as small as possible, especially for the low and high injection rates.

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.

Effects of route guidance strategies on traffic emissions in intelligent transportation systems

This paper studied the effects of different route guidance strategies on traffic emissions in intelligent transportation systems. Six route guidance strategies were applied in three different two-route scenarios based on the Nagel–Schreckenberg cellular automaton model. The real data of traffic emissions under different vehicle operational modes were used. The simulations of the traffic emissions, the emissions per vehicle, the emissions per unit flux, average travel time per vehicle and the relationship between the emissions per unit flux and the ratio of dynamic vehicles by using six route guidance strategies were obtained. Results showed that mean velocity route guidance strategy (MVS) and congestion coefficient route guidance strategy (CCS) were the best ones. They can effectively reduce the traffic emissions and improve the efficiency of traffic network. In terms of the total emissions, the value of emissions on the symmetrical two-route scenario with two exits was much lower than that on the one with one exit. Finally, we drew two conclusions based on the simulation results: (i) The route guidance strategy based on traffic data of the whole road is beneficial to reduce traffic emissions. (ii) The simpler and smoother road can lead to more reduction of traffic emissions and higher efficiency of traffic network.