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Recently a new approach to modeling cellular networks has been proposed based on the Poisson point process (PPP). Unlike the traditional, popular hexagonal grid model for the locations of base stations, the PPP model is tractable. It has been shown by Andrews et al. (in IEEE Trans Commun 59(11):3122–3134, 2011) that the hexagonal grid model provides upper bounds of the coverage probability while the PPP model gives lower bounds. In this paper, we perform a comprehensive comparison of the PPP and the hexagonal grid models with real base station deployments in urban areas worldwide provided by the open source project OpenCellID. Our simulations show that the PPP model gives upper bounds of the coverage probabilities for urban areas and is more accurate than the hexagonal grid model. In addition, we show that the Poisson cluster process is able to accurately model the base station …