Methods commonly used for estimating origin-destination (O-D) matrices can be divided into three categories: direct sample estimation, model estimation and estimation from traffic counts. In this paper a generalized least squares estimator of the O-D matrix is proposed combining direct or model estimators with traffic counts via an assignment model. The presence of measurement errors and time variability in the observed flows is explicitly considered. A special case is also presented in which the flows are assumed to be deterministically known. For the proposed estimators, means and dispersion matrices are expressed in function of the possible bias in the direct or model estimators and assignment model misspecification. The variance of the O-D matrix obtained with the generalized least squares (GLS) estimators is proved to be lower than that obtained with direct or model estimators but, because of possible biases and misspecifications, it is suggested that their performances have to be compared by using risk or generalized mean square error criteria.

Estimation of trip matrices from traffic counts and survey data: A generalized least squares estimator

In this research, we propose a methodology to develop OD matrices using mobile phone Call Detail Records (CDR) and limited traffic counts. CDR, which consist of time stamped tower locations with caller IDs, are analyzed first and trips occurring within certain time windows are used to generate tower-to-tower transient OD matrices for different time periods. These are then associated with corresponding nodes of the traffic network and converted to node-to-node transient OD matrices. The actual OD matrices are derived by scaling up these node-to-node transient OD matrices. An optimization based approach, in conjunction with a microscopic traffic simulation platform, is used to determine the scaling factors that result best matches with the observed traffic counts. The methodology is demonstrated using CDR from 2.87 million users of Dhaka, Bangladesh over a month and traffic counts from 13 key locations over 3 days of that month. The applicability of the methodology is supported by a validation study.

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Development of origin–destination matrices using mobile phone call data

Previous methods for estimating a trip matrix from traffic volume counts have used the principles of maximum entropy and minimum information. These techniques implicitly give as little weight to prior information on the trip matrix as possible. The new method proposed here is based on Bayesian statistical inference and has several advantages over these earlier approaches. It allows complete flexibility in the degree of belief placed on the prior estimate of the trip matrix and also allows for different degrees of belief in diffeent parts of the prior estimate. Furthermore under certain assumptions the method reduces to a simple updating scheme in which observations on the link flows successively modify the trip matrix. At the end of the scheme confidence intervals are available for the estimates of the trip matrix elements.

Inferences on trip matrices from observations on link volumes: a bayesian statistical approach

This paper presents an in-depth study of the methodology for estimating or updating origin-to-destination trip matrices from traffic counts. Following an analysis of the statistical foundation of the estimation and updating problems, various basic approaches are reviewed using a generic traffic assignment map. Computational issues related to specific assignment maps and estimation models for both road and transit networks are then discussed. Finally, additional insight into the relative performance of several estimators is provided by a set of test problems with varying input data.

A unified framework for estimating or updating origin/destination matrices from traffic counts

Conventional methods for estimating origin-destination (O-D) trip matrices from link traffic counts assume that route choice proportions are given constants. In a network with realistic congestion levels, this assumption does not hold. This paper shows how existing methods such as the generalized least squares technique can be integrated with an equilibrium traffic assignment in the form of a convex bilevel optimization problem. The presence of measurement errors and time variations in the observed link flows are explicitly considered. The feasibility of the model is always guaranteed without a requirement for estimating consistent link flows from counts. A solution algorithm is provided and numerical simulation experiments are implemented in investigating the model's properties. Some related problems concerning O-D matrix estimation are also discussed.

Estimation of origin-destination matrices from link traffic counts on congested networks

For a large number of applications conventional methods for estimating an origin destination matrix become too expensive to use. Two models, based on information minimisation and entropy maximisation principles, have been developed by the authors to estimate an O-D matrix from traffic counts. The models assume knowledge of the paths followed by the vehicles over the network. The models then use the traffic counts to estimate the most likely O-D matrix consistent with the link volumes available and any prior information about the trip matrix. Both models can be used to update and improve a previous O-D matrix. An algorithm to find a solution to the model is then described. The models have been tested with artificial data and performed reasonably well. Further research is being carried out to validate the models with real data.

Luis G. Willumsen

Papers

The most likely trip matrix estimated from traffic counts