On Modeling Low-Power Wireless Protocols Based on Synchronous Packet Transmissions

Mathematical models play a pivotal role in understanding and designing advanced low-power wireless systems. However, the distributed and uncoordinated operation of traditional multi-hop low-power wireless protocols greatly complicates their accurate modeling. This is mainly because these protocols build and maintain substantial network state to cope with the dynamics of low-power wireless links. Recent protocols depart from this design by leveraging synchronous transmissions (ST), whereby multiple nodes simultaneously transmit towards the same receiver, as opposed to pair wise link-based transmissions (LT). ST improve the one-hop packet reliability to an extent that efficient multi-hop protocols with little network state are feasible. This paper studies whether ST also enable simple yet accurate modeling of these protocols. Our contribution to this end is two-fold. First, we show, through experiments on a 139-node test bed, that characterizing packet receptions and losses as a sequence of independent and identically distributed (i.i.d.) Bernoulli trials-a common assumption in protocol modeling but often illegitimate for LT-is largely valid for ST. We then show how this finding simplifies the modeling of a recent ST-based protocol, by deriving (i) sufficient conditions for probabilistic guarantees on the end-to-end packet reliability, and (ii) a Markovian model to estimate the long-term energy consumption. Validation using test bed experiments confirms that our simple models are also highly accurate, for example, the model error in energy against real measurements is 0.25%, a figure never reported before in the related literature.