The Multi Processor Periodic Resource (MPR) model has been proposed for modeling compositional real-time systems which run on a shared multi processor hardware. In this paper we extend the MPR model such that the execution of virtual processors (servers) is not assumed to be synchronized i.e., the servers can have different phases. We believe that relaxing the server synchronization requirement provides greater deal of compatibility for implementing such a compositional method on various hardware platforms. We derive the resource supply bound function of the extended MPR model using an algorithm. Furthermore, we suggest an approach to calculate an approximate supply bound function with lower computational complexity for systems where calculating their supply bound function is computationally expensive.