Analyses Of Stochastic Factors And Phase Transition In Traffic Flows

Recently, traffic has become a global exasperating problem, and the increasing traffic jams and traffic pollution are exerting great pressure on society and causing enormous economic losses. How to make effective use of existing transportation resources so as to improve the relationship between traffic demand and supply, and how to guide transport development and operation with the aid of scientific theories are of great importance, drawing general concern of the international community. Over the past decades, a lot of scholars in different fields have been conducting extensive research on this subject and proposing a variety of traffic flow theories, yielding an enormous amount of results. In this dissertation, based on the previous work, several improved mathematical models are presented through analyzing emphatically the stochastic factors and spatial inhomogeneity in real transportation systems, and the corresponding theoretical analysis and numerical simulation are performed. Moreover, the phase transtion in lattice hydrodynamic model with some real traffic effects considered is investigated. The main contents are as follows.â… . From a global viewpoint of the stochastic acceleration behavior of drivers, a weighted probabilistic cellular automaton model (the WP model, for short) is established by introducing a random acceleration probabilistic distribution function.Owing to the variety of vehicle acceleration behavior from a synthetic viewpoint, a weighted probabilistic cellular automaton model (the WP model, for short) for traffic flow is constructed on the basis of the classical NaSch model and FI model. A probabilistic distribution function for random acceleration, which can be widely used in treating general traffic situations, e.g., those with or without speed limit, is introduced. The numerical simulations show that the speed limit WP model leads to the results consistent with the empirical data rather well, and a new kind of traffic phenomenon called neo-uniform flow, consisting of the high-speed and low-speed ones, is resulted. Furthermore, we give the criterion for distinguishing the high-speed and low-speed neo-uniform flows and elucidate the mechanism of this kind of transportation characteristics. As for the non-speed-limit WP model, we compare the numerical results with those obtained with the NaSch model and FI model from four different aspects, and show that the maximum traffic flux is closer to the observed data. All these are helpful in understanding and depicting the realistic traffic behavior.â…¡. The traffic breakdown caused by the reduction of lanes at a highway bottleneck in the spatially inhomogeneous open road system is examined via a proposed stochastic master-equation model with the three-phase theory.Based on the Markov processes, a new stochastic approach to the spatially inhomogeneous open traffic system at a highway bottleneck caused by the reduction of lanes is developed. The model is in the context of three-phase traffic theory, where the breakdown phenomenon is associated with a first-order phase transition from the free flow phase to the synchronized flow phase. In addition, a permanent and motionless non-homogeneity that can be considered a deterministic vehicle cluster localized in a neighborhood of the bottleneck is assumed. An appropriate master equation for the car cluster evolution is derived. The mean time delay and the associated nucleation rate of traffic breakdown are found and the nucleation rate of traffic breakdown as a function of the reduction of lane numbers and the coming flow rate per lane is studied. The studied example further verifies the analytical results.â…¢. A generalized optimal velocity model is presented and applied to investigate the traffic charactersitics under the changed road conditions, i.e., the speed limit traffic for the roads with upgrade (or downgrade).Through introducing a generalized optimal velocity function to consider the spatial position, slope grade and variable safety headway, the effect of slope on a single-lane highway is investigated with a generalized optimal velocity model. The theoretical analysis and simulation results show that the flux of the whole road with the upgrade (or downgrade) increases monotonously with density, saturates at a critical density, then maintains this saturated value in a certain density range and finally decreases with density. The value of saturated flux is equal to the maximum flux of the upgrade (or downgrade) without considering the slight influence of the driver's sensitivity. And the fundamental diagrams also depend on the sensitivity, slope grade and slope length. The spatio-temporal pattern gives the segregation of different traffic phases caused by the rarefaction wave and shock wave for a certain initial vehicle number. The comparison between the upgrade and the downgrade indicates that the value of saturated flux of the downgrade is larger than that of the upgrade under the same condition. This result is in accordance with the real traffic.â…£. Two extended cooperative driving lattice hydrodynamic models are proposed by considering the backward looking effect. The influnce of more preceding vehicles and one following vehicle on the studied vehicle is investigated. And the anisotropy of traffic flow is further discussed through examining the negative propagation velocity as the effect of following vehicle is involved.In light of the different influences of the preceding and following vehicles on the considered vehicle in real traffic, the proper forward and backward optimal velocities are defined, respectively. The neutral stability line is obtained by using the linear stability theory and it is found that considering the following vehicle effect and adopting the appropriate backward optimal velocity funciton could lead to the improvement of the traffic flow stability. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations. It is shown that in the unstable region, to a certain extent, the negative propagation velocity appears as the effect of following vehicle is involved. Moreover, the related anisotropy of traffic flow with the negative propagation velocity is discussed in detail and corresponding physical nature is explored.â…¤. Based on two extended lattice hydrodynamic models, the traffic characteristics are anaylzed with considering the effect of stepwise acceleration of a vehicle, in which emphasis is particularly laid on the investigation of the influence of optimal velocity function on the system stability.With the consideration of the behavior of stepwise vehicle acceleration, two extended lattice hydrodynamic models are proposed. A new optimal velocity function is introduced to take the stepwise acceleration into account and to fit the obtained results to observed data better than those with the original lattice hydrodynamic models, which leads to a better description of the dynamical phase transition for single-lane traffic flow. Linear stability analysis shows that the multiple phase transitions occur through considering the effect of stepwise acceleration, and their properties depend on the vehicle density and sensitivity. Moreover, it is concluded that the complexity degree of phase transition is closely related with the turning points of the introduced optimal velocity function. The validity and correctness of the presented model is confirmed by direct simulations.The final chapter of this dissertation is devoted to a summary and prospect of further study of the road traffic flow.