In the distributed processing area, mapping and scheduling are very important issues in order to exploit the gain from parallelization. The generation of efficient static mapping techniques implies a previous modelling phase of the parallel application as a task graph, which properly reflects its temporal behaviour. In this paper we use a new model, the Temporal Task Interaction Graph (TTIG), which explicitly captures the temporal behaviour of program tasks; and we evaluate the advantages that derive from the use of the TTIG model in task allocation. Experimentation was performed in a current PVM environment, for a set of synthetic graphs which exhibit different ratios of computation/ communication cost (coarse-grain, medium-grain). The execution times when these programs were mapped using the information contained in the TTIG model, were compared with the times obtained using the two following mapping alternatives: (a) PVM default scheme and, (b) mapping strategy based on the classical model TIG (Task Interaction Graph). The results confirm that with the TTIG model, better assignments are obtained, providing improvements of up to 49% compared with the PVM assignments and up to 30% compared with TIG assignments.