Stochastic Cellular-Automaton Model for Traffic Flow

For traffic flow models, calibration and validation are essential. Cellular automaton (CA) models are a special class of models, describing the movement of vehicles in discretised space and time. However, the previous work on calibration and validation does not discuss CA models systematically. This study calibrates and validates a stochastic CA model. The authors use a simple CA model, which only has two important parameters to be calibrated. The methodology for optimisation is to minimise the relative root mean square error between two properties: the averaged velocity and the variation of velocities in a platoon at a given density. Three different sites are used as cases to show the methodology, for which different types of data (video trajectories or GPS data) are available. The authors find that the best model parameters vary for the different locations. This may result from various driving strategies and potential tendencies. Thus, it is concluded that for CA models, various traffic flow phenomena need to be simulated by various parameters.

Based on Nasch model of single lane traffic flow, a modified Cellular Automaton traffic flow model incorporating s-t-s effect among vehicles given in Lagrange model for traffic flow is proposed to simulate homogeneous and mixed type traffic flow. The model is developed with modified cell size, incorporating different acceleration characteristics depending upon the speed of each individual vehicle. Comparisons are made between Nasch model and modified model. It is observed that slope of congested branch is changed for modified model due to variable acceleration rate. 

Study on traffic flow is an attractive topic from physical viewpoint as well as from engineering viewpoint, and many researchers have studied it. Some of them have proposed a cellular-automata model of traffic flow on a trail, and showed some interesting results. Chowdhury et al. have proposed a cellular automata model motivated by the motion of ants with using pheromone, and reported that there is a critical density of elements where the traffic flow increases drastically under a certain condition. In this paper, we discuss the robustness of this phenomenon using real robot system with light sensors and device to simulate chemical signals by computer graphics.

According to different driving behavioral characteristics of bus drivers, a cellular automata traffic model considering the bus lane changing behavior with scheduling parameters is proposed in this paper. Traffic bottleneck problems caused by bus stops are simulated in multiple lanes roads with no-bay bus stations. With the mixed traffic flow composed of different bus arrival rate, flow-density graph, density distribution graph, and temporal-spatial graph are presented. Furthermore, the mixed traffic flow characteristics are analyzed. Numerical experiment results show that the proposed model can generate a variety of complicated realistic phenomena in the traffic system with bus stops and provide theoretical basis for better using of traffic flow model.

A novel cellular learning automaton traffic flow model is proposed to solve the problem that the probability of randomization in the NaSch model is not consistent with the actual traffic. The learning mechanism is introduced in this model. Cellular can learn traffic information from cellular neighbors in real time. The traffic environment information, such as, relative speed and safety distance will be cellular parallel ruler through the randomization probability form after learning. Finally through numerical simulation, the space-time characteristics were obtained, and comparison with the NaSch model is analyzed. The results show that the improved model can reduce the blocking the road to a certain extent and traffic jam dissolving efficiency is higher. The stability analysis of vehicle running from two aspects of speed fluctuation and headway fluctuation shows that the method in this paper can make traffic flow more stable.

Base on the NaSch model, an improved single-lane cellular automaton traffic flow model for especial road is proposed via considering effects of curvature radii, arc length and friction factor on the vehicle movement. By numerical simulation for the traffic flow with different curvature radii, arc length and friction factor, it is found that our improved model can reflect accurately the influence of special sections of a road on the running vehicles, meanwhile visualize the complex nonlinear phenomenon traffic waves of alternate running and stopping as in actual traffics. The reflecting phenomenon in actual traffics indicates that traffic accidents and congestion can be avoided by increase the curvature radii, friction factor of road turning, the capacity of road can be enhanced also.

In this paper, we propose the ultradiscrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultradiscrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the modified Korteweg-de Vries (mkdV) equation, a soliton equation. Meanwhile, the ultradiscrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.

KEY FEATURES The key features of this chapter are Newton's laws of motion, the definitions of mass and force , the law of gravitation , the principle of equivalence , and gravitation by spheres . This chapter is concerned with the foundations of dynamics and gravitation . Kinematics is concerned purely with geometry of motion, but dynamics seeks to answer the question as to what motion will actually occur when specified forces act on a body. The rules that allow one to make this connection are Newton's laws of motion . These are laws of physics that are founded upon experimental evidence and stand or fall according to the accuracy of their predictions. In fact, Newton's formulation of mechanics has been astonishingly successful in its accuracy and breadth of application, and has survived, essentially intact, for more than three centuries. The same is true for Newton's universal law of gravitation which specifies the forces that all masses exert upon each other. Taken together, these laws represent virtually the entire foundation of classical mechanics and provide an accurate explanation for a vast range of motions from large molecules to entire galaxies. NEWTON'S LAWS OF MOTION Isaac Newton's three famous laws of motion were laid down in Principia , written in Latin and published in 1687. These laws set out the founding principles of mechanics and have survived, essentially unchanged, to the present day. Even when translated into English, Newton's original words are hard to understand, mainly because the terminology of the seventeenth century is now archaic.

Elementary cellular automata (ECA) rule 184 can be used as mathematical models of traffic flows. The slow-to-start model is obtained from the ECA rule 184 model by taking time lag for restart into consideration and is represented by 3-state 3-neighbor cellular automata (CA). In the present paper, we propose a traffic model where vehicles following the slow-to-start rule and those not following the slow-to-start rule are mixed. This model, called the mixed slow-to-start model, is represented by 4-state 3-neighbor CA. Further, we introduce the vector representation of CA with the slow-to-start rule and with the mixed slow-to-start rule, and then get their corresponding fuzzy CA. These fuzzy CA provide continuous-valued traffic models with the slow-to-start effect. Comparing the fundamental diagrams of the the slow-to-start model, the mixed slow-to-start model, and their fuzzy counterparts, we investigate the influence of the density and the mixing ratio of vehicles on traffic jams.

Phase diagram in multi-phase heterogeneous traffic flow model integrating the perceptual range difference under human-driven and connected vehicles environment

Traffic flow in large and complex freeway networks is a highly nonlinear phenomenon, which makes traffic forecast a difficult task. In this article an approach to traffic forecast is presented, which uses a micro-simulator for traffic flow combined with current and historical traffic data. The micro-simulator and locally measured current traffic data are used to reconstruct the current network-wide traffic state. Then, this state is combined with historical traffic data to forecast the traffic development. This framework is applied to the freeway network of the German state North Rhine-Westphalia. The micro-simulator uses an advanced cellular-automaton model for traffic flow, and the data are supplied from more than 4,000 locally installed loop-detectors, which deliver information on the (local) traffic state online minute by minute.

This paper proposes an improved cellular automaton traffic flow model based on the brake light model, taking into account that the desired time gap of vehicles is larger than one second. Although the hypothetical steady state of vehicles in the deterministic limit corresponds to a unique relationship between speeds and gaps in the proposed model, the traffic states of vehicles dynamically span a two-dimensional region in the plane of speed versus gap, due to the various randomizations. We show that our model reproduces (i) the free flow, synchronized flow, wide moving jams, as well as transitions among the three phases; (ii) the evolution features of disturbances and the spatiotemporal patterns in a car-following platoon; (iii) the empirical time series of traffic speed obtained from Next Generation Simulation data. Furthermore, the basic feature of time headway distribution is also qualitatively reproduced. Therefore, we argue that a model has the potential to reproduce the empirical and experimental features of traffic flow, provided that the traffic states can dynamically span a 2D speed-gap region.

Based on the NaSch model, this paper establishes a cellular automaton traffic flow model considering driver characteristics is established in this paper. The vehicle driving characteristics under the disturbance of the driver are simulated. Numerical analysis shows that at low density, the maximum speed can be reached without the driver interference factor. With the increase of density, the critical density of the system is larger and the influence of driver behavior on traffic flow is increased. When the driver's interference factor is below the p=0.8 ratio, the impact of the system's flow is tiny and the purpose of safe driving is achieved by observing the trend of traffic. However, when the driver interference factor ratio is large, in the high density area, the system traffic will be more affected, the traffic than the above situation is smaller.

In this article, a new cellular automaton traffic flow model, in which randomisation effect is enhanced with the decrease of time gap and the long time stopped vehicle has large randomisation probability, is presented. Both periodic and open boundary conditions are considered. Under periodic boundary condition, the fundamental diagram and the properties of synchronised flow are studied in detail. Under open boundary condition, different congested patterns induced by an on-ramp are analysed. The results are consistent with the well-known results of Kerner's three-phase traffic theory published before.

"Marine Traffic Simulation System" has been developed by the first author and others for long years. It has three simulation modes. First mode is normal navigation mode. It reproduces realistic traffic flows according to the predefined planed route. Second mode is collision avoidance mode. It has the feature of automatic collision avoidance for all ships besides the normal navigation mode. Third mode is external data mode. It reproduces traffic flow according to the data given by such as AIS. With collision avoidance mode, more realistic traffic flow can be reproduced. However, the validation of the simulation result is not yet done, because it was difficult to get the real traffic flow data before AIS data acquisition system established. This is one of the main purposes of this paper. The system is applied for southward area from Tokyo Bay. Assuming external mode as a real traffic flow, other two modes are evaluated. Normal navigation mode overestimates the navigational risk, while collision avoidance mode reproduces it fairly well in terms of several indices to represent the risk of the area. Three indices; number of occurrence of CR≧0.9, near-miss, and collision respectively, are proposed to assess the navigational risk and discussed. The normalization of these indices, traffic density and gaming area is also proposed and verified including the simulation results of two other areas.