Estimating Origin-destination Matrices Of Transportation Network Using Bayesian Statistic Method

O-D(Origin-Destination)matrices,including static and dynamic O-D matrices,are important foundamental inputs for urban traffic planning and management strategies.Static O-D matrices are important data for long-term transportation planning,while dyanamic O-D matrices are foundamental inputs for real-time traffic management and control.Traditional O-D matrices are obtained from large-scale household surveys,which are not only costly but also difficult to be organized.With the development of urban traffic detection technologies,the use of traffic counts to estimate O-D matrices becomes attractive.Urban transportation systems tend to reserve a large number of historical traffic data.Since Bayesian statistical method can use these historical traffic information well,this paper constructs two Bayesian statistic models for static and dynamic O-D matrices estimation respectively.For solving the network sensor location problem(NSLP),as sub-problem of O-D matrices estimation problem,this paper constructs two NSLP models for static and dynamic O-D matrices estimation respectively.The main research content of this paper is summarized as follows:(1)Bayesian statictic methods for static O-D matrices estimation.Under the multivariate normal distribution assumption,considering the level of overall average traffic flow and the available type of historical data,two models for static O-D matrices estimation are constructed based on prior O-D matrices and prior link flows,respectively.Bayesian statictic methods for O-D matrices estimation can not only provide point estimates of O-D matrices,but also the corresponding confidence intervals.(2)Static network sensor location problem model.Under the budget constraints,a NSLP model for static O-D matrices estimation is constructed to identify the optimal set of sensor locations so as to maximize the quality of traffic flow estimation.In the model,the trace of the covariance matrix of the posterior traffic flow estimation is adopted as a measure of variability.By changging parameters in the objective function,the constructed NSLP model can be used for alternative objectives for traffic operations other than the traditional O-D matrices estimation problem,such as link flow estimation problem.(3)Dynamic O-D matrices estimation model synthesizing multiple sources of data.A Bayesian statistic model for dynamic matrices estimation is constructed,which can synthesize multiple sources of data,including link counts,turning movements at intersections,flows and travel times on partial paths.By analyzing the relationships among time-dependent O-D matrices and these multiple sources of data,the proposed model can effectively improve the accuracy of O-D matrices estimation.(4)Dynamic network sensor operation and deployment model.In order to minimize the variabilty of dynamic O-D matrices estimates,a NSLP model that integrates optimal heterogeneous sensor operation and deployment strategies under a budget constraint is proposed.Two types of sensor are considered in the model,that is,link sensors to detect link flows and node sensors to detect intersection turning movements.The operation strategy consists of sensor start time and duration of operation.The sensor deployment strategy consists of the numbers of link and node sensors,and their installation locations.The cost of a sensor is not fixed as past studies,and is made up of a fixed installation cost and an operation cost which is assumed to be positively linearly correlated with its duration of operation.(5)Algorithm for solving the O-D matrices estimation model.Under the assumption of multivariate normal distribution,to solve the Bayesian O-D matrices estimation models,we use a sequential algorthim,in which the observed variables are updated one by one.This algorithm can reduce the dimension of matrices and avoid matrix inversions.(6)Algorithm for sovling the NSLP model.Similar to the algorithm for solving the O-D matrices estimation model,to solve the proposed NSLP models,we also use a sequential algorthim.By sequentially adding one sensor at a time,this algorithm can avoid matrix inversions and simplify the computation.This algorithm can also give the priorities of the identified sensor locations.Based on the Bayesian statistical theory,this research studies the O-D matrices estimation problem in urban traffic planning and the related NSLP.This research can make full use of existing traffic data detected by traffic sensors and historical data reserved in urban traffic sysytems.Under limited resources,this research can maximize the efficiency and precision of O-D matrices estimation,and provide fundamental data for long-term and real-time transportation planning and management strategies.