The typical cell in anisotropic tessellations
Authors
- Hirsch, Christian
- Jahnel, Benedikt
ORCID: 0000-0002-4212-0065 - Hinsen, Alexander
- Cali, Eli
2010 Mathematics Subject Classification
- 60D05 90B15
Keywords
- Palm calculus, typical cell, Cox point process, random tessellation, anisotropy
DOI
Abstract
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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