Mesoscopic And Microscopic Models For Traffic Flows And Their Applications

This thesis is concerned with the modeling and simulation of traffic flows from mesoscopic and microscopic viewpoints. In view of the realistic characteristics of plane, low-velocity and mixed transportation systems in China and the trend of widely applying real-time information in traffic planning and management, based on the Nagel-Schreckenberg (NaSch) cellular automaton (CA) model, an improved CA model is proposed for mixed traffic flow with motorcycles, and the decision dynamics in a realistic two-route scenario is investigated. Then in order to overcome the difficulties in applying the traditional mesoscopic models with the appearance of integro-differential terms in the models, a lattice Boltzmann model for road traffic flows is established and then extended to modeling and simulating urban network traffic flows. The related simulations show that the presented models can be employed to reproduce the complicated nonlinear dynamic characteristics in traffic flows.The main contents of the dissertation are as follows.I. Cellular automaton model for the mixed traffic flow with motorcyclesA single-lane cellular automaton model is firstly proposed to simulate the traffic flow of cars mixed with motorcycles by dividing a single lane into three virtual sub-lanes and extending the NaSch model for single-lane car flows. Through performing numerical simulations under the periodic boundary conditions, some flow-density relations and the "lane-changing"behavior of motorcycles are investigated in detail. It is found that the maximum car flow remarkably decreases due to the "lane-changing "behavior of motorcycles, while the maximum total flow increases first and then decreases with increasing motorcycle density. Moreover, the phase transition of the total flow from the free flow to the congested flow is smooth in this model. The "lane-changing" rate of motorcycles will finally decrease to zero with the increase of the car density. But its evolutionary trend is considerably complex. Another interesting fact found in the simulation is that, with the increase of the motorcycle density, the "lane-changing" rate increases first and decreases later. This phenomenon is very similar to the findings in previous work on multi-lane pure car flows. The "lane-changing" is almost of no use in increasing the flow of motorcycles as the motorcycle density is small. But it distinctly causes the increase in the flow of motorcycles as the motorcycle density is sufficiently high, and in this density regime, the flow of motorcycles gradually decreases to the one given with the NaSch model for motorcycles with the increase of the car density. The simulation results indicate that it is necessary to set a barrier or a partition lane for separating the motorcycle flow from the car flow except for the situation of higher motocycle density and lower car density.II. Decision dynamics in a realistic two-route scenarioThe optimal information feedback is of great importance in making full use of the existing transportation resources and improving the performance of traffic systems. Thus, several information feedback strategies were proposed in literature and their effects on the traffic systems were also investigated. However, there is still a paradox remaining in some research reports that no information feedback strategy seems to be the best ones. For examining this paradox, a further study is conducted with a realistic two-route traffic scenario containing a longer route and a shorter route and appropriate open boundary conditions. The effects of several previous strategies on traffic systems are reconsidered in detail. Meanwhile, through analyzing the shortcomings of the existing strategies, a new approach of combing a prediction strategy with various prediction-free strategies is proposed in this work. By conducting numerical simulations, it is found that all the strategies can more or less improve the efficiency compared with the situation with no information feedback. However, various information feedback strategies might have different consequences. Generally speaking, two-route strategies are superior to single-route ones, and strategies based on prediction are better than prediction-free ones. Except for several strategies with prediction, most of the strategies will cause the oscillations of average density and velocity. In addition, the influence of various strategies on the traffic on the longer route is studied, which proves to exist in general, but less remarkable for the strategies with prediction. Especially, the appropriate strategy with prediction is helpful for improving the traffic efficiency and stabilizing the traffic flow. Nevertheless, further simulations show that the information feedback is not very helpful for improving the efficiency if the traffic load on the longer route is too heavy. This study shows that it is essential to correctly choose information feedback strategies.III. Lattice Boltzmann model for road traffic flowTraditional mesoscopic models for traffic flows are usually difficult to be directly employed because of the appearance of integro-differential terms in the models. Thus, a more applicable lattice Boltzmann model (LBM) for road traffic flows is constructed on the basis of the Bhatnagar-Gross-Krook (BGK)-like approximation for the Boltzmann equation and its discretization in time and phase-space. The so-obtained model is a simpler discrete version of the gas kinetics model with the physically meaningful distinct parameters, which can be easily used to investigate numerically the behavior of traffic flows. In consequence, the macroscopic dynamics of the model is derived through the Taylor expansion and Chapman-Enskog expansion. For validating the model, numerical simulations are conducted under the periodic boundary conditions. It is found that the presented model could reasonably reproduce the fundamental diagram. Moreover, certain interesting physical phenomena can be captured, such as the metastability and stop-and-go phenomena, etc. The results imply that the presented model is one of the effective and efficient traffic models.IV. Modeling of urban network traffic flows with lattice Boltzmann modelIt is of great importance to uncover the characteristics of traffic networks. However, there have appeared few researches concerning kinetics models for traffic networks. Thus, an LBM for road traffic networks is proposed by incorporating the ideas of the Biham-Middleton-Levine (BML) CA model into the LBM for road traffic. In the present model, situations at intersections with the traffic signals are treated as a kind of boundary conditions varying with time. Thus, the network traffic flow could be described in the mesoscopic level. By performing numerical simulations under the periodic boundary conditions, the evolution of average velocity is investigated in detail. The numerical results agree quite well with those given by the Chowdhury-Schadschneider (ChSch) CA model. Furthermore, the statistical noise is reduced in this discrete kinetics model, and thus the present model has considerably higher computational efficiency. This study shows that the meso-scopic traffic model could find its extensive applications, provided that reasonable assumptions and techniques are introduced.