WIAS Preprint No. 2557, (2018)

The typical cell in anisotropic tessellations


  • Hirsch, Christian
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Hinsen, Alexander
  • Cali, Eli

2010 Mathematics Subject Classification

  • 60D05 90B15


  • Palm calculus, typical cell, Cox point process, random tessellation, anisotropy




The typical cell is a key concept for stochastic-geometry based modeling in communication networks, as it provides a rigorous framework for describing properties of a serving zone associated with a component selected at random in a large network. We consider a setting where network components are located on a large street network. While earlier investigations were restricted to street systems without preferred directions, in this paper we derive the distribution of the typical cell in Manhattan-type systems characterized by a pattern of horizontal and vertical streets. We explain how the mathematical description can be turned into a simulation algorithm and provide numerical results uncovering novel effects when compared to classical isotropic networks.

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