  In this paper we propose two analytically tractable stochastic-geometric
models of interference in ad-hoc networks using pure (non-slotted) Aloha as the
medium access. In contrast the slotted model, the interference in pure Aloha
may vary during the transmission of a tagged packet. We develop closed form
expressions for the Laplace transform of the empirical average of the
interference experienced during the transmission of a typical packet. Both
models assume a power-law path-loss function with arbitrarily distributed
fading and feature configurations of transmitters randomly located in the
Euclidean plane according to a Poisson point process. Depending on the model,
these configurations vary over time or are static. We apply our analysis of the
interference to study the Signal-to-Interference-and-Noise Ratio (SINR) outage
probability for a typical transmission in pure Aloha. The results are used to
compare the performance of non-slotted Aloha to the slotted one, which has
almost exclusively been previously studied in the same context of mobile ad-hoc
networks.
