带有最优流量信息中断期望影响的一类新格子模型  

A new lattice hydrodynamics model considering the anticipation impact of optimal current interruption

作　　者：刘丽梅 化存才[2] LIU Li-mei;HUA Cun-cai(School of Preparatory Education,Yunnan Minzu University,Kunming 650504,Yunnan,China;School of Mathematics,Yunnan Normal University,Kunming 650500,Yunnan,China)

机构地区：[1]云南民族大学预科教育学院,云南昆明650504 [2]云南师范大学数学学院,云南昆明650500

出　　处：《云南大学学报（自然科学版）》2024年第1期8-14,共7页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(12161095)。

摘　　要：交通中断是导致交通扰动的一个重要因素.为研究最优流量信息中断的期望行为对交通流稳定性的影响,基于Nagatani’s模型考虑最优流量中断概率的影响,提出一类新的格子流体力学模型.首先,根据线性稳定分析方法,得到新模型的线性稳定条件;其次,通过非线性稳定理论,获得该模型的modified Korteweg-de Vries(mKdV)方程,并根据求解方程得到的扭结-反扭结孤立波解描述交通堵塞的演变过程;最后,通过仿真算例验证了理论分析结果.结果表明,考虑最优流量中断期望影响的新格子流体力学模型比Nagatani’s模型更稳定,当添加最优流量信息中断的期望影响时,交通流的稳定性得到显著提高.Traffic interruption is an important factor resulting in traffic congestion.To study the influence of the anticipation behavior of the optimal flow information interruption on traffic flow stability,a new lattice hydrodynamics model is proposed considering the effect of optimal traffic interruption probability based on Nagatani's model.Firstly,the linear stability condition of the new model is obtained according to the method of linear stability analysis.Secondly,the modified Korteweg-de Vries(mKdV)equation of the model is derived from the nonlinear stability theory,and the evolution of traffic jams is described according to the kink−antikink soliton solution obtained by solving the equation.Finally,the results of the theoretical analysis are verified by numerical simulations.The results show that the new lattice hydrodynamics model considering the anticipation effect of optimal current interruption is more stable than Nagatani's model.The stability of traffic flow can be effectively improved when the anticipation effect of the optimal current information interruption is added.

关 键 词：交通流 格子模型 交通中断概率 MKDV方程 数值模拟 

分 类 号：O175[理学—数学]