  We analyze a class of distributed quantized consen- sus algorithms for
arbitrary networks. In the initial setting, each node in the network has an
integer value. Nodes exchange their current estimate of the mean value in the
network, and then update their estimation by communicating with their neighbors
in a limited capacity channel in an asynchronous clock setting. Eventually, all
nodes reach consensus with quantized precision. We start the analysis with a
special case of a distributed binary voting algorithm, then proceed to the
expected convergence time for the general quantized consensus algorithm
proposed by Kashyap et al. We use the theory of electric networks, random
walks, and couplings of Markov chains to derive an O(N^3log N) upper bound for
the expected convergence time on an arbitrary graph of size N, improving on the
state of art bound of O(N^4logN) for binary consensus and O(N^5) for quantized
consensus algorithms. Our result is not dependent on graph topology.
Simulations on special graphs such as star networks, line graphs, lollipop
graphs, and Erd\"os-R\'enyi random graphs are performed to validate the
analysis. This work has applications to load balancing, coordination of
autonomous agents, estimation and detection, decision-making networks,
peer-to-peer systems, etc.
