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An automatic task-to-processor mapping algorithm is analyzed in parallel systems that run over loosely coupled distributed architectures. This research is based on the TTIGHa model that allows predicting parallel application performance running over heterogeneous architectures. In particular, the heterogeneity of both processors and communications is taken into consideration. From the results obtained with the TTIGHa model, the MATEHa algorithm for task-to-processors assignment is presented and its implementation is analyzed. Experimental results working on subsets of two-cluster heterogeneous machines are presented, analyzing the resulting mapping scheme with MATEHa and two previous mapping methods: MATE and HEFT. Finally, the algorithm robustness is considered based on the variation of model parameters: inter-process communication times and processing times.