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Distance Distribution in Convex n-Gons: Mathematical Framework and Wireless Networking Applications

Wireless Personal Communications volume 71, pages 1487–1503 (2013)Cite this article

Abstract

The performance of a wireless network is related to the Euclidean distance distribution between the communication nodes, which in turn depends on network geometry. In this paper, we provide an analytical framework for the description of distance statistics in convex polygons with arbitrary number and length of sides. Simulation results validate the formulation. Comparisons with models in the literature indicate that our approach is a generalization of previous works. Representative examples show the merits of the proposal and assess its applicability in wireless networking. The main contribution of this work is the consideration of polygonal-shaped networks. The obtained formulation reduces the complexity and computational cost of the modeling and simulation of wireless systems and it is more convenient than other approaches when network planning considers n-gonal coverage areas. Moreover, it provides adequate results for the calculation of distance-dependent parameters and performance metrics of wireless networks.

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Authors and Affiliations

  1. Radio Communications Laboratory, Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Konstantinos B. Baltzis

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  1. Konstantinos B. Baltzis
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Correspondence to Konstantinos B. Baltzis.

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Baltzis, K.B. Distance Distribution in Convex n-Gons: Mathematical Framework and Wireless Networking Applications. Wireless Pers Commun 71, 1487–1503 (2013). https://doi.org/10.1007/s11277-012-0887-9

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  • DOI: https://doi.org/10.1007/s11277-012-0887-9

Keywords

  • Euclidean distance
  • Polygon
  • Distance-related metrics
  • Routing protocol
  • Voronoi diagram
  • Wireless network

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