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Register a new userOn some experimental features of car-following behavior and how to model them
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We have carried out car-following experiments with a 25-car-platoon on an open road section to study the relation between a cars speed and its spacing under various traffic conditions, in the hope to resolve a controversy surrounding this fundamental relation of vehicular traffic. In this paper we extend our previous analysis of these experiments, and report new experimental findings. In particular, we reveal that the platoon length (hence the average spacing within a platoon) might be significantly different even if the average velocity of the platoon is essentially the same. The findings further demonstrate that the traffic states span a 2D region in the speed-spacing (or density) plane. The common practice of using a single speed-spacing curve to model vehicular traffic ignores the variability and imprecision of human driving and is therefore inadequate. We have proposed a car-following model based on a mechanism that in certain ranges of speed and spacing, drivers are insensitive to the changes in spacing when the velocity differences between cars are small. It was shown that the model can reproduce the experimental results well.
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As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation pattern of disturbances. However, the traffic theories have been controversial due to a lack of precise traffic data. We have studied traffic flow from a new perspective by carrying out large-scale car-following experiment on an open road section, which overcomes the intrinsic deficiency of empirical observations. The experiment has shown clearly the nature of car-following, which runs against the traditional traffic flow theory. Simulations show that by removing the fundamental notion in the traditional car-following models and allowing the traffic state to span a two-dimensional region in velocity-spacing plane, the growth pattern of disturbances has changed qualitatively and becomes qualitatively or even quantitatively in consistent with that observed in the experiment.
A fair simple car driving simulator was created based on the open source engine TORCS and used in car-following experiments aimed at studying the basic features of human behavior in car driving. Four subjects with different skill in driving real cars participated in these experiments. The subjects were instructed to drive a car without overtaking and losing sight of a lead car driven by computer at a fixed speed. Based on the collected data the distributions of the headway distance, the car velocity, acceleration, and jerk are constructed and compared with the available experimental data for the real traffic flow. A new model for the car-following is proposed to capture the found properties. As the main result, we draw a conclusion that human actions in car driving should be categorized as generalized intermittent control with noise-driven activation. Besides, we hypothesize that the car jerk together with the car acceleration are additional phase variables required for describing the dynamics of car motion governed by human drivers.
This article considers a model for alternative processes for securities prices and compares this model with actual return data of several securities. The distributions of returns that appear in the model can be Gaussian as well as non-Gaussian; in particular they may have two peaks. We consider a discrete Markov chain model. This model in some aspects is similar to well-known Ising model describing ferromagnetics. Namely we consider a set of N investors, each of whom has either bullish or bearish opinion, denoted by plus or minus respectively. At every time step each of N investors can change his/her sign. The probability of a plus becoming a minus and the probability of a minus becoming a plus depends only on the bullish sentiment described as the number of bullish investors among the total of N investors. The number of bullish investors then forms a Markov chain whose transition matrix is calculated explicitly. The transition matrix of that chain is ergodic and any initial distribution of bullish investors converges to stationary. Stationary distributions of bullish investors in this Markov chain model are similar to continuous distributions of the theory of social imitation of Callen and Shapero. Distributions obtained this way can represent 3 types of market behavior: one-peaked distribution that is close to Gaussian, transition market (flattening of the top), and two-peaked distribution.
This paper analyzes the car following behavioral stochasticity based on two sets of field experimental trajectory data by measuring the wave travel time series of vehicle n. The analysis shows that (i) No matter the speed of leading vehicle oscillates significantly or slightly, wave travel time might change significantly; (ii) A followers wave travel time can vary from run to run even the leader travels at the same stable speed; (iii) Sometimes, even if the leader speed fluctuates significantly, the follower can keep a nearly constant value of wave travel time. The Augmented Dickey-Fuller test indicates that the time series the changing rate of wave travel time follows a mean reversion process, no matter the oscillations fully developed or not. Based on the finding, a simple stochastic Newell model is proposed. The concave growth pattern of traffic oscillations has been derived analytically. Furthermore, simulation results demonstrate that the new model well captures both macroscopic characteristic of traffic flow evolution and microscopic characteristic of car following.
Different from previous models based on scatter theory and random matrix theory, a new interpretation of the observed log-normal type time-headway distribution of vehicles is presented in this paper. Inspired by the well known Galton Board, this model views drivers velocity adjusting process similar to the dynamics of a particle falling down a board and being deviated at decision points. A new car-following model based on this idea is proposed to reproduce the observed traffic flow phenomena. The agreement between the empirical observations and the simulation results suggests the soundness of this new approach.
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