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 convergence still holds, and analyze the error of the final common value we get for the essential case of two nodes, both theoretically and numerically. We compare this error performance

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... that of the standard consensus algorithm. For the multi-node case, we deduce fundamental properties that implicitly describe the distribution of the final value obtained. * B. Gerencsér and J. M. Hendrickx are with ICTEAM Institute, Université catholique de Louvain, Belgium balazs.gerencser@uclouvain.be and julien.hendrickx@uclouvain. In this work, we follow an alternative approach, we analyze the performance of the original push-sum algorithm in the presence of such transmission failures if no additional corrective mechanism is applied, similarly to what was done for traditional consensus in [15] . We present new tools that help understanding the nature of the resulting consensus value. Using these tools, we then derive bounds on the error in the simple case of two nodes. In addition, we perform a numerical comparison of the push-sum algorithm and the traditional consensus method, allowing to determine which is the most efficient one depending on the transmission failure rate and the error tolerance. The rest of the paper is organized as follows. In Section 2 we formally describe the push-sum algorithm. Section 3 provides the tools needed to preform our analysis. We then develop error bounds in Section 4 for two nodes. Comparison of the push-sum algorithm and traditional consensus is performed in Section 5. Conclusions and further research directions are discussed in Section 6.