Neveu's exchange formula for analysis of wireless networks with hotspot clusters

TL;DR

This paper introduces a new form of Neveu's exchange formula that simplifies the analysis of wireless networks with hotspot clusters by avoiding Voronoi tessellation, enhancing the tools available for spatial stochastic modeling.

Contribution

The paper presents an alternative version of Neveu's exchange formula that does not depend on Voronoi tessellation, specifically tailored for analyzing wireless networks with hotspot clusters.

Findings

New form of Neveu's exchange formula introduced

Applicable to wireless networks with hotspot clusters

Simplifies analysis by removing Voronoi tessellation dependence

Abstract

Theory of point processes, in particular Palm calculus within the stationary framework, plays a fundamental role in the analysis of spatial stochastic models of wireless communication networks. Neveu's exchange formula, which connects the respective Palm distributions for two jointly stationary point processes, is known as one of the most important results in the Palm calculus. However, its use in the analysis of wireless networks seems to be limited so far and one reason for this may be that the formula in a well-known form is based upon the Voronoi tessellation. In this paper, we present an alternative form of Neveu's exchange formula, which does not rely on the Voronoi tessellation but includes the one as a special case. We then demonstrate that our new form of the exchange formula is useful for the analysis of wireless networks with hotspot clusters modeled using cluster point processes.