When designing a parallel computer it is very important that it has the predicted performances. The challenge for a computer designer is to discover the minimum organization and equipement necessary to achieve given level of performance. So, the developing analythical model for characterizing and understanding the parallel system performances is of a crucial interest. In order to avoid erroneous conclusions about the behaviour of parallel system a severe mathematical formulations should be involved. In this paper we give a survey of axioms that were proposed in the literature in order to introduce a scientific approach in studing the parallel system performances. Further we shall propose a modified and reduced set of axioms based on discrete mathematical apparatus.