  In this paper we study the distributed average consensus problem in
multi-agent systems with directed communication links that are subject to
quantized information flow. Specifically, we present and analyze a distributed
averaging algorithm which operates exclusively with quantized values (i.e., the
information stored, processed and exchanged between neighboring agents is
subject to deterministic uniform quantization) and relies on event-driven
updates (e.g., to reduce energy consumption, communication bandwidth, network
congestion, and/or processor usage). The main idea of the proposed algorithm is
that each node (i) models its initial state as two quantized fractions which
have numerators equal to the node's initial state and denominators equal to
one, and (ii) transmits one fraction randomly while it keeps the other stored.
Then, every time it receives one or more fractions, it averages their
numerators with the numerator of the fraction it stored, and then transmits
them to randomly selected out-neighbors. We characterize the properties of the
proposed distributed algorithm and show that its execution, on any static and
strongly connected digraph, allows each agent to reach in finite time a fixed
state that is equal (within one quantisation level) to the average of the
initial states. We extend the operation of the algorithm to achieve finite-time
convergence in the presence of a dynamic directed communication topology
subject to some connectivity conditions. Finally, we provide examples to
illustrate the operation, performance, and potential advantages of the proposed
algorithm. We compare against state-of-the-art quantized average consensus
algorithms and show that our algorithm's convergence speed significantly
outperforms most existing protocols.
