Dimension Reduction for OriginDestination Flow Estimation: Blind Estimation Made Possible
This paper studies the problem of estimating origindestination (OD) flows from link flows. As the number of link flows is typically much less than that of OD flows, the inverse problem is severely illposed and hence prior information is required to recover the ground truth. The basic approach in t... Full description
Main Author:  Xia, Jingyuan 
Other Authors:  Dai, Wei , Polak, John , Bierlaire, Michel 
Format:  Electronic Article 
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Quelle:  Cornell University 
ID:  Arxiv ID: 1810.06077 
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recordid:  arxiv1810.06077 
title:  Dimension Reduction for OriginDestination Flow Estimation: Blind Estimation Made Possible 
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description:  This paper studies the problem of estimating origindestination (OD) flows from link flows. As the number of link flows is typically much less than that of OD flows, the inverse problem is severely illposed and hence prior information is required to recover the ground truth. The basic approach in the literature relies on a forward model where the so called traffic assignment matrix maps OD flows to link flows. Due to the illposedness of the problem, prior information on the assignment matrix and OD flows are typically needed. The main contributions of this paper include a dimension reduction of the inquired flows from $O(n^2)$ to $O(n)$, and a demonstration that for the first time the ground truth OD flows can be uniquely identified with no or little prior information. To cope with the illposedness due to the large number of unknowns, a new forward model is developed which does not involve OD flows directly but is built upon the flows characterized only by their origins, henceforth referred as Oflows. The new model preserves all the OD information and more importantly reduces the dimension of the inverse problem substantially. A GaussSeidel method is deployed to solve the inverse problem, and a necessary condition for the uniqueness of the solution is proved. Simulations demonstrate that blind estimation where no prior information is available is possible for some network settings. Some challenging network settings are identified and discussed, where a remedy based on temporal patterns of the Oflows is developed and numerically shown effective. 
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source:  Cornell University 
identifier:  Arxiv ID: 1810.06077 
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