Origin-destination Matrices Estimation Method Based On Bayesian Inference Using Multi-types Traffic Data

The Origin-Destination(OD)matrices give the traffic flow information between all origin and destination nodes in road network during a time period.It reflects travelers'travel demands on the road network.OD flow is a basic type of input data for urban traffic planning and control,and it is also the foundation of traffic modeling for some further researches.The traditional way of obtaining OD matrices is time-consuming and has low precision.For this reason,we design an alternative method to estimate the OD matrices by applying the observed traffic information in road network.The proposed method can provide high-precision OD matrices estimation result for related work.In this paper,we introduced some basic knowledge which is necessary to establish the Bayesian OD matrices estimation model.Route choice model is a basic content in the established model,it includes the user equilibrium(UE)and stochastic user equilibrium(SUE)route choice model;Bayesian inference is the main logic to establish the model.We introduced the fundamental of Bayesian inference,the relationship between Bayesian inference and OD matrices estimation and how to implement the Bayesian inference.According to Bayesian inference theory,a Bayesian OD matrices estimation model is built by using the observed link volume.In this model,we assume that route volume follows the SUE principle.Based on this assumption,the likelihood of traffic flow is deduced.What's more,the prior distribution of route flow is deduced according to the maximun entropy principle.The posterior distribution of the route flow is solved by combining the likelihood function and the prior distribution.A Markov Chain Monte Carlo(MCMC)algorithm is designed to solve the model in this paper.Parts of route volume,turn flow and traffic speed were further added into the above model to enhance the OD matrices estimation efficiency.First we analyzed the quantitative relationships among the above-mentioned four types of traffic detected data.Then we implement data hierarchy and put forward the concept of network independent data.Finally we established the Bayesian OD matrices estimation model using the above-mentioned four types of data as the input and designed the corresponding MCMC algorithm.A numerical example on the Sioux-Falls road network is designed to verify the rationality of the model and the reliability of the algorithm.In the example,the relationship between the actual link flow and the estimated link flow,the actual OD flow and the estimated OD flow are respectively analyzed and four types of precision indicators were analyzed to check the precision of the final estimation results.The following conclusions are drawn from this paper:(1)Due to the limit of single link flow,the additional route/trajectory data and the intersection turning flow data can be treated as supplement information to improve our Bayesian model.This can effectively optimize the estimation results.The example results show that the accuracy of Bayesian OD matrices estimation model using four types of data is higher than the model with single link flow as input.(2)A Markov Chain Monte Carlo sampling algorithm was designed for the Bayesian inference model in the paper.This algorithm avoids the difficulty of calculating the normalized constants of the Bayesian posterior distribution.Under the given proposal distribution,the acceptance rate of the sample reaches a satisfactory level and hence the algorithm is quite efficient.(3)The proposed Bayesian inference model has obvious advantages compared with the traditional OD matrices estimation methods.On one hand,Bayesian inference model can effectively make use of the prior information of OD matrices,and on the other hand,this model can give both the point estimation of OD flow and the corresponding confidence interval.The methods proposed by this paper provide a good way to supplement the existing OD estimation problem.