A Bayesian Based Hierarchical Optimization Problem To Estimate Origin-Destination Matrices

Origin-destination(OD)matrices describe the traffic flows from the origins to destinations in the road network over a certain time.OD demand modeling and estimation in urban road network is a fundamental component when a transportation planner or operator makes long-term transportation planning and short-term traffic management.Accurate OD demand estimation is essential to capture on the traffic characteristics of road network,and hence alleviate traffic congestion when doing some transportation planning and management.The traditional approach to obtain OD matrices is to implement large-scale survey,with the drawbacks of high costs,low accuracy,and long cycle of data update.However,with the development of technology,the mathematicsbased solution to derive OD matrices stands out that utilizes traffic network flows.This thesis first reviews the literature of traffic network equilibrium and OD demand estimation methods from domestic and abroad,and then summarizes the current work,which is the basis of its research objective.Bayesian inference,as compared to frequentist inference,is a promising approach in traffic networks where large amount of history traffic data is available,due to its capability of capturing the history prior information.This thesis estimates the parameters of the Gamma distribution of OD demand according to Bayes theory using history OD matrices and link flow samples.The traditional matrices estimation method is transformed to the hierarchical optimization problem in the context of Bayesian methods.The model consists of three levels of mathematical programming:1)lower-level: UE-minimum variance optimization problem.Minimum variance is incorporated to the objective function of user equilibrium model,where link flow becomes the determinants.By doing that,route enumeration is omitted,and the link flows are obtained that are distributed from OD,which serves as the constraints of OD matrices estimation(the link choice proportions).2)mid-level: least squares method.Under the constraint of link choice proportions,observed link flows are used to derive the OD matrices.3)upper-level: Bayesian posterior modes estimation.Using Bayes' Theorem,sample information is used to update the prior and to derive the posterior distribution.In this study,the history OD matrices and OD matrices associated with the observed sample are used to derive the posterior distribution,and posterior mode is used as the node estimation for OD demand.The three levels of optimization problems have clear hierarchy,and can be considered as a hierarchical optimization problem.In this thesis,a multi-level iterative approach is proposed.In the end,three Bayesian models with different combinations of sizes of priors and samples and one bi-level model are compared on GAMS platform in Nguyen-Dupuis network and Sioux-Falls network.Multiple statistics are used to measure the estimation accuracy,and prove the validity and robustness of the proposed method.