  In this paper we propose two analytically tractable stochastic models of
non-slotted Aloha for Mobile Ad-hoc NETworks (MANETs): one model assumes a
static pattern of nodes while the other assumes that the pattern of nodes
varies over time. Both models feature transmitters randomly located in the
Euclidean plane, according to a Poisson point process with the receivers
randomly located at a fixed distance from the emitters. We concentrate on the
so-called outage scenario, where a successful transmission requires a
Signal-to-Interference-and-Noise Ratio (SINR) larger than a given threshold.
With Rayleigh fading and the SINR averaged over the duration of the packet
transmission, both models lead to closed form expressions for the probability
of successful transmission. We show an excellent matching of these results with
simulations. Using our models we compare the performances of non-slotted Aloha
to previously studied slotted Aloha. We observe that when the path loss is not
very strong both models, when appropriately optimized, exhibit similar
performance. For stronger path loss non-slotted Aloha performs worse than
slotted Aloha, however when the path loss exponent is equal to 4 its density of
successfully received packets is still 75% of that in the slotted scheme. This
is still much more than the 50% predicted by the well-known analysis where
simultaneous transmissions are never successful. Moreover, in any path loss
scenario, both schemes exhibit the same energy efficiency.
