  We consider the average-consensus problem in a multi-node network of finite
size. Communication between nodes is modeled by a sequence of directed signals
with arbitrary communication delays. Four distributed algorithms that achieve
average-consensus are proposed. Necessary and sufficient communication
conditions are given for each algorithm to achieve average-consensus. Resource
costs for each algorithm are derived based on the number of scalar values that
are required for communication and storage at each node. Numerical examples are
provided to illustrate the empirical convergence rate of the four algorithms in
comparison with a well-known "gossip" algorithm as well as a randomized
information spreading algorithm when assuming a fully connected random graph
with instantaneous communication.
