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<p>System decomposition is a novel technique for modeling the dependability of complexsystems without constructing a single-level Markov Chain (MC). This is demonstrated inthis paper for the availability computation of a class of multiprocessors that uses 4*4switching elements for the multistage interconnection network (MIN). The availabilitymodel is known as task-based availability, where a system is considered operational aslong as the task requirements are satisfied. The authors develop two simple MC's for theprocessors and memories and solve them using a software package, called HARP. Theprobabilities 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 then validated through simulation.</p>
Index Termsavailability model; MIN-based multiprocessors; multistage interconnection network;task-based availability; software package; HARP; processing elements; memory modules; steady state availabilities; transient availabilities; simulation; Markov processes; multiprocessor interconnection networks

L. Tien, L. Bhuyan, P. Mohapatra and C. Das, "An Availability Model for MIN-Based Multiprocessors," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 1118-1129, 1993.
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