Mathematical Models And Numerical Simulation Of Three-lane Traffic Flow Based On The Measurement

With the rapid development of China's economy, people's living standards continue improved, so the traffic conditions are put forward higher requirements. The motor vehicles are increasing sharply in some well developed cities. The increasing of the vehicles put up higher requirements of the road infrastructure. Some cities have built multi-lane freeways. Despite widening of the road and various other measures, the traffic problems are not solved, and have a more serious trend. Traffic congestion is a major inconvenience problem to people of everyday lives, people often waste a lot of precious time on this question. Traffic jams have also affected the overall efficiency of all industrialized countries in economic and social development. So this issue requires urgent solution. To solve the traffic congestion it is necessary for an in-depth study of the formation and evolution of congestion. Therefore, the study of the cause of traffic jams and the evolution of the development of actual congestion is very meaningful. The causes of congestion can be divided into absolute super-saturated traffic congestion and the disturbance of the road vehicles in caused by some other reasons. Usually the law of super-saturated traffic congestion is relatively simple, but traffic jams cause of disturbance is more complex. We believe that the study of traffic disturbance on the development and dissemination have meaningful in traffic management, intelligent transportation system design and application of all.This article is based on the study of multi-lane traffic disturbance: the process and the development of disturbance after it appeared. In order to make the conclusion more closely fit the actual situation, we put up a new experimental observation of high-speed urban roads. Based on Beijing, Shanghai and other places high-speed multi-lane road measured video, we use computer software with artificial methods of intervention, extracted vehicle speed, density and other relevant parameters, such as probability under different traffic conditions. And we use of statistical methods, under a certain error, get these statistical data.Numerical simulation of traffic flow can have cellular automaton model, the continuum differential equations model, the network distribution model, and so many ways. The continuum differential equations model and the general equation of fluid mechanics are very close, so that we can take advantage of some computational fluid dynamics research results, and because of this we use macro model of continuous to study the disturbance of development and dissemination. This paper has established three numerical simulation models: First, set up Payne model that consider the changing lanes effect of vehicles, which made reference to the effect of vehicles change between two lanes. In this Payne model, we don't consider the difference between left and right lanes. Second, we take the difference between left and right lanes into consideration. So based on observation data and the actual anastomosis we set up new Payne model. Third, due to Payne model on behalf of the isotropic model for traffic flow model vehicles, there is a retrogression and "gas act" flawed. As a comparison, we have established three-lane traffic flow model anisotropy, which is the Jiangrui momentum equation. We use different methods of discrete and calculate the three different models.Through numerical calculation, we have selected different balance functions for different models. And from the numerical results of the analysis we see that the multi-lane disturbance in the development and dissemination has different characteristics: The same disturbance, multi-lane is more easily decay than single lane. The development of disturbance of different models have a certain connection of the internal laws of vehicle density: if the vehicle density is relatively low, the disturbance will gradually decay over time; and if density of vehicles is high, the disturbance will also gradually decay, but in the medium-density, the disturbance will have strongly nonlinear action, the disturbance maybe decrease first and the increased after the first attenuation trend. Greater intensity of the disturbance will have a greater scope of the impact: in addition to impact the adjacent lane, there will be affects on no adjacent lane. The disturbance spread and vehicle density also have a close correlation: when the vehicle density is relatively low, the disturbance will travel downstream; with the increasing of vehicle density, velocity of disturbance gradually decreased; when the vehicle density is high, the disturbance will transmit upstream.