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Non-planar hole-generated networks and link flow observability based on link counters

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  • Castillo, Enrique
  • Calviño, Aida
  • Lo, Hong K.
  • Menéndez, José María
  • Grande, Zacarías

Abstract

The concepts of hole, cycle added link and non-planar hole-generated network are introduced for the first time and used to determine (a) the immediate solution of the node conservation equations in terms of hole and cycle added vectors, and (b) the paths as linear combinations of hole vectors. Two equivalent formulas to obtain the number of links to be observed for complete link observability in non-planar hole-generated networks are given in terms of the numbers of links, nodes, holes, cycle added links and centroid node types. These formulas are applicable without any limitation in the number of centroids and possible link connections. Some simple methods are given to obtain first the maximum number of linearly independent (l.i.) paths and next a minimum set of links to be counted in order to get observability of all link flows. It is demonstrated that the number of l.i. paths in a non-planar hole-generated network coincides with the number of holes and cycle added links in the network and that any path can be obtained by linear combinations of the vectors associated with the hole and cycle added links. The methods are illustrated by their application to several networks.

Suggested Citation

  • Castillo, Enrique & Calviño, Aida & Lo, Hong K. & Menéndez, José María & Grande, Zacarías, 2014. "Non-planar hole-generated networks and link flow observability based on link counters," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 239-261.
    • Handle: RePEc:eee:transb:v:68:y:2014:i:c:p:239-261
    DOI: 10.1016/j.trb.2014.06.015
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    Cited by:

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    9. Zhu, Ning & Fu, Chenyi & Zhang, Xuanyi & Ma, Shoufeng, 2022. "A network sensor location problem for link flow observability and estimation," European Journal of Operational Research, Elsevier, vol. 300(2), pages 428-448.
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