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This paper investigates the on-chip stochastic communication and proposes an analytical model for computing its mean hitting time. Toward this end, we model the on-chip stochastic communication of any source-destination pair as a branching and annihilating random walk taking place on a finite mesh. The evolution of this branching process is studied via a master equation which helps us estimate the mean number of communication rounds needed to reach a destination node from a particular source node. Besides the probabilistic performance analysis, we also present experimental results for two concrete platforms and assess the potential of stochastic communication for future nanotechnologies.