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This paper presents a new LogP-based model, called LoOgGP, which allows an accurate characterization of MPI applications based on microbenchmark measurements. This new model is an extension of LogP for long messages in which both overhead and gap parameters perform a linear dependency with message size. The LoOgGP model has been fully integrated into a modelling framework to obtain statistical models of parallel applications, providing the analyst with an easy and automatic tool for LoOgGP parameter set assessment to characterize communications. The use of LoOgGP model to obtain a statistical performance model of an image deconvolution application is illustrated as a case of study.