Interval Cyclic Hypergraphs for Modeling of Transportation Systems

The paper presents mathematical foundations of a matrix description of interval cyclic hypergraphs relevant for the modeling of widespread ring transport routes such as different urban transport routes, taxi fixed-routes, airplane and rail routes, etc. Transport routes are spatially distributed systems. Thus grapho-structural modeling is a relevant mathematical tool for the simulation of such systems. The vertex set of an interval cyclic hypergraph is defined as a cyclic group. Intervals are defined as consecutive sequences of vertices in cyclic groups, i.e. sequences of vertices without gaps in correspondence with transport routes. The matrix description includes incidence, valence, adjacency matrices, Laplacians and relations which interconnect them. Laplacian is a product of incidence matrix by its conjugation; simultaneously it is a sum or difference of valence and adjacency matrices. This relation plays a controlling role for matrix manipulations in grapho-structural modeling. Both indirected and directed (oriented) complete interval cyclic hypergraphs are considered. The orientation serves for the fixation of the order of vertices in intervals. This is essential for ring transport routes. Incidence matrices of complete interval cyclic hypergraphs are circulants in contrast with incidence matrices of general complete hypergraphs. Consequently Laplacians of complete interval cyclic hypergraphs are circulants just as Laplacians of general complete hypergraphs. The circulants can be presented as polynomials from cyclic permutation matrices. The eigenvalues of circulants are efficiently calculated as the same polynomials from primitive unity roots of a suitable degree. Circulantness is very useful for mathematical analysis of ring transport routes. Some examples of applications of interval cyclic hypergraphs for modeling of urban ring transport routes are presented.


  • English

Media Info

  • Media Type: Digital/other
  • Features: Figures; References;
  • Pagination: pp 157-163
  • Monograph Title: Proceedings of Second International Conference on Traffic and Transport Engineering (ICTTE)

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Filing Info

  • Accession Number: 01600742
  • Record Type: Publication
  • ISBN: 9788691615321
  • Files: TRIS
  • Created Date: May 21 2016 2:43AM