Study On The Complex Dynamic Properties Of Unidirectional Pedestrian Flow Based On Parallel Lattice Gas Method

We are in a fast developing society, so people are quickening rhythm of life and work. And the demanding for traveling and participating in collective activities are increasing. Reducing congestion and ensuring pedestrian safety have become a hot issue that people pay increasingly attention to. Revealing the microscopic mechanisms resulting congestion and gaining a clear idea of complex dynamic characteristics of pedestrian flow become core issues of studying pedestrian flow. Recent years, many scholars dedicated to research in this area and they have made some important research results. But due to the complexity of pedestrian flow, there are many problems remain to be further explored. There are many methods for studying pedestrian flow. This paper employs research methods of the modeling-numerical simulation and analytical analysis.As discrete model has some advantages, such as small amount of calculation, convenient operation, this thesis establishes discrete model with the lattice gas method to study characteristics of pedestrian flow. Generally, random sequential update rule is used in lattice gas models studying pedestrian flow. Taking into account the synchronization of actual pedestrians walking, we introduce parallel update rule to the lattice gas model of pedestrian flow, which is an innovation of this thesis.We model unidirectional pedestrian flow using the parallel lattice gas method and analyze the fundamental diagram in detail, and compare it with that of the lattice gas model with random sequential update.We find that in the same density, the flow corresponding to parallel update is smaller than that corresponding to random sequential update. This is because the conflicts that several pedestrians intend to move to the same site happen owing to parallel update, which affects the flow of the system. The right branch of fundamental diagram curve of our model appears the inflection point with the increase of the parameter (the drift strength) in the model from0to1, namely, the fundamental diagram becomes convex from the concave curve. This indicates that our model can reproduce different fundamental diagrams obtained via realistic observations and experiments corresponding to some pedestrians under different culture backgrounds by adjusting the parameter value. When the parameter is equal to1, the fundamental diagram of parallel update model has two congested flow branches:it is different from that of random sequential update model with the reverse lambda structure. Without taking into account the correlation between adjacent sites, we analyze the flow rate of system in parallel update model by mean-field method. When the drift strength parameter in the model is small, analysis results are in approximate agreement with simulation results. But with the increase of the drift strength, analysis results gradually deviate from the simulation results because of the correlation of the system is growing.In reality, when a pedestrian walks, he (her) has expectation effect (anticipation ability) to front pedestrian’s movement according to front situations. Considering this fact, we add expectation effect rule to parallel lattice gas model. In order to facilitate to discuss how expectation effect influences on the property of the system and get analytical solution, this paper studies just one lane case. In fact, this model is an expansion of the totally asymmetric exclusion process (TASEP). Theoretical analysis for the model is carried out mainly by the mean field in the paper. As expectation effect is considered in the model, we adopt asymmetric cluster mean field method that is different from general symmetry cluster mean field theory, which is also an innovation of this thesis. Through analysis, we obtain the analytical expression of the system flow. Analysis result agrees excellently with simulation result, which indicates that the analytical expression might be the exact expression. And of course, these remain to be proven in the future. Analyzing further the analytical expression of the flow, we also obtain the relationship between the density corresponding to maximum flow and the probability of expectation effect.In order to better solve the conflict 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 psychology, personality traits, we introduce game theory to the lattice gas pedestrian flow model with parallel update. We divide pedestrians into two categories’cooperator and "defector". Cooperators are gentle with good temper and defectors are aggressive with quick temper. We give a payoff matrix of game and a rule that participant in the game change strategies after game according to. Through simulations, we discuss natures of the cooperators fraction. When an initial cooperator fraction is not equal to1, the steady-state cooperators fraction has nothing to do with it and shows non-monotonic with increase of the density. Thus initial cooperators fraction does not influence system flow. We also examine other properties of system, such as the proportions of various game types, pedestrian distribution in the channel. For the case of the drift strength being equal to1, we focus on dynamic characteristics of the system with different widths. We find a first-order phase transition of cooperators fraction in two-lane system, in which defectors fraction decays exponentially when system density is less than the critical density, otherwise it remains constant after a period of evolution. Interestingly, this phase transition behavior is same as that about nature in other system. However, this phase transition behavior does not exist in the multi-lane system. By analyzing a small system in detail, we present an interpretation about the microscopic mechanism of the phenomenon. We also find that flow rate of the system is connected with whether the initial cooperators fraction is equal to1. The flow rate difference is generated by two factors: different spatial distributions of pedestrians for different initial cooperators fraction and different transition probabilities for cooperator and defector in the game. Dominant position of the two factors producing flow rate difference changes with the increase of system width. The paper also carries out a preliminary study on how evolution rules of the game influence dynamic characteristics of the system. In addition, we analyze probabilities of various types of game using the mean-field theory. Analysis results and simulation results agree quite well in a certain range.