Trip matrix and path flow reconstruction and estimation based on plate scanning and link observations

This paper deals with the problem of trip matrix and path flow reconstruction and estimation based on plate scanning and link flow observations. To solve the problem, the following steps are used. First, the class of feasible subsets of scanned links for single users is identified. Second, the conservation laws are stated in terms of flows associated with the class and path flows. Finally, the path flows are reconstructed based on minimizing a quadratic (weighted) function of the errors with respect to a given set of prior path flows, subject to the conservation law constraints, stated for each of the possible subsets in , and to the observed information. Once the path flows have been reconstructed, the trip matrix and other link flow estimates become immediately available. In addition, an algorithm for selecting optimal sets of links to be scanned for predicting path flows is provided. Finally, the methods are illustrated by their application to the Nguyen-Dupuis network, showing the important gain obtained, in estimating path and OD-pair flows, if one uses the extra information contained in the scanned data, which is shown to be much more informative than the traditional link count information. This has important practical implications on an efficient estimation of traffic flows.

[1]  Hillel Bar-Gera,et al.  Origin-Based Algorithm for the Traffic Assignment Problem , 2002, Transp. Sci..

[2]  William H. K. Lam,et al.  Estimation of an origin-destination matrix with random link choice proportions : a statistical approach , 1996 .

[3]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[4]  Hai Yang,et al.  Estimation of origin-destination matrices from link traffic counts on congested networks , 1992 .

[5]  Moshe E. Ben-Akiva,et al.  Alternative Approaches for Real-Time Estimation and Prediction of Time-Dependent Origin-Destination Flows , 2000, Transp. Sci..

[6]  Moshe Ben-Akiva,et al.  Discrete Choice Analysis: Theory and Application to Travel Demand , 1985 .

[7]  Michael J. Maher,et al.  A STATISTICAL PROCEDURE FOR ESTIMATING A MEAN ORIGIN-DESTINATION MATRIX FROM A PARTIAL REGISTRATION PLATE SURVEY , 1992 .

[8]  Giulio Erberto Cantarella,et al.  A General Fixed-Point Approach to Multimode Multi-User Equilibrium Assignment with Elastic Demand , 1997, Transp. Sci..

[9]  Hai Yang,et al.  Optimal traffic counting locations for origin–destination matrix estimation , 1998 .

[10]  M. Ferris,et al.  Computing Wardropian equilibria in a complementarity framework , 1999 .

[11]  Sang Nguyen,et al.  A unified framework for estimating or updating origin/destination matrices from traffic counts , 1988 .

[12]  Martin L. Hazelton,et al.  Estimation of origin-destination matrices from link flows on uncongested networks , 2000 .

[13]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[14]  Martin L. Hazelton,et al.  Inference for origin–destination matrices: estimation, prediction and reconstruction , 2001 .

[15]  Hai Yang.  Heuristic algorithms for the bilevel origin-destination matrix estimation problem , 1995 .

[16]  C. B. Mcguire,et al.  Studies in the Economics of Transportation , 1958 .

[17]  Francisco G. Benitez,et al.  An approach to estimating and updating origin-destination matrices based upon traffic counts preserving the prior structure of a survey matrix , 2005 .

[18]  J. Wardrop.  ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[19]  Antonio J. Conejo,et al.  Decomposition Techniques in Mathematical Programming: Engineering and Science Applications , 2006 .

[20]  E. Cascetta.  Estimation of trip matrices from traffic counts and survey data: A generalized least squares estimator , 1984 .

[21]  M. West,et al.  Bayesian Inference on Network Traffic Using Link Count Data: Rejoinder , 1998 .

[22]  Y. Vardi,et al.  Network Tomography: Estimating Source-Destination Traffic Intensities from Link Data , 1996 .

[23]  Terry L. Friesz,et al.  Sensitivity Analysis for Equilibrium Network Flow , 1988, Transp. Sci..

[24]  Michael A. West,et al.  Bayesian Inference on Network Traffic Using Link Count Data , 1998 .

[25]  Santos Sánchez-Cambronero,et al.  Predicting traffic flow using Bayesian networks , 2008 .

[26]  Enrique Castillo,et al.  Building and Solving Mathematical Programming Models in Engineering and Science , 2001 .

[27]  M. Maher.  INFERENCES ON TRIP MATRICES FROM OBSERVATIONS ON LINK VOLUMES: A BAYESIAN STATISTICAL APPROACH , 1983 .

[28]  M Maher,et al.  ALGORITHMS FOR THE SOLUTION OF THE CONGESTED TRIP MATRIX ESTIMATION PROBLEM , 1999 .

[29]  Michael J. Maher,et al.  A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows , 2001 .

[30]  Enrique F. Castillo,et al.  Observability in linear systems of equations and inequalities: Applications , 2007, Comput. Oper. Res..

[31]  Enrique F. Castillo,et al.  The Observability Problem in Traffic Network Models , 2008, Comput. Aided Civ. Infrastructure Eng..

[32]  C. Fisk.  Some developments in equilibrium traffic assignment , 1980 .

[33]  Theodore G. Faticoni,et al.  Pure and Applied Mathematics: A Wiley‐Interscience Series of Texts, Monographs and Tracts , 2006 .

[34]  Baibing Li,et al.  Bayesian Inference for Origin-Destination Matrices of Transport Networks Using the EM Algorithm , 2005, Technometrics.

[35]  Hani S. Mahmassani,et al.  Baysian Updating of Trip Generation Parameters , 1981 .

[36]  David Watling,et al.  MAXIMUM LIKELIHOOD ESTIMATION OF AN ORIGIN-DESTINATION MATRIX FROM A PARTIAL REGISTRATION PLATE SURVEY , 1994 .