Game Theory Approach To Some Problems In Transportation Planning

While modern means of transportation bring convenience to human, there are more and more prominent problems, such as congestion, pollution. Then how to maximize its role in promoting socio-economic and reduce its negative effects is especially important. In addition, the high cost of construction of transportation has a strong stimulating effect on the development trend of region and city, In order to give play to the function of transport facilities and lead to sustainable urban development, it is very meaningful to improve the science of transportation planning before starting construction. Thus, the field of "Transportation Planning" is emerged.Game theory provides framework for the model of more than one player involved in the decision-making process. The first appearing of the concept of game theory in the traffic study is in the traveler route choice behavior assumptions. The situation of the first principle of Wardrop is same to the Nash non-cooperative game, so each of the travelers can be considered as a player. There are fewer literatures about evolutionary game theory approach to the transportation planning, but there are still some domestic and foreign scholars studying in the areas of traffic guidance and assignment. There are all kinds of transportation planning theory and research methods, in this paper we use game theory to study some problems in transportation planning, the main contents include:(1) We firstly introduce the basic elements of transportation planning, traffic situation in China and the significance of the implementation of transport planning. Then we give the equilibrium solution concepts and property of the game theory and evolutionary game theory. The game theory and evolutionary game theory are applied in four key areas:the game between the travelers and the destroyers, the game between the travelers and the travelers, the game between the travelers and managers, the game between the managers and managers.(2)We use game theory to analyze the static equilibrium flow assignment, and indicate that Wardrop user equilibrium based on path is equivalent to the Nash equilibrium. Then, the game problem of the traffic flow based on link is analyzed, and the relationship between the user equilibrium based on link and the Nash equilibrium is studied. At last we propose a more effective way to solve the equilibrium model.(3)Because of the limitation of the classical game theory, the evolution dynamic methods applied in traffic flow is more realistic. We introduce four kinds of evolution dynamic:replication dynamic, logit dynamic, BNN dynamic and potential games. Further, we establish the joint control model of the charges and the capacity based on the logit dynamic. Markov chain is introduced to the BNN dynamics, which research and analysis object is short-term traffic flow forecasting in real-time control. Then combing general game theory and Markov chain, we construct a Markov process of evolution dynamic.(4)We have studied on choice behavior of traveler based on the evolutionary game, and established the trip model choice behavior of traveler based on the evolutionary game under the participation of government, analyzed some key parameters of choice behavior. The results show that the government’s incentive effect to public buses and controlling effect to private cars play a vital role in the evolution.(5)We introduce several common Stackelberg models in transportation planning, and analyze the ideas and methods of modeling, further focus on the discrete network design problem. In this paper traditional discrete network design problem is improved, and the discrete network design problem with budget constraint based on link is proposed. The problem was solved by evolutionary game algorithm.(6)We give a summary of research work based on the conclusions in this paper, and pointed out the problems in-depth studying.The innovations in this dissertation include:(1) The game problem of the traffic flow based on link is analyzed, and the relationship between the user equilibrium based on link and the Nash equilibrium is studied. Then we give the equivalent mathematical programming model, and solve this problem by affine scaling algorithm, which is verified an effective method.(2)The road network toll models are generally carried out in static situation, now we establish the joint control model of the charges and the capacity based on the logit dynamic, which can optimize transportation system by controlling the level of time-varying road pricing and capacity. Through a simple example, we give analysis and prediction to traffic flow based on logit dynamic, and provide theoretic support for guidance strategy in this paper. Markov chain is introduced to the BNN dynamics, in which the choice probability meets Markov chain. Then combing general game theory and Markov chain, we construct a Markov process of evolutionary dynamic, which research and analysis object is short-term traffic flow forecasting in real-time control. Then we analyze its stability and give an example to verify the stability.(3)The main reason causing a traffic jam is the conflict between the growing traffic of private cars and the limited resource. This paper gives analysis to how to establish a rational mechanism to make travelers choose the right trip model. We have established the trip model choice behavior of traveler based on the evolutionary game under the participation of government, analyzed some key parameters of choice behavior. The results show that the government’s incentive effect to public buses and controlling effect to private cars play a vital role in the evolution.(4)Network design problem is an important part of transportation planning, which usually is described as a Stanckelberg game model. In this paper traditional discrete network design problem is improved, and the discrete network design problem with budget constraint based on link is proposed. The discrete bilevel programming problem is difficult, so we solve this problem by evolutionary game algorithm.