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This Letter, for the first time, proposes the look-back-upon tree recurrence (LTR) method based on the Poisson statistics for discrete time to predict the performance of Geiger-mode avalanche photodiodes with a short dead time. The results of the proposed method correspond to the results of previous methods for diverse input fluxes. The LTR method possesses very low time and space complexity to allow for the real-time analysis of the Geiger-mode avalanche photodiodes' performance over the entire ranges of dead time and input diversity.