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 Physics , 2007, DOI: 10.1088/1674-1056/17/7/008 Abstract: From the macroscopic viewpoint for describing the acceleration behavior of drivers, this letter presents a weighted probabilistic cellular automaton model (the WP model, for short) by introducing a kind of random acceleration probabilistic distribution function. The fundamental diagrams, the spatio-temporal pattern are analyzed in detail. It is shown that the presented model leads to the results consistent with the empirical data rather well, nonlinear velocity-density relationship exists in lower density region, and a new kind of traffic phenomenon called neo-synchronized flow is resulted. Furthermore, we give the criterion for distinguishing the high-speed and low-speed neo-synchronized flows and clarify the mechanism of this kind of traffic phenomena. In addition, the result that the time evolution of distribution of headways is displayed as a normal distribution further validates the reasonability of the neo-synchronized flow. These findings suggest that the diversity and randomicity of drivers and vehicles has indeed remarkable effect on traffic dynamics.
 中国物理 B , 2009, Abstract: This paper modifies the weighted probabilistic cellular automaton model (Li X L, Kuang H, Song T, et al 2008 Chin. Phys. B 17 2366) which considered a diversity of traffic behaviors under real traffic situations induced by various driving characters and habits. In the new model, the effects of the velocity at the last time step and drivers' desire for acceleration are taken into account. The fundamental diagram, spatial-temporal diagram, and the time series of one-minute data are analyzed. The results show that this model reproduces synchronized flow. Finally, it simulates the on-ramp system with the proposed model. Some characteristics including the phase diagram are studied.
 Physics , 1998, DOI: 10.1023/A:1004521326456 Abstract: We present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions, e.g. cars can enter and leave a part of a highway with certain probabilities. The model studied is the asymmetric exclusion process (ASEP) with {\it simultaneous} updating of all sites. It is equivalent to a special case ($v_{\rm max}=1$) of the Nagel-Schreckenberg model for highway traffic, which has found many applications in real-time traffic simulations. The simultaneous updating induces additional strong short range correlations compared to other updating schemes. The stationary state is written in terms of a matrix product solution. The corresponding algebra, which expresses a system-size recursion relation for the weights of the configurations, is quartic, in contrast to previous cases, in which the algebra is quadratic. We derive the phase diagram and compute various properties such as density profiles, two point functions and the fluctuations in the number of particles (cars) in the system. The current and the density profiles can be mapped onto the ASEP with other time discrete updating procedures. Through use of this mapping, our results also give new results for these models.
 Ryan Gantner ISRN Probability and Statistics , 2013, DOI: 10.1155/2013/246045 Abstract: A cellular automaton model for traffic flow is analyzed. For this model, it is shown that under ergodic initial configurations, the distribution of cars will converge in time to a mixture of free flow and solid blocks. Furthermore, the nature of the free flow and solid block distributions is fully described, thus allowing for a specific computation of throughput in terms of the parameters. The model is also shown to exhibit a hysteresis phenomenon, which is similar to what has been observed on actual highways. 1. Introduction and Description of the Model 1.1. Introduction There have been various cellular automaton models introduced to model traffic flow [1–3]. Many of these models gain computational advantage over older so-called car-following, fluid dynamical, and kinetic (gas-type) models by discretizing both space and time (see [4] for an overview of various models). For these discrete models, simple rules are developed to govern car movement. While, on a small scale, the rules oversimplify traffic behavior, the goal is that large scale traffic phenomena, such as the formation and persistence of traffic jams, present themselves in this simplified approach. The model used in this paper is a discrete time probabilistic cellular automaton model developed by Gray and Griffeath in [2]. We will be concerned with macroscopic limiting phenomena on an infinitely long one-dimensional highway. In this paper, we show the existence of a limiting throughput (flux) of cars and describe these regions explicitly. For traffic densities above a critical value, we are able to show that the traffic organizes itself into regions of free flow and regions of traffic jam, both of which will be given precise mathematical definitions in this context. We also observe the existence of metastable states: conditions which allow certain ergodic traffic distributions to have higher throughput than others with the same density of cars. The existence of metastable states has been sought after [5] due to the fact that such states have been shown to be exhibited in real-world traffic flow [6]. These metastable states exhibit a hysteresis phenomenon in the sense that minor perturbations of the cars in these states may eventually lead to a drastic change in the traffic throughput. As mentioned in [2], a property which may be related to the hysteresis phenomenon encountered with the metastable states is the so-called slow-to-start feature, which may be the key element which gives realistic macroscopic behavior to the cellular automaton model. Other slow-to-start models can be found in [3,
 Physics , 1993, DOI: 10.1088/0305-4470/26/15/011 Abstract: A recently introduced cellular automaton model for the description of traffic flow is investigated. It generalises asymmetric exclusion models which have attracted a lot of interest in the past. We calculate the so-called fundamental diagram (flow vs.\ density) for parallel dynamics using an improved mean-field approximation which takes into account short-range correlations. For maximum velocity 1 we find that the simplest non-trivial of these approximations gives already the exact result. For higher velocities our results are in excellent agreement with numerical data.
 Physics , 1998, DOI: 10.1103/PhysRevE.58.1286 Abstract: We systematically investigate the effect of blockage sites in a cellular automaton model for traffic flow. Different scheduling schemes for the blockage sites are considered. None of them returns a linear relationship between the fraction of green'' time and the throughput. We use this information for a fast implementation of traffic in Dallas.
 Pratip Bhattacharyya Physics , 1998, DOI: 10.1142/S0129183199000115 Abstract: A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton which is known to show a transition from a active phase to a absorbing phase at a critical probability associated with two particular components of the evolution rule. In one of these models, called model $A$ in this paper, the surface growth is defined in terms of the evolving front of the cellular automaton on the space-time plane. In the other model, called model $B$, surface growth takes place by a solid-on-solid deposition process controlled by the cellular automaton configurations that appear in successive time-steps. Both the models show a depinning transition at the critical point of the generating cellular automaton. In addition, model $B$ shows a kinetic roughening transition at this point. The characteristics of the surface width in these models are derived by scaling arguments from the critical properties of the generating cellular automaton and by Monte Carlo simulations.
 Physics , 2009, Abstract: Traffic fluctuation has so far been studied on unweighted networks. However many real traffic systems are better represented as weighted networks, where nodes and links are assigned a weight value representing their physical properties such as capacity and delay. Here we introduce a general random diffusion (GRD) model to investigate the traffic fluctuation in weighted networks, where a random walk's choice of route is affected not only by the number of links a node has, but also by the weight of individual links. We obtain analytical solutions that characterise the relation between the average traffic and the fluctuation through nodes and links. Our analysis is supported by the results of numerical simulations. We observe that the value ranges of the average traffic and the fluctuation, through nodes or links, increase dramatically with the level of heterogeneity in link weight. This highlights the key role that link weight plays in traffic fluctuation and the necessity to study traffic fluctuation on weighted networks.
 Physics , 2005, DOI: 10.1143/JPSJ.75.014801 Abstract: We investigate a simple multisegment cellular automaton model of traffic flow. With the introduction of segment-dependent deceleration probability, metastable congested states in the intermediate density region emerge, and the initial state dependence of the flow is observed. The essential feature of three-phased structure empirically found in real-world traffic flow is reproduced without elaborate assumptions.
 Physics , 2004, DOI: 10.1103/PhysRevE.70.016115 Abstract: Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: 1) models that do not reproduce even qualitatively the most important empirical observations, 2) models that are on a macroscopic level in reasonable agreement with the empirics, and 3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed new light on the relevant interactions in traffic flow.
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