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In this paper, we propose a two-lane cellular automata model that explains the relationship between traffic-related parameters and likelihood of accidents Pac at a signalized intersection. It is found that, the risk of collision rises as well as the lane-changing probability Pchg augments, besides, the accidents and inflow α show a nonlinear relationship. Moreover, Pac exhibits three different phases (I, II and III) depending on α. Likewise, the system exhibits a second (first) order transition from phase I to phase II when Pchg>0 (Pchg=0). Nevertheless, the transition from phase II to phase III is of first (second) order when Pchg>0 (Pchg=0). In addition, the result analysis shows that the distribution of accidents according to the intersection sites is not equiprobable. Furthermore, when the traffic arriving strength is not very high, the green light length of one road should be increased to restrain Pac and enhance the road safety. Finally, the model results illustrated that the traffic at the intersection is more dangerous adopting asymmetric lane-changing rules than symmetric ones.

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... Fuzzy automata have been frequently employed since the introduction of fuzzy technology and neural networks [3][4][5][6][7][8][9][10][11][12][13]. Furthermore, there were a variety of problems to be resolved, for example, medical diagnosis, car anti-crash radar, freeway management, urban road traffic control, and obstacle recognition in front of a vehicle, which required flexible, quick, and accurate decisions, and then, fuzzy neural network automata (FNNA) [14][15][16][17] are an excellent choice. FNNA had an increasingly prominent role, particularly in data communications. ...

... Step 1: the intuitionistic fuzzy relation matrix F can be calculated using Premise 1 and the formula (11), as well as the intuitionistic fuzzy degree of membership and nonmembership given by the aforementioned expressions (16) and (17). (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0, 0.9) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) (0.9, 0.1) ...

Regenerative braking is one of the most promising and ecologically friendly solutions for improving energy e ciency and vehicle stability in electric and hybrid electric cars. is research describes a data-driven method for detecting and diagnosing issues in hybrid electric vehicle regenerative braking systems. Early fault identi cation can help enhance system performance and health. is study is centered on the construction of an inference system for fault diagnosis in a generalized fuzzy environment. For such an inference system, nite-state deterministic fully intuitionistic fuzzy automata (FDFIFA) are established. Semigroup of FDFIFA and its algebraic properties including substructures and structure-preserving maps are investigated. e inference system uses FDFIFA semigroups as variables, and FDFIFA semigroup homomorphisms are employed to illustrate the relationship between variables. e newly established model is then applied to diagnose the possible fault and their nature in the regenerative braking systems of hybrid electric vehicles by modeling the performance of superchargers and air coolers. e method may be used to evaluate faults in a wide range of systems, including autos and aerospace systems.

... Hence, they may not be feasible for executing maneuvers at hustling areas such as traffic intersections. This is important since a sizable fraction of vehicle collisions occur at traffic intersections [13] which also tend to be more severe [14]. • Each vehicle has an independent sensor and a separate processing setup. ...

Traditional approaches to prediction of future trajectory of road agents rely on knowing information about their past trajectory. This work rather relies only on having knowledge of the current state and intended direction to make predictions for multiple vehicles at intersections. Furthermore, message passing of this information between the vehicles provides each one of them a more holistic overview of the environment allowing for a more informed prediction. This is done by training a neural network which takes the state and intent of the multiple vehicles to predict their future trajectory. Using the intention as an input allows our approach to be extended to additionally control the multiple vehicles to drive towards desired paths. Experimental results demonstrate the robustness of our approach both in terms of trajectory prediction and vehicle control at intersections. The complete training and evaluation code for this work is available here: \url{https://github.com/Dekai21/Multi_Agent_Intersection}.

... Использование клеточного автомата позволило реализовать как поведение агентов, так и учесть необходимость изменения стратегии их поведения. В статье [22] на основе клеточных автоматов описано моделирование поведения толпы с учетом ментальных особенностей пешеходов. ...

The purpose of this work is to develop a formal model for describing the properties of the environment for the functioning of unmanned aerial vehicles and to increase the speed of calculating the trajectory of their flight when monitoring critical infrastructure objects based on the mathematical apparatus of 3D cellular automata. This goal is achieved by solving the following problems: developing a method for describing the operating environment of unmanned aerial vehicles based on 3D cellular automata, developing a method for calculating the flight path of unmanned aerial vehicles. The construction of formal models is based on the apparatus of 3D cellular automata. The most significant results are a formalized description of the space, properties of zones and objects that restrict movement, as well as the development of a method for modeling the flight of an unmanned aerial vehicle in space when solving the monitoring problem, which will increase the speed of calculating the flight path. The significance of the results obtained lies in solving the complex problem of calculating the trajectory of movement of unmanned aerial vehicles for monitoring critical infrastructure objects using the apparatus of 3D cellular automata. The conducted studies have shown the effectiveness of using 3D - cellular automata to solve the problems of finding flight paths when monitoring critical infrastructure objects in various conditions. The proposed approach to the implementation of cellular automata will allow creating an effective monitoring system.

... An influencing factor of rain was also considered in their study. R. Marzoug et al. [21] studied the relationships between different contributing factors and accidents at intersections, and illustrated them with a two-lane cellular automata model. They found the probability of collision increased as the lane-changing probability increased, and the influence of inflow was more complicated. ...

Crashes involving vulnerable road users (VRUs) are types of traffic accidents which take up a large proportion and cause lots of casualties. With methods of statistics and accident reconstruction, this research investigates 378 actual traffic collisions between vehicles and VRUs in China in 2021 to obtain human, vehicle, and road factors that affect the injury severity. The paper focuses on risky behaviors of VRUs and typical scenarios such as non-use of the crosswalk, violation of traffic lights, stepping into the motorway, and riding against traffic. Then, based on the Bayesian General Ordinal Logit model, influencing factors of injury severity in 168 VRU accidents are analyzed. Results demonstrate that the probability of death in an accident will rise when the motorist is middle-aged and the VRU is an e-bicycle rider; the probability of death in an accident will greatly decrease when the VRU bears minor responsibility. Therefore, middle-aged motorists and e-bicycle riders should
strengthen safety consciousness and compliance with regulations to prevent accident and reduce
injury for VRUs. In addition, helmet-wearing will help to reduce riders’ injuries. This research may
provide ideas for intelligent vehicles to avoid collisions with risky VRUs.

... In recent decades, the investigation of vehicular traffic and their related problems have received the attention of several scholars in the fields of statistical physics and applied mathematics. In this context, various traffic models have been proposed [1][2][3][4][5][6]. ...

Traffic emission is one of the most severe issues in our modern societies. A large part of emissions occurs in cities and especially at intersections due to the high interactions between vehicles. In this paper, we proposed a cellular automata model to investigate the different traffic emissions (CO2, PM, VOC, and NOx) and speeds at a two-lane signalized intersection. The model is designed to analyze the effects of signalization by isolating the parameters involved in vehicle-vehicle interactions (lane changing, speed, density, and traffic heterogeneity). It was found that the traffic emission increases (decreases) with the increasing of green lights duration (Tg) at low (high) values of vehicles injection rate (α). Moreover, by taking CO2 as the order parameter, the phase diagram shows that the system can be in four different phases (I, II, III, and IV) depending on α and Tg. The transition from phase II (I) to phase III (II) is second order, while the transition from phase II to phase IV is first order. To reduce the traffic emission and enhance the speed, two strategies were proposed. Simulation results show a maximum reduction of 13.6% in vehicles’ emissions and an increase of 9.5% in the mean speed when adopting self-organizing intersection (second strategy) at low and intermediate α. However, the first strategy enhances the mean speed up to 28.8% and reduces the traffic emissions by 3.6% at high α. Therefore, the combination of both strategies is recommended to promote the traffic efficiency in all traffic states. Finally, the model results illustrate that the system shows low traffic emission adopting symmetric lane-changing rules than asymmetric rules.

... Особого внимания заслуживают метаэвристические алгоритмы группового поиска [8,23,24] Group search optimizer (GSO), основанный на принципах поведения животных, поиск стратегии достижения цели осуществляется путем определения максимумов/минимумов целевой функции. ...

The purpose of this work is the development of mathematical tools for formalizing decisionmaking problems in open expert real-time control systems. The goal was achieved by defining and formally describing all the elements of a formal system. The most significant result was the proposed approach to formalization. With its help, within the framework of a single formalism, the dynamic properties of the subject area and the logical-analytical activity of the power system dispatcher, presented in different classes of formal logics, were described. The significance of the results obtained lies in the possibility of a rigorous description of various aspects of knowledge within the framework of a single formal apparatus with further pragmatic interpretation in the management process. The proposed approach was distinguished by using the axioms of aletic and deontic logics and the development of axioms that reflect the specifics of the problems being solved. The introduced system of basic concepts and relations makes it possible to classify many decision-making problems for the power systems management. The goals were described within the framework of a single formalism form the basis of the apparatus for formalizing the decision-making problems of the class under consideration. The formalization apparatus provides a description of the dynamic properties of the system within each aspect of knowledge of the content paradigm. The direction of further research is the construction of an appropriate formal theory based on the proposed formal system.

Road traffic deaths continue to rise, reaching 1.35 million in recent years. Road traffic injuries are the eighth leading cause of death for people of all ages. Note that there is a wide difference in the crash rate between developed and developing countries and that developed countries report much lower crash rates than developing and underdeveloped countries. World Health Organization reports that over 80% of fatal road crashes occur in developing countries, while developed countries account for about 7% of the total. The rate of road crashes in developing countries is higher than the global average, despite some measures reducing deaths over the last decade. Numerous studies have been carried out on the safety of urban roads. However, comprehensive research evaluating influential factors associated with rural crashes in developing countries is still neglected. Therefore, it is crucial to understand how factors influence the severi-ty of rural road crashes. In the present study, rural roads in Mazandaran province were considered a case study. The Crash data collected from the Iranian Legal Medicine Organization covers 2018 to 2021, including 2047 rural crash-es. Dependent variables were classified as damage crashes and injury-fatal crashes. Besides, independent variables such as driver specifications, crash specifications, environment specifications, traffic specifications, and geometrical road specifications were considered parameters. The logit model data indicate that factors associated with driver and crash specifications influence rural crashes. The type of crashes is the most critical factor influencing the severity of crashes, on which the fatal rate depends. The findings suggested that implementing solutions that minimize the effect of the factors associated with injury and death on rural roads can reduce the severity of crashes on rural roads that share the same safety issues as the case study. Further studies can also be conducted on the safety and mechanics of the vehicle by focusing the research on the types of vehicles and the sources of the damage.

Road traffic accidents are one of the world’s most serious problems, as they result in numerous fatalities and injuries, as well as economic losses each year. Assessing the factors that contribute to the severity of road traffic injuries has proven to be insightful. The findings may contribute to a better understanding of and potential mitigation of the risk of serious injuries associated with crashes. While ensemble learning approaches are capable of establishing complex and non-linear relationships between input risk variables and outcomes for the purpose of injury severity prediction and classification, most of them share a critical limitation: their “black-box” nature. To develop interpretable predictive models for road traffic injury severity, this paper proposes four boosting-based ensemble learning models, namely a novel Natural Gradient Boosting, Adaptive Gradient Boosting, Categorical Gradient Boosting, and Light Gradient Boosting Machine, and uses a recently developed SHapley Additive exPlanations analysis to rank the risk variables and explain the optimal model. Among four models, LightGBM achieved the highest classification accuracy (73.63%), precision (72.61%), and recall (70.09%), F1-scores (70.81%), and AUC (0.71) when tested on 2015–2019 Pakistan’s National Highway N-5 (Peshawar to Rahim Yar Khan Section) accident data. By incorporating the SHapley Additive exPlanations approach, we were able to interpret the model’s estimation results from both global and local perspectives. Following interpretation, it was determined that the Month_of_Year, Cause_of_Accident, Driver_Age and Collision_Type all played a significant role in the estimation process. According to the analysis, young drivers and pedestrians struck by a trailer have a higher risk of suffering fatal injuries. The combination of trailers and passenger vehicles, as well as driver at-fault, hitting pedestrians and rear-end collisions, significantly increases the risk of fatal injuries. This study suggests that combining LightGBM and SHAP has the potential to develop an interpretable model for predicting road traffic injury severity.

Driven by the high social costs and emotional trauma that result from traffic accidents around the world, research into understanding the factors that influence accident occurrence is critical. There is a lack of consensus about how the management of congestion may affect traffic accidents. This paper aims to improve our understanding of this relationship by analysing accidents at 120 intersections in Adelaide, Australia. Data comprised of 1629 motor vehicle accidents with traffic volumes from a dataset of more than five million hourly measurements. The effect of rainfall was also examined. Results showed an approximately linear relationship between traffic volume and accident frequency at lower traffic volumes. In the highest traffic volumes, poisson and negative binomial models showed a significant quadratic explanatory term as accident frequency increases at a higher rate. This implies that focusing management efforts on avoiding these conditions would be most effective in reducing accident frequency. The relative risk of rainfall on accident frequency decreases with increasing congestion index. Accident risk is five times greater during rain at low congestion levels, successively decreasing to no elevated risk at the highest congestion level. No significant effect of congestion index on accident severity was detected.

U-turn behavior of vehicle is one of the main causes of urban traffic congestion and accidents. A collaborative U-turn merging control algorithm is studied with collision avoidance and delay minimization for vehicles under Cooperative Vehicle Infrastructure System (CVIS) environment. Two control strategies, zip merging and platoon merging control, are proposed. The applicability of these two strategies is compared from the perspective of efficiency and driving comfort. The cellular automaton simulation system composed of a two-way four-lane traffic flow with a U-turn facility in middle of road is established with cooperative control algorithm imbedded. The influence of cooperative U-turn merging behaviors on traffic performance is evaluated by analyzing the arrival rates of main lane and U-turn vehicles and their relationship between one another. The simulation results show that the arrival rate of vehicles on target lane has a great impact on traffic delay. The cooperative control can improve the traffic flow only in the condition that the arrival rate of vehicles on target lane is less than 0.7. It provides some practical references for transportation agencies to meet efficiency requirements of the U-turn section when they apply cooperative control strategy.

In this paper, we proposed a model based on the connected vehicles to control the traffic flow at the intersection. To evaluate this model, we studied its impact on the flux and the probability of accidents at the intersection. On the one hand, simulation results showed that the increase in the number of connected vehicles decreases the congestion coefficient and enhances the traffic situation in the system. On the other hand, connected vehicles reduce the probability of accidents at the intersection. In this way, the vehicle intersection (central controller) communication can decrease the congestion and enhance road safety, especially in the intermediate and high traffic conditions.

The technology of autonomous vehicles is expected to revolutionize the operation of road transport systems. The penetration rate of autonomous vehicles will be low at the early stage of their deployment. It is a challenge to explore the effects of autonomous vehicles and their penetration on heterogeneous traffic flow dynamics. This paper aims to investigate this issue. An improved cellular automaton was employed as the modeling platform for our study. In particular, two sets of rules for lane changing were designed to address mild and aggressive lane changing behavior. With extensive simulation studies, we obtained some promising results. First, the introduction of autonomous vehicles to road traffic could considerably improve traffic flow, particularly the road capacity and free-flow speed. And the level of improvement increases with the penetration rate. Second, the lane-changing frequency between neighboring lanes evolves with traffic density along a fundamental-diagram-like curve. Third, the impacts of autonomous vehicles on the collective traffic flow characteristics are mainly related to their smart maneuvers in lane changing and car following, and it seems that the car-following impact is more pronounced.

Freeway traffic was observed over multiple days and was found to display certain regular features. Oscillations arose only in queues; they had periods of several minutes; and their amplitudes stabilized as they propagated upstream. They propagated at a nearly constant speed of about 22 to 24 kilometers per hour, independent of the location within the queues and the flow measured there; this was observed for a number of locations and for queued flows ranging from about 2,000 to 850 vehicles per hour per lane. The effects of the oscillations were not felt downstream of the bottleneck. Thus, the only effect on upstream traffic was that a queue's tail meandered over time by small amounts. (For the long queues studied here, the tails deviated by no more than about 16 vehicle spacings, as compared with predictions that ignored the oscillations). Notably, the character of queued traffic at fixed locations did not change with time, despite the oscillations; i.e., traffic did not decay. There were changes over space, however. New oscillations formed in moderately dense queues near ramp interchanges and then grew to their full amplitudes while propagating upstream, even though the range of wave speeds was narrow. The formations of these new oscillations are strongly correlated with vehicle lane changing. But this pattern of formation and growth was less evident in a very dense queue (caused by an incident), although frequent lane changing occurred near the interchanges. It thus appears that the oscillations were triggered by random lane changing in moderately dense queues more than by car-following effects. Finally, kinematic wave theory was found to describe the propagation of the oscillations to within small errors. For distances approaching one kilometer, and for 2-hour periods, the theory predicted the locations of vehicles to within about 5 vehicle spacings. Further analysis showed that some of these small discrepancies are explained by differences in car-following behavior across drivers.

Using cellular automata (CA) Nagel-Schreckenberg (NaSch) model, we numerically study the probability Pac of the occurrence of car accidents at nonsignalized intersection when drivers do not respect the priority rules. We also investigated the impact of mixture lengths and velocities of vehicles on this probability. It is found that in the first case, where vehicles distinguished only by their lengths, the car accidents start to occur above a critical density ρc. Furthermore, the increase of the fraction of long vehicles (FL) delays the occurrence of car accidents (increasing ρc) and increases the risk of collisions when ρ 〉 ρc. In other side, the mixture of maximum velocities (with same length for all vehicles) leads to the appearance of accidents at the intersection even in the free flow regime. Moreover, the increase of the fraction of fast vehicles (Ff) reduces the accident probability (Pac). The influence of roads length is also studied. We found that the decrease of the roads length enhance the risk of collision.

We introduce a stochastic discrete automaton model to freeway traffic. Monte-Carlo simulations of the model show a transition from laminar traffic flow to start-stop-waves with increasing vehicle density, as is observed in real freeway traffic. For special cases analytical results can be obtained.

Freeway traffic was observed over multiple days and was found to display certain regular features. Oscillations arose only in queues; they had periods of several minutes; and their amplitudes stabilized as they propagated upstream. They propagated at a nearly constant speed of about 22 to 24 kilometers per hour, independent of the location within the queues and the flow measured there; this was observed for a number of locations and for queued flows ranging from about 2,000 to 850 vehicles per hour per lane. The effects of the oscillations were not felt downstream of the bottleneck. Thus, the only effect on upstream traffic was that a queue's tail meandered over time by small amounts. (For the long queues studied here, the tails deviated by no mo re than about 16 vehicle spacings, as compared with predictions that ignored the oscillations). Notably, the character of queued traffic at fixed locations did not change with time, despite the oscillations; i.e., traffic did not decay. There were changes over space, however. New oscillations formed in moderately dense queues near ramp interchanges and then grew to their full amplitudes while propagating upstream, even though the range of wave speeds was narrow. The formations of these new oscillations are strongly correlated with vehicle lane changing. But this pattern of formation and growth was less evident in a very dense queue (caused by an incident), although frequent lane changing occurred near the interchanges. It thus appears that the oscillations were triggered by random lane changing in moderately dense queues more than by car-following effects. Finally, kinematic wave theory was found to describe the propagation of the oscillations to within small errors. For distances approaching one kilometer, and for 2-hour periods, the theory predicted the locations of vehicles to within about 5 vehicle spacings. Further analysis showed that some of these small discrepancies are explained by differences in car -following behavior across drivers.

Passing rate measurements of backward-moving kinematic waves in congestion are applied to quantify two traffic features; a relaxation phenomenon of vehicle lane-changing and impact of lane-changing in traffic streams after the relaxation process is complete. The relaxation phenomenon occurs when either a lane-changer or its immediate follower accepts a short spacing upon insertion and gradually resumes a larger spacing. A simple existing model describes this process with few observable parameters. In this study the existing model is reformulated to estimate its parameter using passing rate measurements. Calibration results based on vehicle trajectories from two freeway locations indicate that the revised relaxation model matches the observation well. The results also indicate that the relaxation occurs in about 15 seconds and that the shoulder lane exhibits a longer relaxation duration. The passing rate measurements were also employed to quantify the post-relaxation impact of multiple lane changing maneuvers within a platoon of 10 or more vehicles in queued traffic stream. The analysis of the same datasets shows that lane-changing activities do not induce a long-term change in traffic states; traffic streams are perturbed temporarily by lane-changing maneuvers but return to the initial states after relaxations.

Articial intelligence research is ushering in a new era of sophisticated, mass-market transportation technology. While computers can already y a passenger jet better than a trained human pilot, people are still faced with the dangerous yet tedious task of driving au- tomobiles. Intelligent Transportation Systems (ITS) is the eld that focuses on integrating information technology with vehicles and transportation infrastructure to make transporta- tion safer, cheaper, and more ecien t. Recent advances in ITS point to a future in which vehicles themselves handle the vast majority of the driving task. Once autonomous vehicles become popular, autonomous interactions amongst multiple vehicles will be possible. Cur- rent methods of vehicle coordination, which are all designed to work with human drivers, will be outdated. The bottleneck for roadway eciency will no longer be the drivers, but rather the mechanism by which those drivers' actions are coordinated. While open-road driving is a well-studied and more-or-less-solved problem, urban trac scenarios, especially intersections, are much more challenging. We believe current methods for controlling trac, specically at intersections, will not be able to take advantage of the increased sensitivity and precision of autonomous vehicles as compared to human drivers. In this article, we suggest an alternative mechanism for coordinating the movement of autonomous vehicles through intersections. Drivers and intersections in this mechanism are treated as autonomous agents in a multiagent system. In this multiagent system, intersections use a new reservation-based approach built around a detailed communication protocol, which we also present. We demonstrate in simulation that our new mechanism has the potential to signican tly outperform current intersection control technology|trac lights and stop signs. Because our mechanism can emulate a trac light or stop sign, it subsumes the most popular current methods of intersection control. This article also presents two extensions to the mechanism. The rst extension allows the system to control human-driven vehicles in addition to autonomous vehicles. The second gives priority to emergency vehicles without signican t cost to civilian vehicles. The mechanism, including both extensions, is implemented and tested in simulation, and we present experimental results that strongly attest to the ecacy of this approach.

The effects of the damaged car evacuation (P(exit)) and the collision (P(col)) probabilities on the traffic flow behavior of a car accident are investigated in the one-dimensional cellular automaton Nagel-Schreckenberg model, with injecting (alpha) and extracting (beta) rates in parallel dynamics. In this study, we suppose that the car involved in collision is evacuated from the road, with an exit probability P(exit). It is found that the behaviors of density, current, and (alpha,beta) phase diagram topology depend strongly on the values of P(exit) and P(col). Indeed, the high-density region shrinks when increasing P(exit). Moreover, the critical value alpha(c)(beta), at which the low-density-high-density transition occurs, increases when increasing P(col) and/or P(exit). Furthermore, the critical value at which the transition high-density-low-density occurs decreases when increasing beta and increases with alpha.

Using computer simulations we investigate, in a version of the Biham-Middleton-Levine model with random sequential update on a square lattice, the anisotropy effect of the probabilities of the change of the motion directions of cars, from up to right (p(ur)) and from right to up (p(ru)), on the dynamical jamming transition and velocities under periodic boundaries on one hand and the phase diagram under open boundaries on the other hand. However, in the former case, the sharp jamming transition appears only for p(ur)=0=p(ru)=0 (i.e., when the cars alter their motion directions). In the open boundary conditions, it is found that the first-order line transition between jamming and moving phases is curved. Hence, by increasing the anisotropy, the moving phase region expands as well as the contraction of the jamming and maximal current phases takes place. Moreover, in the anisotropic case, the transition between the jamming phase (or moving phase) and the maximal current phase is of second order while in the isotropic case, and when each car changes its direction of motion at every time step (p(ru)=p(ur)=1), the transition is of first order. Furthermore, in the maximal current phase, the density profile decays with an exponent gamma approximately 1/4.

Using the cellular automata Nagel-Schreckenberg (NaSch) model, we numerically study the impact of traffic lights on the probability of car accidents (Pac) at the intersection of two roads. It is found that, the probability Pac is more stable with variation of the green light (T) when the symmetric lights are adopted. Moreover, simulation results show the existence of a critical time Tc, below which (T<Tc) Pac increases as the injection rate (α) increases, however, above which (T>Tc) the growing of α has for effect the decrease of Pac. Furthermore, the decrease of Pac 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 Pac as small as possible, especially for the low and high injection rates.

Various feedback strategies are proposed to improve the traffic flow. However, most of these works did not take road safety into consideration. In this paper, we studied the impact of four feedback strategies on the probability of rear-end collisions (Pac). We proposed a new feedback strategy named Accidents Coefficient Feedback Strategy (ACFS) in which dynamic information can be generated and displayed on a board at the entrance of two-route scenario with intersection to help drivers to choose the appropriate road. This new strategy can greatly improve road safety and make the flow smooth as possible at the same time. Moreover, the impact of the intersection and boundary rates (α and β) on Pac is also studied.

Lane-changing may be a source for many traffic jams. But current microscopic models, especially the rule-based models cannot accurately describe the lane-changes. In this paper we discuss the mechanisms for discretionary lane-changing behavior in traffic flow. NGSIM video data is used to check the validity of different lane-changing rules, and 373 lane changes at 4 locations in US-101 highway are analyzed. We find the classical lane-changing rules of rule-based model, cannot explain many cases in the empirical dataset. Therefore, we propose one new decision rule, comparing the position after a time horizon of several seconds without a lane-change. This rule can be described as “to have a further position within 9 seconds”, which is simple and easy to understand. The tests on NGSIM data show that this rule can explain most (76%) of the lane-changing cases. It can be implemented in microscopic traffic models, leading to more realistic description of discretionary lane changes. Besides, some data when lane changes do not occur is also studied. We find most (81%) of non-lane-changing vehicles do not fulfill the new rule. Thus it can be considered as one sufficient and necessary condition for discretionary lane-changing.

As a new cross-discipline, the complexity science has penetrated into every field of economy and society. With the arrival of big data, the research of the complexity science has reached its summit again. In recent years, it offers a new perspective for traffic control by using complex networks theory. The interaction course of various kinds of information in traffic system forms a huge complex system. A new mesoscopic traffic flow model is improved with variable speed limit (VSL), and the simulation process is designed, which is based on the complex networks theory combined with the proposed model. This paper studies effect of VSL on the dynamic traffic flow, and then analyzes the optimal control strategy of VSL in different network topologies. The conclusion of this research is meaningful to put forward some reasonable transportation plan and develop effective traffic management and control measures to help the department of traffic management.

Based on the Nagel-Schreckenberg model (NS) we study the probability of car accidents to occur (Pac) at the entrance of the merging part of two roads (i.e. junction). The simulation results show that the existence of non-cooperative drivers plays a chief role, where it increases the risk of collisions in the intermediate and high densities. Moreover, the impact of speed limit in the bottleneck (Vb) on the probability Pac is also studied. This impact depends strongly on the density, where, the increasing of Vb enhances Pac in the low densities. Meanwhile, it increases the road safety in the high densities. The phase diagram of the system is also constructed.

The aim of this work is to investigate the influence of rainy weather on traffic accidents of a freeway. The micro-scale driving behaviors in rainy weather and possible vehicle rear-end and sideslip accidents are analyzed. An improved CA model of two lanes one-way freeway is presented, where some vehicle accidents will occur when the necessary conditions are simultaneously satisfied. The characteristics of traffic flow under different rainfall intensities are discussed and the accident probabilities are analyzed via the simulation experiments by using variable speed limit (VSL) and incoming flow control. The results indicate that the measures are effective especially during heavy rainstorms or short-time heavy rainfall. According to different rainfall intensities, an appropriate strategy should be adopted in order to reduce the probability of vehicle accidents and enhance traffic flux as well.

Recently, electric bicycle (EB) has been one important traffic tool due to its own merits. However, EB’s motion behaviors (especially at a signalized/non-signalized intersection) are more complex than those of vehicle since it always has lane-changing and retrograde behaviors. In this paper, we propose a model to explore EB’s lane-changing and retrograde behaviors on a road with a signalized intersection. The numerical results indicate that the proposed model can qualitatively describe each EB’s lane-changing and retrograde behaviors near a signalized intersection, and that lane-changing and retrograde behaviors have prominent impacts on the signalized intersection (i.e., prominent jams and congestions occur). The above results show that EB should be controlled as a vehicle, i.e., lane-changing and retrograde behaviors at a signalized intersection should strictly be prohibited to improve the operational efficiency and traffic safety at the signalized intersection.

Based on the symmetric two-lane Nagel-Schreckenberg (STNS) model, a three-lane cellular automaton model between two intersections containing a bus stop with left-turning buses is established in which model the occurrences of vehicle accidents are taken into account. The characteristics of traffic flows with different ratios of left-turn lines are discussed via the simulation experiments. The results indicate that the left-turn lines have more negative effects on capacity, accident rate as well as delay if the stop is located close to the intersections, where the negative effect in a near-side stop is more severe than that in a far-side one. The range of appropriate position for a bus stop without the bottleneck effect becomes more and more narrow with the increase of the ratio of left-turn bus lines. When the inflow is small, a short signal cycle and a reasonable offset are beneficial. When the inflow reaches or exceeds the capacity, a longer signal cycle is helpful. But if the stop position is inappropriate, the increase of cycle fails in reducing the negative effect of left-turning buses and the effectiveness of offset is weakened.

Using the extended Nagel–Schreckenberg (NS) model, we numerically study the impact of the heterogeneity of traffic with speed limit zone (SLZ) on the probability of occurrence of car accidents (Pac). SLZ in the heterogeneous traffic has an important effect, typically in the mixture velocities case. In the deterministic case, SLZ leads to the appearance of car accidents even in the low densities, in this region Pac increases with increasing of fraction of fast vehicles (Ff). In the nondeterministic case, SLZ decreases the effect of braking probability Pb in the low densities. Furthermore, the impact of multi-SLZ on the probability Pac is also studied. In contrast with the homogeneous case [X. Li, H. Kuang, Y. Fan and G. Zhang, Int. J. Mod. Phys. C 25 (2014) 1450036], it is found that in the low densities the probability Pac without SLZ (n = 0) is low than Pac with multi-SLZ (n > 0). However, the existence of multi-SLZ in the road decreases the risk of collision in the congestion phase.

Based on the cellular automata model, a meticulous two-lane cellular automata model is proposed, in which the driving behavior difference and the difference of vehicles’ accelerations between the moving state and the starting state are taken into account. Furthermore the vehicles’ motion is refined by using the small cell of one meter long. Then accompanied by coming up with a traffic management measure, a two-lane highway traffic model containing a work zone is presented, in which the road is divided into normal area, merging area and work zone. The vehicles in different areas move forward according to different lane changing rules and position updating rules. After simulation it is found that when the density is small the cluster length in front of the work zone increases with the decrease of the merging probability. Then the suitable merging length and the appropriate speed limit value are recommended. The simulation result in the form of the speed-flow diagram is in good agreement with the empirical data. It indicates that the presented model is efficient and can partially reflect the real traffic. The results may be meaningful for traffic optimization and road construction management.

At signalized intersections, the decision-making process of each individual driver is a very complex process that involves many factors. In this article, a fuzzy cellular automata (FCA) model, which incorporates traditional cellular automata (CA) and fuzzy logic (FL), is developed to simulate the decision-making process and estimate the effect of driving behavior on traffic performance. Different from existing models and applications, the proposed FCA model utilizes fuzzy interface systems (FISs) and membership functions to simulate the cognition system of individual drivers. Four FISs are defined for each decision-making process: car-following, lane-changing, amber-running, and right-turn filtering. A field observation study is conducted to calibrate membership functions of input factors, model parameters, and to validate the proposed FCA model. Simulation experiments of a two-lane system show that the proposed FCA model is able to replicate decision-making processes and estimate the effect on overall traffic performance.

The aim of this work is to investigate the traffic impact of low visibility weather on a freeway including the fraction of real vehicle rear-end accidents and road traffic capacity. Based on symmetric two-lane Nagel–Schreckenberg (STNS) model, a cellular automaton model of three-lane freeway mainline with the real occurrence of rear-end accidents in low visibility weather, which considers delayed reaction time and deceleration restriction, was established with access to real-time traffic information of intelligent transportation system (ITS). The characteristics of traffic flow in different visibility weather were discussed via the simulation experiments. The results indicate that incoming flow control (decreasing upstream traffic volume) and inputting variable speed limits (VSL) signal are effective in accident reducing and road actual traffic volume’s enhancing. According to different visibility and traffic demand the appropriate control strategies should be adopted in order to not only decrease the probability of vehicle accidents but also avoid congestion.

A study is conducted to compare two simulation methods for estimating conflicts between road users. An improved cellular automata (CA) model is proposed to estimate the occurrences and severity of traffic conflicts (both vehicle-vehicle and vehicle-pedestrian) at signalized intersections. The proposed CA model is compared with a calibrated method of a surrogate safety assessment model (SSAM) based on Vissim. Simulated conflicts from both methods are compared with observed vehicle conflicts from automated vehicle tracking for both occurrences and severity. Simulation results show that the CA approach is able to replicate realistic conflicts. However, SSAM tends to overestimate occurrences and underestimate the severity of rear-end and lane-change conflicts. SSAM has also been found to overestimate the severity of crossing conflicts. Furthermore, the proposed CA model is able to estimate conflicts between vehicles and pedestrians.

The analysis of highway-crash data has long been used as a basis for influencing highway and vehicle designs, as well as directing and implementing a wide variety of regulatory policies aimed at improving safety. And, over time there has been a steady improvement in statistical methodologies that have enabled safety researchers to extract more information from crash databases to guide a wide array of safety design and policy improvements. In spite of the progress made over the years, important methodological barriers remain in the statistical analysis of crash data and this, along with the availability of many new data sources, present safety researchers with formidable future challenges, but also exciting future opportunities. This paper provides guidance in defining these challenges and opportunities by first reviewing the evolution of methodological applications and available data in highway-accident research. Based on this review, fruitful directions for future methodological developments are identified and the role that new data sources will play in defining these directions is discussed. It is shown that new methodologies that address complex issues relating to unobserved heterogeneity, endogeneity, risk compensation, spatial and temporal correlations, and more, have the potential to significantly expand our understanding of the many factors that affect the likelihood and severity (in terms of personal injury) of highway crashes. This in turn can lead to more effective safety countermeasures that can substantially reduce highway-related injuries and fatalities.

At intersection, vehicles coming from different directions conflict with each other. Improper geometric design and signal settings at signalized intersection will increase occurrence of conflicts between road users and results in a reduction of the safety level. This study established a cellular automata (CA) model to simulate vehicular interactions involving right-turn vehicles (as similar to left-turn vehicles in US). Through various simulation scenarios for four case cross-intersections, the relationships between conflict occurrences involving right-turn vehicles with traffic volume and right-turn movement control strategies are analyzed. Impacts of traffic volume, permissive right-turn compared to red-amber-green (RAG) arrow, shared straight-through and right-turn lane as well as signal setting are estimated from simulation results. The simulation model is found to be able to provide reasonable assessment of conflicts through comparison of existed simulation approach and observed accidents. Through the proposed approach, prediction models for occurrences and severity of vehicle conflicts can be developed for various geometric layouts and traffic control strategies.

Right-angle crashes are prone to be severe at signalized intersections. To understand right-angle crash occurrence better and eventually to develop efficient countermeasures, this study investigated the effect of intersection traffic volume, geometric design features, and traffic control and operational features on right-angle crash occurrence at four-leg signalized intersections. Data from a total of 197 such intersections were collected from the Central Florida area. Right-angle crashes were modeled at the intersection, roadway, and approach levels. For the models at roadway and approach levels, crashes were assigned to a certain level, and then the disaggregated crashes were related to the specific roadway or approach features. The generalized estimating equations, which can account for site correlation among repeated observations from the same intersections, were used for the disaggregated models. The cumulative residuals method was used to evaluate the functional forms of the traffic volume and the models' overall performance. For the significant factors identified, the logarithm of the product of the conflicting through volumes, the number of through lanes, and the late-night and early-morning flashing operations is found to affect right-angle crash occurrence consistently. Left-turn offset, angle of the intersection, speed limit on the intersecting roadways, and yellow and all-red intervals also are significant in some models. The variables' relative significance was identified.

In this paper, the unsignalized T-shaped intersection is modeled by a cellular automata model. The main street and the minor street join at the intersection. As to the traffic flow is not controlled by traffic lights, conflict happens between the vehicles from minor street and that from main street. Two different crash avoiding rules are used to dispose the conflicts. In the first rule, the priorities are given to the driving-ahead vehicle and the vehicle on the main street. In the second rule, the vehicle that reaches the conflicting point earlier enters into the intersection. The flux on each lane depending on the inflow rates is studied in detail. The capacity of the system is also investigated. Our simulation results suggest that the two rules do not take the same effect on the capacity under different traffic conditions.

The aim of this work is to investigate the combined effect of the signalized intersection and its near-by bus stop, by using a two-lane CA model. Four cases that the stop locates upstream or downstream the intersection, and ones with the special stop lane or not are considered. The effect of the distance LD between the stop and the intersection on the capacity is studied, with respect to the traffic light cycle T and the bus dwell time Ts. It is found that acting as a bottleneck, the bus stop near the intersection causes the drop of the capacity. The negative effect only appears below a critical point LDc, which is related to the T and the Ts in no stop lane cases. The larger T and Ts have the tendency to create the higher loss of the capacity. While for stop lane cases, the critical value LDc changes little. Comparisons among four cases suggest that the special stop lane can effectively enhance the capacity, and the downstream stops perform better than the upstream ones at small LD or small T or large Ts. The results imply that the capacity can be maximized by adjusting both the position of the bus stop and the cycle time, or adding a special stop lane. These findings may be useful to offer scientific guidance for the management and the design of traffic networks.

In this paper, a new two-dimensional car-following model is proposed to depict the features of mixed traffic flow consisting of motorized vehicles (m-vehicle) and non-motorized vehicles (nm-vehicle), based on the two-dimensional optimal velocity (OV) model by Nakayama et al. [A. Nakayama, K. Hasebe, Y. Sugiyama, Phys. Rev. E 71 (2005) 036121]. In the proposed model, velocity difference terms are introduced, which are regarded as important factors for traffic behavior. Numerical simulations are carried out to investigate the interaction between left-turning nm-vehicle flow and straight-going m-vehicle flow at a typical unsignalized interaction. The results show that the straight-going m-vehicle flow just next to nm-lane is disturbed more seriously than others. In addition, a well-known phenomenon in reality is observed that groups of m-vehicles and nm-vehicles pass through the intersection alternately.

We have developed a modified Nagel–Schreckenberg cellular automata model for describing a conflicting vehicular traffic flow at the intersection of two streets. No traffic lights control the traffic flow. The approaching cars to the intersection yield to each other to avoid collision. Closed boundary condition is applied to the streets. Extensive Monte Carlo simulation is taken into account to find the model characteristics. In particular, we obtain the fundamental diagrams and show that the effect of the interaction of two streets can be regarded as a dynamic impurity located at the intersection point. Our results suggest that yielding mechanism gives rise to a high total flow throughout the intersection especially in the low density regime.

We have developed a Nagel–Schreckenberg cellular automata model for describing vehicular traffic flow at a single intersection. A set of traffic lights operating either in fixed time or in a traffic adaptive scheme controls the traffic flow. A closed boundary condition is applied to the streets, each of which conducts a unidirectional flow. Extensive Monte Carlo simulations are carried out to establish the model characteristics. In particular, we investigate the dependence of the flows on the signalization parameters.

We study the phase structure of a cellular automata model proposed by Belbasi and Foulaadvand to describe the vehicular traffic flow at the intersection of two perpendicular streets. A set of traffic lights operating in a fixed-time scheme controls the traffic flow. A closed boundary condition is applied to the streets, each of which conducts a unidirectional flow. Streets are single-lane and cars cannot turn upon reaching the intersection. Via extensive Monte Carlo simulations it is shown that the model phase diagram consists of ten phases. The flow characteristics in each phase are investigated and the types of phase transitions between phases are specified.

Accurate and timely forecasting of traffic flow is of paramount importance for effective management of traffic congestion in intelligent transportation systems. A detailed understanding of the properties of traffic flow is essential for building a reliable forecasting model. The discrete wavelet packet transform (DWPT) provides more coefficients than the conventional discrete wavelet transform (DWT), representing additional subtle details of a signal. In wavelet multiresolution analysis, an important decision is the selection of the decomposition level. In this research, the statistical autocorrelation function (ACF) is proposed for the selection of the decomposition level in wavelet multiresolution analysis of traffic flow time series. A hybrid wavelet packet-ACF method is proposed for analysis of traffic flow time series and determining its self-similar, singular, and fractal properties. A DWPT-based approach combined with a wavelet coefficients penalization scheme and soft thresholding is presented for denoising the traffic flow. The proposed methodology provides a powerful tool in removing the noise and identifying singularities in the traffic flow. The methods created in this research are of value in developing accurate traffic-forecasting models.

This paper introduces a novel methodology based on disaggregate analysis of two-car crash data to estimate the partial effects of mass, through the velocity change, on absolute driver injury risk in each of the vehicles involved in the crash when absolute injury risk is defined as the probability of injury when the vehicle is involved in a two-car crash. The novel aspect of the introduced methodology is in providing a solution to the issue of lack of data on the speed of vehicles prior to the crash, which is required to calculate the velocity change, as well as a solution to the issue of lack of information on non-injury two-car crashes in national accident data. These issues have often led to focussing on relative measures of injury risk that are not independent of risk in the colliding cars. Furthermore, the introduced methodology is used to investigate whether there is any effect of vehicle size above and beyond that of mass ratio, and whether there are any effects associated with the gender and age of the drivers. The methodology was used to analyse two-car crashes to investigate the partial effects of vehicle mass and size on absolute driver injury risk. The results confirmed that in a two-car collision, vehicle mass has a protective effect on its own driver injury risk and an aggressive effect on the driver injury risk of the colliding vehicle. The results also confirmed that there is a protective effect of vehicle size above and beyond that of vehicle mass for frontal and front to side collisions.

In this article we introduce a new cellular automata approach to construct an urban traffic mobility model. Based on the developed model, characteristics of global traffic patterns in urban areas are studied. Our results show that different control mechanisms used at intersections such as cycle duration, green split, and coordination of traffic lights have a significant effect on intervehicle spacing distribution and traffic dynamics. These findings provide important insights into the network connectivity behavior of urban traffic, which are essential for designing appropriate routing protocols for vehicular ad hoc networks in urban scenarios.

This paper uses the method of kinematic waves, developed in part I, but may be read independently. A functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing (§2). From this a theory of the propagation of changes in traffic distribution along these roads may be deduced (§§2, 3). The theory is applied (§4) to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road. It is suggested that it will move slightly slower than the mean vehicle speed, and that vehicles passing through it will have to reduce speed rather suddenly (at a ‘shock wave’) on entering it, but can increase speed again only very gradually as they leave it. The hump gradually spreads out along the road, and the time scale of this process is estimated. The behaviour of such a hump on entering a bottleneck, which is too narrow to admit the increased flow, is studied (§5), and methods are obtained for estimating the extent and duration of the resulting hold-up. The theory is applicable principally to traffic behaviour over a long stretch of road, but the paper concludes (§6) with a discussion of its relevance to problems of flow near junctions, including a discussion of the starting flow at a controlled junction. In the introductory sections 1 and 2, we have included some elementary material on the quantitative study of traffic flow for the benefit of scientific readers unfamiliar with the subject.

Frequent lane-changes in highway merging, diverging, and weaving areas could disrupt traffic flow and, even worse, lead to accidents. In this paper, we propose a simple model for studying bottleneck effects of lane-changing traffic and aggregate traffic dynamics of a roadway with lane-changing areas. Based on the observation that, when changing its lane, a vehicle affects traffic on both its current and target lanes, we propose to capture such lateral interactions by introducing a new lane-changing intensity variable. With a modified fundamental diagram, we are able to study the impacts of lane-changing traffic on overall traffic flow. In addition, the corresponding traffic dynamics can be described with a simple kinematic wave model. For a location-dependent lane-changing intensity variable, we discuss kinematic wave solutions of the Riemann problem of the new model and introduce a supply–demand method for its numerical solutions. With both theoretical and empirical analysis, we demonstrate that lane-changes could have significant bottleneck effects on overall traffic flow. In the future, we will be interested in studying lane-changing intensities for different road geometries, locations, on-ramp/off-ramp flows, as well as traffic conditions. The new modeling framework could be helpful for developing ramp-metering and other lane management strategies to mitigate the bottleneck effects of lane-changes.

We develop particle-hopping models of two-lane traffic with two different types of vehicles (characterized by two different values of the maximum allowed speed Vmax) generalizing the Nagel-Schrecknnberg stochastic cellular-automata model for single-lane traffic with a single Vmax. The simplest of the two models is symmetric with respect to the two lanes as well as with respect to the two types of vehicles. In the asymmetric model, different rules govern the changing from the the “fast” lanes to the “slow” one and the reverse process. Moreover, in the asymmetric model, the drivers of fast vehicles can anticipate, often well in advance, the possibility of getting trapped behind a slow vehicle and tend to avoid such possibilities.

We examine a simple two lane cellular automaton based upon the single lane CA
introduced by Nagel and Schreckenberg. We point out important parameters
defining the shape of the fundamental diagram. Moreover we investigate the
importance of stochastic elements with respect to real life traffic.

It is shown that all the phase transitions in and out of freely flowing traffic reported earlier for a German site could be caused by bottlenecks, as are all the transitions observed at two other sites examined here. The evidence suggests that bottlenecks cause these transitions in a predictable way, and does not suggest that stoppages (jams) appear spontaneously in free flow traffic for no apparent reason. It is also shown that many of the complicated instability phenomena observed at all locations can be explained qualitatively in terms of a simple Markovian theory specific to traffic that does not necssarily include spontaneous transitions into the queued state as a feature.

The objective of this study was to examine age-related differences in visual scanning as drivers performed three separate maneuvers (going straight across, making a left and right turn) at two median-divided highway intersections with different crash frequencies. An on-road study was conducted with 60 drivers in three age groups: younger (18-25), middle-aged (35-55), and older (65-80). The study consisted of two between-subject (age and gender) and two within-subject variables (drive maneuver and intersection type). Drivers' behavior was measured by the proportion of time they visually sampled towards the left, right and rearview mirror, and by an entropy rate representative of randomness in visual scanning. The results showed that older and younger drivers do not utilize their full scanning range when compared to middle-aged drivers, as indicated by lower entropy rate and the tendency to check fewer areas before executing a maneuver through the intersections. This trend was more obvious during left and right turn maneuvers indicating a greater likelihood to miss an unexpected event. Older drivers had a significantly smaller proportion of visual sampling to the left and right during intersection negotiations when compared to younger and middle-aged drivers. Older and younger drivers checked the rearview mirror significantly less when compared to middle-aged drivers.

This paper presents a simple representation of traffic on a highway with a single entrance and exit. The representation can be used to predict traffic's evolution over time and space, including transient phenomena such as the building, propagation, and dissipation of queues. The easy-to-solve difference equations used to predict traffic's evolution are shown to be the discrete analog of the differential equations arising from a special case of the hydrodynamic model of traffic flow. The proposed method automatically generates appropriate changes in density at locations where the hydrodynamic theory would call for a shockwave; i.e., a jump in density such as those typically seen at the end of every queue. The complex side calculations required by classical methods to keep track of shockwaves are thus eliminated. The paper also shows how the equations can mimic the real-life development of stop-and-go traffic within moving queues.

The author examines the relationship between risk of vehicle occupant death and injury and crash severity, measured by velocity change (delta v), in car-car collisions. He uses nationally representative data from the National Accident Sampling System (NASS) for passenger cars of model years 1980 and later involved in accidents from 1980 through 1986. He concludes that, as a rule of thumb, the exponent 4 may reasonably reflect the relation between the fatality risk and delta v.

A simple model that describes traffic flow in two dimensions is studied. A sharp {\it jamming transition } is found that separates between the low density dynamical phase in which all cars move at maximal speed and the high density jammed phase in which they are all stuck. Self organization effects in both phases are studied and discussed. Comment: 6 pages, 4 figures

We study analytically the occurrence of car accidents in the Nagel-Schreckenberg traffic model. We obtain exact results for the occurrence of car accidents P(ac) as a function of the car density rho and the degree of stochastic braking p(1) in the case of speed limit v(max)=1. Various quantities are calculated analytically. The nontrivial limit p(1)-->0 is discussed.

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.