Variational Inequality Method Of Mixed Traffic Equilibrium Problems

Traffic congestion, has brought a lot of inconvenience to the road transport and people’s lifein our country, so studying the causes of traffic congestion, analyzing the rule of traffic, It has imp-ortant practical and theoretical significance to transportation planning, energy conservation, trafficcongestion easing and construction of subject.Through studying the studies of domestic and foreign scholars, combined with my own unde-rstanding, this research has a study of traffic model and analysis. The main work and achievementas follows:1. Through the relevant data of road traffic in Ganzhou, I have a basic understanding of the ur-ban traffic. Then through a questionnaire survey, I have understood the residents’ travel rate, the c-hoice of travel mode and travel purpose, it’s the preparation for building a model that comply withthe traffic in Ganzhou.2. After discussing several types of the classical impedance function, such as BPR function,Davidson function and so on, combined with characteristics of Ganzhou city road traffic, first clas-sify the road type. Considering codirectional motor vehicles, codirectional non-motor vehicles, andmotor vehicles and non-motor vehicles in the opposite direction, then put forward different imped-ance function to different types of the road, and analyze the characteristics of the new impedance f-unction.3. With the new impedance function, a new mixed traffic equilibrium model has been built.According to the existence approve of standard UE acme model by Smith, it is unable to set up amodel for asymmetric type mixed traffic. Mixed with the Lagrangian function which correspondedwith the symmetrical traffic model, by using the theory of mathematical programming, the equival-ence of the model has been proved by the equivalence between the first order condition of the Lag-rangian function and the UE condition. Then according to the qualitative and the strict convexity ofthe objective function, and the linear of constraint conditions, the uniqueness of the optimal soluti-on of the model has been proved.4. According to the direction search method, the algorithm of the model has been put forward.Based on controlling this method, the solution algorithms of the symmetric and asymmetric mixedtraffic have been obtained. Compared with the previous studies, this paper consider more factors i-nfluence, so it can comprehensive response the state of mixed traffic. 5. Finally, by using a simple network to simulate the actual traffic network equilibrium pro-blems, it shows the effectiveness of the computing method of the model.In the end of the research, the work and conclusions are summarized, then put forward somesecurity countermeasures to automobile-bicycle conflict in the road, such an building bicycle shari-ng system, separating the vehicles, restricting the speed of the motor vehicles, developing a varietyof pubic transportation and so on. Finally put a outlook and direction of improvement to the resear-ch.