基于平均场博弈理论的交通流分析问题  

Traffic Flow Analysis Based on Mean-Field Game Theory

作　　者：程榕 付博洋 魏雅薇 Cheng Rong;Fu Boyang;Wei Yawei(School of Mathematical Sciences,Nankai University,Tianjin 300071,China;School of Mathematical Sciences,Peking University,Bejing 100871,China)

机构地区：[1]南开大学数学科学学院,天津300071 [2]北京大学数学科学学院,北京100871

出　　处：《南开大学学报(自然科学版)》2023年第5期77-84,共8页Acta Scientiarum Naturalium Universitatis Nankaiensis

摘　　要：应用平均场博弈理论将传统交通动力学模型中类气体宏观模型和类粒子微观模型结合在一起,通过定义道路容通量这一概念,研究交通流问题.考虑到加速制动等微观动力学约束,将几种不同交通情形抽象为数学模型,给出相应的平均场博弈问题对应的正倒向偏微分方程系统.通过构造基本无振荡格式对上述系统进行数值模拟,分析了交通容通量对交通流产生的影响.The mean field game theory is used to combine the gas-like macroscopic model and the particlelike microscopic model of traditional traffic dynamics models. Considering micro-dynamic constraints such asacceleration and braking, the concept of traffic capacity flux is defined to abstract complex traffic conditions intomathematical models and to get the corresponding mean-field-game model as well as the system of forwardand backward partial differential equations that satisfy it. By constructing essentially non-oscillatory schemes,this system is simulated numerically and the influence of traffic capacity flux on traffic flow is analyzed.

关 键 词：交通流模型 平均场博弈 正倒向偏微分方程系统 基本无振荡格式 

分 类 号：O212.8[理学—概率论与数理统计]