Availability evaluation of MIN-connected multiprocessors using decomposition technique

An analytical technique for the availability evaluation of multiprocessors using a multistage interconnection network (MIN) is presented. The MIN represents a Butterfly-type connection with a 4*4-switching element (SE). The novelty of this approach is that the complexity of constructing a single-level exact Markov chain (MC) is not required. By use of structural decomposition, the system is divided into three subsystems-processors, memories, and MIN. Two simple MCs are solved by using a software package, called HARP, to find the probability of i working processing elements (PEs) and j working memory modules (MMs) at time t. A second level of decomposition is then used to find the approximate number of SEs (x) required for connecting the i PEs and j MMs. A third MC is then solved to find the probability that the MIN will provide the necessary communication. The model has been validated through simulation for up to a 256-node configuration, the maximum size available for a commercial MIN-connected multiprocessor.<
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