| Pedestrian tra?c is also called the walking tra?c, which is one of the oldest and the most basic form of transportation. It plays the role of a link among all advanced transportation technologies, and is a fundamental element of public transportation.However, there is still a great deal we do not know about walking. With the fast development of modern society and the increase of social activities, the demand for walking infrastructures is growing in recent years. At the same time, various accidents and tragedies have increasingly happened. Gaining a clear idea of macroscopic and microscopic behaviors of pedestrian ?ows, revealing the related microscopic mechanisms and ensuring pedestrian safety have become a hot issue needed to be solved. Thus far, many scholars have dedicated to research in this area and made some important progress. But due to the complexity of pedestrian ?ows, there are many problems to be further explored. There have been many methods for studying pedestrian ?ows. In this dissertation, based on the existing theories of pedestrian ?ows, several improved models with the application of game theory are proposed to investigate pedestrian evacuation, unidirectional and bidirectional pedestrian ?ows, respectively. And the theoretical analysis and numerical simulation are applied. The main contents of the dissertation are as follows.(1) When a large group of pedestrians leave from a room, especially in an emergency, most pedestrians do not follow the shortest path, but try to minimize the travel time based on the observed environment and are routed dynamically. In order to describe the involved behaviors, the method to calculate the ?oor ?eld is improved based on the ?oor ?eld cellular automaton model. In this method, the pedestrians are treated as the movable obstacles which will increase the value of the ?oor ?eld. The additional value δ is interpreted as the blocking effect of proceeding pedestrians. If a pedestrian’s way is blocked by other ones, he or she will ?nd another way to avoid the blocking person. The value of δ indicates how far he or she has to detour. If δ is large, the following pedestrian has to make a longer detour. Because the distribution of pedestrians evolves with time, the improved ?oor ?eld is dynamic. Firstly, the evacuation from a room with a single door is investigated. The evacuation time is much smaller than that of original method which is the case of δ = 0. When the width of the door is not larger than six, there is a power law relationship between the evacuation time and the exit width with a negative exponent. Mean ?ow rates obtained by our model are higher than Nagai’s and Müller’s results under laboratory conditions, but is close to Müller’s data for the exit with medium width under alarm condition. The using e?ciency of each exit cell is higher. And it is found that pedestrians choose the evacuation path by considering the distance to the exit and the congestion of the path in the presented model. Next, the evacuations from a room with two doors who have three typical con?gurations are investigated. The phase diagrams between the evacuation and the positions of doors are obtained. All of the results we have obtained may be for architecture designers’ reference.(2) In order to better solve the con?ict that several pedestrians intend to move to the same site at the same moment under parallel update rule, and to better embody the actual pedestrian’s attitude, we introduce game theory to the cellular automaton model. We divide pedestrians into two categories “cooperator” and “defector”. Cooperators are humble, while detectors are impatient. The payoff matrix of game and the cost of the detectors who are participant in the game are given. In the presented model, the element of the payoff matrix is the transition rates to the objective cell in the game. Through simulations, we examine the process of evacuation in which evacuees update or do not update their strategies. In the case that evacuees do not update their strategies, detectors go through the exit and leave the room easily when the cost of the detectors is smaller, but cooperators detain in the room and form a cluster. When the the cost of the detectors is larger, cooperators leave the room easily at the beginning. For the case of updating, cooperators and defectors always arrive at a consistent state in which they have the same number and follow the same rule in the evolving time, irrespective of the probability and period of updating strategies. In addition, different dynamics work before they reach the consistent state: for the larger probability of updating strategies, the number of cooperators and defectors oscillates on the initial stage, while for the smaller probability, no oscillation happens. And the longer of the updating strategy’s period, the later the consistent state happens.(3) During the evacuation, evacuee will take different attitudes according to the distance to the exit when the con?ict happens. For example, when an evacuee has a longer way to the exit, his or her sense of crisis will become stronger. In order to get out of danger quickly, he or she will like to pay more to obtain the target cell. When the evacuee is close to the exit, he or she will become quite and the competition is not?erce. On this basis, we improve the model. In the new model, the competitive cost of evacuees is the function of the distance from the target cell to the exit. There are two games: the prisoner’s dilemma game and the stag-hunt game, in the room at the same time. The prisoner’s dilemma game appears near the exit, while the stag-hunt game appears far away from exit. The parameter of cost n determines the area of two game appearing. The smaller the parameter n, the bigger area the prisoner’s dilemma game appearing, but the smaller area the stag-hunt game appearing. The asymmetrical updating rule is introduced in the improved model. The process of evacuation from a room with a single door has been investigated. In the case that evacuees do not update their strategies, the fraction of cooperators in the room is larger than the initial one all the time, and the defectors pass through the door ?rstly for n > 0. But when n = 0,the cooperators arrive at the door easily. For the case of updating strategies, when the number of cooperators is smaller at the beginning, the number of cooperators increases?rstly and then decreases, but that of defectors reduces all the time. The evacuation time will increase if the period of updating is long. For the small β, more defectors change their strategies, so the number of cooperators is larger. But for large β, more cooperators change their strategies and the number of cooperators is smaller. When the number of cooperators is larger initially, the evacuation time increases ?rstly and then decreases with prolonging the updating period. The evacuation time is maximum when the updating period τ = 7.(4) Based on the two-dimensional optimal velocity model, an improved optimal velocity model is proposed by applying the asymmetrical force in the place of the symmetrical force and introducing the interaction with following pedestrians. The stability condition of the transverse mode and longitudinal mode along the direction of φ = 0, π/6, π/3, π/2 and that of elliptically polarized mode. The related phase diagrams are given. When the perturbation travels along the x axis, the stability condition of pedestrian ?ow is in?uenced by the sensitivity a, the distance r among pedestrians and the intensity λ of interaction with the following pedestrians. But in the other cases, the stability conditions are only in?uenced by the distance r. The critical curve of longitudinal mode which travels along the x axis moves leftward along the r-axis and the regions below the critical curve becomes small. But the critical curve of transverse mode which travels along the x axis moves rightward along the r-axis and the regions below the critical curve becomes large. Finally, the numerical simulation is applied to study the case of λ = 0. For the unidirectional pedestrian?ow, there is stable transverse wave in the phase B. But in phase C, there is regular longitudinal wave in the early stage. In the state after relaxation, we can see clearly irregular density wave. For the counter ?ow, clear lanes are formed in the phase A.(5) Based on the two-dimensional lattice hydrodynamic model, a new two dimensional lattice hydrodynamic model by considering the turning capability of pedestrians is proposed. We have investigated the jamming transition between the freely moving phase and the jamming phase both numerically and analytically. Based on this model,the stability condition and the mKdV equation describing the density wave of tra?c congestion are obtained by using the linear stability theory and the nonlinear analysis method, respectively. We have derived the TDGL(time-dependent Ginzburg–Landan)equation to investigate the jamming transition by applying the reductive perturbation method. The spinodal line and the coexisting line have been calculated from the TDGL equation. There exist kink–antikink density waves in dense tra?c. The results indicate that at this time the pedestrians moving along only one direction are most stable.In the ?nal part of this dissertation, the summary of the thesis and a prospect of further study of the pedestrian ?ows is devoted. |
PDF Full Text Request