The performance of the MPI's collective communications is critical in most MPI-based applications. A general algorithm for a given collective communication operation may not give good performance on all systems due to the di®erences in architectures, network parameters and the storage capacity of the underlying MPI implementation. Hence, collective communications have to be tuned for the system on which they will be executed. In order to determine the optimum parameters of col- lective communications on a given system in a time-e±cient manner, the collective communications need to be modeled e±ciently. In this paper, we discuss various techniques for modeling collective communications. We also discuss a dynamic topology method that uses the tuned static topology shape, but re-orders the logical addresses to compensate for changing run time variations.