Spatial Birth-Death Wireless Networks

Abstract

We propose and study a novel continuous space-time model for wireless networks which takes into account the stochastic interactions in both space through interference and in time due to randomness in traffic. Our model consists of an interacting particle birth-death dynamics incorporating information-theoretic spectrum sharing. Roughly speaking, particles (or more generally wireless links) arrive according to a Poisson Point Process on space-time, and stay for a duration governed by the local configuration of points present and then exit the network after completion of a file transfer. We analyze this particle dynamics to derive an explicit condition for time ergodicity (i.e. stability) which is tight. We also prove that when the dynamics is ergodic, the steady-state point process of links (or particles) exhibits a form statistical clustering. Based on the clustering, we propose a conjecture which we leverage to derive approximations, bounds and asymptotics on performance characteristics such as delay and mean number of links per unit-space in the stationary regime. The mathematical analysis is combined with discrete event simulation to study the performance of this type of networks.

Submitted to IEEE Transactions on Information Theory. Corrected some typos from an earlier version and made some minor modifications to the introduction

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• Structural properties of proportional fairness: stability and insensitivity
• Diffusion approximation for a processor sharing queue in heavy traffic
• Spatial birth and death processes as solutions of stochastic equations
• Existence and spatial limit theorems for lattice and continuum particle systems

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