An Availability Model for MIN-Based Multiprocessors

System decomposition is a novel technique for modeling the dependability of complex systems without constructing a single-level Markov Chain(MC). This is demonstrated in this paper for the availability computation of a class of multiprocessors that use 4 4 switching elements for the multistage interconnection network (MIN). The availability model is known as task-based availability, where a system is considered operational as long as the task requirements are satissed. We develop two simple MCs for the processors and memories and solve them using a software package, called HARP. The probabilities of i processing elements(PEs) and j memory modules(MMs) working at any time t, denoted as P i (t) and P j (t), are obtained from their corresponding MCs. The eeect of the MIN is captured in the model by nding the number of switches required for the connection of i PEs and j MMs. A third MC is then developed for the switches to nd the probability that the MIN provides the required (i j) connection. Multiplying this term with P i (t) and P j (t), the probability of an (i j) working group is obtained. The methodology is generalized to model arbitrary as well as larger size systems. Using this approach the transient and steady state availability are computed for a variety of MIN conngurations and the results are validated through simulation.