Deriving the upper bound of the number of sensors required to know all link flows in a traffic network

  • Enrique Castillo /
  • Aida Calvino /
  • Jose Maria Menendez /
  • Pilar Jimenez /
  • Ana Rivas
Journal ar
IEEE Transactions on Intelligent Transportation Systems
  • Volumen: 14
  • Número: 2
  • Fecha: 18 enero 2013
  • Páginas: 761-771
  • ISSN: 15249050
  • Tipo de fuente: Revista
  • DOI: 10.1109/TITS.2012.2233474
  • Tipo de documento: Artículo
It is demonstrated that the minimum number of sensors required to know all link flows in a traffic network can be determined only if path information is available. However, not all paths need to be enumerated but, at most, a small subset defining the rank rw of the link-path incidence matrix {\bf W}. If this rank for a reduced subset of paths is already m - n, where m and n are the number of links and noncentroid nodes, respectively, we can conclude that m - n sensors are sufficient. It is also shown that the formulas providing the dependent link flows in terms of the independent link flows can be obtained by the node-based or path-based approaches with the same results only when r-{w} = m - n. Finally, an algorithm to obtain the small subsets of linearly independent path vectors is given. The methods are shown by a parallel network example and the Ciudad Real and Cuenca networks, for which the savings in link counts with respect to the m - n bound are larger than 16%. The corresponding savings in path enumeration are larger than 80%. © 2000-2011 IEEE.

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