L1-minimization method for link flow correction

Penghang Yin University of California, Los Angeles Zhe Sun University of California, Irvine Wen-Long Jin University of California, Irvine Jack Xin University of California, Irvine

Information Theory mathscidoc:1802.19001

Transportation Research Part B: Methodological, (104), 398-408, 2017
A computational method, based on l1-minimization, is proposed for the problem of link flow correction, when the available traffic flow data on many links in a road network are inconsistent with respect to the flow conservation law. Without extra information, the problem is generally ill-posed when a large portion of the link sensors are unhealthy. It is possible, however, to correct the corrupted link flows accurately with the proposed method under a recoverability condition if there are only a few bad sensors which are located at certain links. We analytically identify the links that are robust to miscounts and relate them to the geometric structure of the traffic network by introducing the recoverability concept and an algorithm for computing it. The recoverability condition for corrupted links is simply the associated recoverability being greater than 1. In a more realistic setting, besides the unhealthy link sensors, small measurement noises may be present at the other sensors. Under the same recoverability condition, our method guarantees to give an estimated traffic flow fairly close to the ground-truth data and leads to a bound for the correction error. Both synthetic and real-world examples are provided to demonstrate the effectiveness of the proposed method.
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@inproceedings{penghang2017l1-minimization,
  title={l1-minimization method for link flow correction},
  author={Penghang Yin, Zhe Sun, Wen-Long Jin, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180214111048224167925},
  booktitle={Transportation Research Part B: Methodological},
  number={104},
  pages={398-408},
  year={2017},
}
Penghang Yin, Zhe Sun, Wen-Long Jin, and Jack Xin. l1-minimization method for link flow correction. 2017. In Transportation Research Part B: Methodological. pp.398-408. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180214111048224167925.
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