Laplace Functional Ordering of Point Processes in Large-scale Wireless Networks

TL;DR

This paper introduces Laplace functional ordering for point processes to compare wireless network deployments, showing it preserves under various operations and helps evaluate performance metrics.

Contribution

It demonstrates that Laplace functional ordering is preserved under key operations and can compare network performance metrics without explicit formulas.

Findings

Ordering is preserved under marking, thinning, clustering, superposition, translation.

Can compare coverage, rate, resource allocation metrics.

Simulations support analytical results.

Abstract

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless networks. It is shown that the ordering of point processes is preserved under independent operations such as marking, thinning, clustering, superposition, and random translation. Laplace functional ordering can be used to establish comparisons of several performance metrics such as coverage probability, achievable rate, and resource allocation even when closed form expressions of such metrics are unavailable. Applications in several network scenarios are also provided where tradeoffs between coverage and interference as well as fairness and peakyness are studied. Monte-Carlo simulations are used to supplement our analytical results.