  The push-sum algorithm allows distributed computing of the average on a
directed graph, and is particularly relevant when one is restricted to one-way
and/or asynchronous communications. We investigate its behavior in the presence
of unreliable communication channels where messages can be lost. We show that
exponential convergence still holds and deduce fundamental properties that
implicitly describe the distribution of the final value obtained. We analyze
the error of the final common value we get for the essential case of two nodes,
both theoretically and numerically. We provide performance comparison with a
standard consensus algorithm.
