Journal of Southeast University ( English Edition) Vol． 29，No． 3，pp． 322-327 Sept． 2013 ISSN 1003 —7985 Bayesian network model for traffic flow estimation using prior link flows Zhu Senlai Cheng Lin Chu ZhaoMing ( School of Transportation， Southeast University， Nanjing 210096， China) Abstract: In order to estiMate traffic floW， a bayesian netWork ( bN) Model using prior link floWs is proposed． This Model sets link floWs as parents of the origin-destination ( OD ) floWs． Under norMal distribution assuMptions， the Model considers the level of total traffic floW， the variability of link floWs and the violation of the conservation laW． Using prior link floWs， the prior distribution of all the variables is deterMined． by updating soMe observed link floWs， the posterior distribution is given． The variances of the posterior distribution norMally decrease With the progressive update of the link floWs． based on the posterior distribution， point estiMations and the corresponding probability intervals are provided． To reMove inconsistencies in OD Matrices estiMation and traffic assignMent， a coMbined bN and stochastic user equilibriuM Model is proposed， in Which the equilibriuM solution is obtained through iterations． Ｒesults of the nuMerical exaMple deMonstrate the efficiency of the proposed bN Model and the coMbined Method． Key words: traffic floW estiMation; Gaussian bayesian netWork; evidence propagation; coMbined Method doi: 10． 3969 / j． issn． 1003 － 7985． 2013． 03． 017 Ｒeceived 2013-03-11． Biographies: Zhu Senlai ( 1989—) ， Male， graduate; Cheng Lin ( corre- sponding author) ， Male， doctor， professor， gist@ seu． edu． cn． Foundation item: The National Natural Science Foundation of China ( No． 51078085， 51178110) ． Citation: Zhu Senlai， Cheng Lin， Chu ZhaoMing． bayesian netWork Model for traffic floW estiMation using prior link floWs［J］． Journal of Southeast University ( English Edition) ，2013，29( 3) : 322-327． ［doi: 10． 3969 / j． issn． 1003 － 7985． 2013． 03． 017］ D uring the last decades， traffic floW estiMation has becoMe an iMportant aspect of transportation plan- ning． TWo iMportant probleMs in the traffic floW estiMation field are: the origin-destination ( OD) Matrices estiMation and the traffic assignMent probleMs． The first one is to try to estiMate the nuMber of users traveling froM each origin to each destination based on soMe link floW observations， While the second is to try to estiMate hoW the OD floWs dis- aggregate aMong different possible routes and links of the OD pairs． The OD Matrices estiMation probleM can be dealt With by Many different Methods， such as least squares ［1］ and generalized least squares ［2］ Methods， entropy or inforMa- tion-based Methods ［3］ ， and statistical-based Methods． The statistical-based Methods can be classified into classical Methods ［4］ and bayesian Methods ［5-10］ ． In statistical-based Methods， the traffic floWs are assuMed to be Multivariate randoM variables given soMe paraMetric faMilies， such as Poisson， GaMMa， Multivariate norMal， etc． And the pa- raMeters are considered as randoM variables theMselves in bayesian Methods． The traffic assignMent probleM is pri- Marily dealt With using tWo different Methods: deterMinis- tic user equilibriuM ( DUE ) ［11-12］ and stochastic user equilibriuM ( SUE ) ［13-14］ ． If the OD Matrices estiMation and traffic assignMent are treated separately， soMe incon- sistencies norMally arise in the solutions of both probleMs． To reMove these inconsistencies， several coMbined Meth- ods of the tWo probleMs have been proposed in Ｒefs． ［15- 17］． More recently， Castillo et al． ［6］ proposed a bayesian netWork ( bN) Model using prior OD floWs for traffic floW estiMation and then coMbined it With the Multino- Mial logit ( MNL) SUE Model． In their bayesian net- Work， OD floWs are assuMed to be parents of link floWs． Thus they need to give the relative Weights of all OD floWs With respect to the total traffic floW， as part of the inputs of the bN Model． HoWever， generally， for a real transportation netWork， the nuMber of OD pairs can be very large． For exaMple， in Chicago's Ｒegional Net- Work， there are 12 982 nodes， 39 018 links and 2 297 945 OD pairs． It can be seen that the nuMber of links is usually Much sMaller than the nuMber of OD pairs and the relative Weights of link floWs are coMparatively con- venient to be obtained in a real traffic netWork． based on these facts， We build a neW bayesian netWork using prior link floWs， in Which the link floWs are parents of OD floWs， and the relative Weights of link floWs With re- spect to the total traffic floW are part of the inputs of the bN Model． FurtherMore， to obtain an equilibriuM solu- tion， We coMbine the proposed bN Model With a SUE Model and give the procedures to solve it． 1 Proposed bayesian NetWork Model 1. 1 Model assuMptions Assumption 1 The vector V of link floWs is a Multi- variate norMal randoM variable With Mean μ V and vari- ance-covariance Matrix Σ V ． Assumption 2 The conditional distribution of each OD floW T i given the link floWs is a norMal distribution: