Is ALOHA Causing Power Law Delays?

Renewed interest in ALOHA-based Medium Access Control (MAC) protocols stems from their proposed applications to wireless ad hoc and sensor networks that require distributed and low complexity channel access algorithms. In this paper, unlike in the traditional work that focused on mean value (throughput) and stability analysis, we study the distributional properties of packet transmission delays over an ALOHA channel. We discover a new phenomenon showing that a basic finite population ALOHA model with variable size (exponential) packets is characterized by power law transmission delays, possibly even resulting in zero throughput. This power law effect might be diminished, or perhaps eliminated, by reducing the variability of packets. However, we show that even a slotted (synchronized) ALOHA with packets of constant size can exhibit power law delays when the number of active users is random. From an engineering perspective, our results imply that the variability of packet sizes and number of active users need to be taken into consideration when designing robust MAC protocols, especially for ad-hoc/sensor networks where other factors, such as link failures and mobility, might further compound the problem.