The Analysis And Algorithm Design Of OD Demand Estimation Introducing The Nodal Flow Equation

OD(Origin-Destination)demand,as the basic data of transportation planning and management,represents the travel flow between the origins and destinations(OD pairs)of transportation networks.Accurate estimation of OD demand is of great significance for alleviating urban road congestion and developing intelligent transportation systems.However,the number of OD pairs in a road network is often larger than that of the observed links.Thus,the number of OD demands is larger than that of constraint equations.How to obtain an accurate and unique solution to the OD demand estimation is one of the hot topics in the interdisciplinary research field of computational mathematics and transportation.To this end,this thesis introduces the nodal flow equation to add the equality constraint conditions of OD demand for narrowing the range of feasible regions,thus,improving the accuracy of OD demand estimation.By analyzing the effectiveness of the nodal flow equation,when introducing maximum effective nodal flow equations,the feasible region can be narrowed to the greatest extent.Therefore,according to the number of equations in the maximum effective nodal flow equations,the full-rank and deficient-rank models of OD demand estimation are established respectively.The unique solution to OD demand can be obtained by solving the proposed models.Considering the impact of observation errors,the upper bounds on relative error of the two models are derived.Numerical examples are carried out to verify the performance of the proposed models and the upper bounds on relative error.The specific contents of each chapter are stated as follows:The first chapter introduces the research significance of OD demand estimation and the research status of traffic flow estimation.The research status of OD demand estimation is reviewed based on the observation data used.It is pointed out that the link flow and nodal flow will be used as observation data in this thesis to decrease the error of OD demand estimation.In chapter 2,the preliminaries of the thesis are presented.The mathematical description of the OD demand estimation problem is given,and the traditional models(maximum entropy model,generalized least squares model)and two kinds of indices of evaluation accuracy are reviewed.Five concepts related to the nodal flow equation are defined.These preliminaries provide a theoretical basis for the establishment of the OD demand estimation model in the following chapter.In chapter 3,the full-rank model and deficient-rank models are proposed for OD demand estimation.The reason why the introduction of the nodal flow equation can improve the accuracy of OD demand estimation is mathematically discussed.And some definitions are given to judge the effectiveness of the nodal flow equation.According to the number of equations in the maximum effective nodal flow equations,we propose the full-rank model and deficient-rank model for OD demand estimation,and an algorithm based on grouping principle is designed and proved to reduce the computational cost of finding the introduced equations.Two existing optimization algorithms are used to solve the two models.Finally,the proposed models are both applied to two transportation networks.The experimental results show that the estimation value of the full-rank model equals to the real value.Compared with the traditional models,the deficient-rank model could decrease at most 53% regarding the average relative error of OD demand estimation.The fourth chapter analyses the error of the full-rank and deficient-rank model with consideration of observation error separately.For the full-rank model,the coefficient matrix of equality constraints satisfies full column rank,so the upper bound on relative error of the full-rank model is derived based on the error analysis theory of linear equations.For the deficient-rank model,the theory above is no longer applicable,and the upper bound on relative error is derived based on the maximum possible relative error model.Finally,numerical examples are conducted to verify the effectiveness of the upper bounds on relative error in the proposed models.The fifth chapter summarizes the thesis and gives future research directions.This thesis has 17 figures,17 tables,and 62 references.