Research On The Traffic Flow Models

The statistical mechanics of nonequilibrium systems is required for understanding the macroscopic behaviors of processes occurring throughout physics, chemistry, biology and even sociology and economics. Nonequilibrium phenomena are encountered whenever systems are relaxing towards an equilibrium steady state and also whenever systems are driven i. e., maintained away from equilibrium by external or self-driven forces. Systems of the self-driven kind, which are the main focus of this work, cannot be described by equilibrium statistical mechanics in general. These systems evolve to a nonequilibrium steady state. Though the statistical mechanics of equilibrium steady states are well understood, analogous general principles to guide the study of steady states far from equilibrium are just beginning.In self-driven many-particle systems, the driving force is not of exerted from outside, but associated with each single particle and self-produced. The traffic system is a typical self-driven system which is far from equilibrium. The study of traffic theory may help to promote the development and cross of such subjects as statistical physics, nonlinear dynamics, applied mathematics, fluid mechanics, traffic engineering and so on, and to better understand the evolution laws of many-particle systems which are far from equilibrium. Therefore, it is not only important for engineering application but also of scientifically significant to study the traffic flow theory.Vehicular traffic dynamics, usually described by deterministic trajectories, is a representative example of nonlinear complex systems. However, we believe it is necessary how fluctuating phenomena arise and how important they are. The various kinds of traffic flow models can be classified into macroscopic continuum traffic models, gas-kinetic traffic models, microscopic models including car-following models and cellular automata models, and probabilistic description of traffic flow. The contents of the paper are as follows.Cellular automata (CA), by design, ideal for computer simulations. However, one can not deny the importance of exact analytical results in providing a testing ground for the computer codes with the finite-size effects and "numerical noise" produced by computer simulations. Choosing the length of inter-car spacing as the dynamical variables and study the global evolution of these spacings. We study a one-dimensional traffic flow cellular automaton model of high-speed vehicles with the Fukui - Ishibashi-type (FI) acceleration rule for all cars, and the Nagel - Schreckenberg-type (NS) stochastic delay mechanism. We obtain analytically the fundamental diagrams of the average speed and vehicle flux depending on the vehicle density and stochastic delay probability.Intelligent decision-making based on the information feedback in a two route traffic flow model is studied. When compared to the mechanical decision-making which induces an oscillation and low efficiency of system, intelligent decision-making will contribute to an improvement of efficiency. Our results suggest that one should not only devote to obtainment of optimal information feedback, but also make an intelligent decision based on information feedback at hand.Furthermore, we obtain analytical results upon the decision dynamics in a two route traffic flow model by using Mean Field Approximation method. Our results are closely consistent with the simulation ones and clearly characterize the effect of the information feedback on the decision-making process. The result is useful for establishing traffic management strategies.The characteristic of asymmetry between deceleration and acceleration in realistic traffic is one important factor to prevent collisions. Based on the earlier works, we propose an asymmetric full velocity difference traffic model. Delay times and the kinematic wave speed of car motions from our model are well consistent with the empirical data. Furthermore, under initial disturbance, our model can describe the phase transition from stable traffic to an unstable one which corresponds to stop-and-go traffic. Additionally, more complex hysteresis effect occurs in our model.