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. We 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 P_i(t) and Pj(t)₉ 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 x j) connection. Multiplying this term with P_t(t) and P_j(i), the probability of an (i x 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.