The efficient mapping of parallel tasks is essential in order to exploit the gain from parallelisation. In this work, we focus on modelling and mapping message-passing applications that are defined by the programmer with an arbitrary interaction pattern among tasks. A new model is proposed, known as TTIG (Temporal Task Interaction Graph), which captures not only computation and communication costs, but also the percentages of concurrency between tasks. From this model, a mapping strategy is developed that minimises expected execution time by properly exploiting task parallelism. The effectiveness of this approach has been proven for a real image-processing application on a cluster of PCs.