  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.
