Traffic Flow Analysis Modeling Based On Network Structure

Transportation network modeling is a hot topic in the interdiscipline of mathematics applied in transportation planning and management.Traffic flow analysis is a fundamental issue in the field of transportation network modeling.As traffic flow can reflect the needs of urban transportation systems,accurate estimation of traffic flows can help traffic management and planning departments make relevant policies.With the development of technology,deploying sensors in transportation networks to automatically collect traffic flow(link traffic flow)has become the major method for traffic flow observation.Thus,research on related sensor deployment issues has been paid increasing attention to.In view of this,this thesis investigates the traffic flow observability problem and proposes a sensor location model for traffic flow analysis.The corresponding theories in graph theory and optimization methods are used with full consideration of the topological structure of the transportation network.Finally,numerical examples are provided to verify the application of the proposed modeling approach.The first chapter introduces the research background and significance of the flow observability problem and classifies the research status of the flow observability problem.The second chapter introduces some preliminary knowledge used in this thesis:several basic definitions in graph theory and the basic concepts of transportation networks are presented.Moreover,the mathematical description of the observable problem and different types of flow observable problems are introduced.In the third chapter,based on the existing research on the installation of passive sensors on transportation network links,some network sensor location problems are solved from the perspective of the topological structure of the graph.Firstly,the concept of “plane” in graph theory is introduced,and the transportation network graph is divided into a “plane graph” and a “non-plane graph”.According to the node type in the transportation network,the virtual network is constructed by using the definition of“isomorphic graph”.Then,the number and location of sensors in the transportation network can be obtained by transforming the node-link incidence matrix and Gaussian elimination method.Next,using the number of links,the number of ordinary nodes,the number of centroid nodes,the number of planes,and the number of added links,the lower bound formula of the number of observations for different transportation networks to achieve complete observability of links traffic flows is given.Finally,the feasibility of the method is verified by several different examples.The fourth chapter uses the topological structure information of the transportation network to improve the sensor location Basic Model(BM)model,which is used to obtain the number of sensors needed to be installed in the network to achieve full observability of the traffic flow of the whole transportation network.In the modified model,only the out-degree(or in-degree)of nodes is considered,which effectively reduces the constraint complexity in the BM model and improves the computational efficiency of the model.Finally,the validity of the model is verified by two networks of different sizes.The fifth chapter presents the conclusions and further studies.The thesis has 19 figures,14 tables,and 76 references.