Stochastic Analysis of Non-slotted Aloha in Wireless Ad-Hoc Networks

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.Comment: accepted for IEEE Infocom 201

A New Phase Transition for Local Delays in MANETs

We consider Mobile Ad-hoc Network (MANET) with transmitters located according to a Poisson point in the Euclidean plane, slotted Aloha Medium Access (MAC) protocol and the so-called outage scenario, where a successful transmission requires a Signal-to-Interference-and-Noise (SINR) larger than some threshold. We analyze the local delays in such a network, namely the number of times slots required for nodes to transmit a packet to their prescribed next-hop receivers. The analysis depends very much on the receiver scenario and on the variability of the fading. In most cases, each node has finite-mean geometric random delay and thus a positive next hop throughput. However, the spatial (or large population) averaging of these individual finite mean-delays leads to infinite values in several practical cases, including the Rayleigh fading and positive thermal noise case. In some cases it exhibits an interesting phase transition phenomenon where the spatial average is finite when certain model parameters are below a threshold and infinite above. We call this phenomenon, contention phase transition. We argue that the spatial average of the mean local delays is infinite primarily because of the outage logic, where one transmits full packets at time slots when the receiver is covered at the required SINR and where one wastes all the other time slots. This results in the "RESTART" mechanism, which in turn explains why we have infinite spatial average. Adaptive coding offers a nice way of breaking the outage/RESTART logic. We show examples where the average delays are finite in the adaptive coding case, whereas they are infinite in the outage case.Comment: accepted for IEEE Infocom 201

Interference in spatial non-slotted Aloha networks

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 to 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 slotted Aloha, which has almost exclusively been previously studied in the same context of mobile ad-hoc networks