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 uses 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 satisfied. The authors develop two simple MC´s for the processors and memories and solve them using a software package, called HARP. The probabilities of i processing elements (PE´s) and j memory modules (MM´s) working at any time t, denoted as Pi(t) and Pj(t), are obtained from their corresponding MC´s. The effect of the MIN is captured in the model by finding the number of switches required for the connection of i PE´s and j MM´s. A third MC is then developed for the switches to find the probability that the MIN provides the required (i×j) connection. Multiplying this term with Pi(t) and Pj(t), the probability of an (i×j) working group is obtained. The methodology is generalized to model arbitrary as well as larger size systems. Transient and steady state availabilities are computed for a variety of MIN configurations and the results are validated through simulation