Despite the existence of a series of applications that demand high performance computing, there are two strong restrictions to the effective use of parallel computing applications: (1) the high costs in the environments of parallel computing (typically, clusters and parallel machines) and (2) the dedicated approach of these architectures (fact that generates a great degree of idleness of these platforms). This paper presents an architecture to provide parallel computing in traditional environments (non-dedicated networks), called MPI-QoS, which is based on the concepts of quality of service (QoS) to assure low response times necessary to this kind of computation.