On Properties of Quantized Consensus in Layered Sensor Networks

In this paper, we study properties of distributed consensus in layered sensor networks of the multi-layer multi-group (MLMG) structure. We show that properly designed MLMG networks maintain decentralized communication, whereas show the advantage of centralized structures. In particular, they require less number of transmissions required to reach consensus. This feature is critical for efficient distributed computing in large-scale sensor network applications. For typical classes of MLMG networks, we mathematically characterize the reduced number of transmissions compared to equivalent egalitarian decentralized structures of the same consensus dynamics. This explicit characterization based on simple graphical characteristics of MLMG structures permits an efficient design of large-scale network structures to meet desired performance requirements. In addition, we characterize the asymptotic and transient properties of consensus in MLMG networks of limited channel rates, using the probabilistic quantization schemes.