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The objective of the paper is to establish a computable upper bound for thealmost sure convergence rate for a class of ratio consensus algorithms definedvia column-stochastic matrices. Our result extends the works of Iutzeler et al.(2013) on similar bounds that have been obtained in a more restrictive setupwith limited conclusions. The present paper complements the results ofGerencs\'er and Gerencs\'er (2021), identifying the exact almost sureconvergence rate of a wide class of ratio consensus algorithms in terms of aspectral gap, which is, however, not computable in general. The upper boundprovided in the paper will be compared to the actual rate of almost sureconvergence experimentally on a range of modulated random geographic graphswith random local interactions.

Computable convergence rate bound for ratio consensus algorithms