AVAILABILITY EVALUATION USING DECOMPOSITION TECHNIQUE' OF MIN-CONNECTED MULTIPROCESSORS
Chita R. Das, Lei Tien, Laxmi Narayan Bhuyan · 1990
System decomposition is a novel technique for modtiling the dependability of complex systems without constructing a single-level Markov (:hain (MC). This is demonstrated in this paper for the availability computation of a class of MIN-connected multiprocessors, known as Butterfly systems. The availability model is known as task-basrd availability, where a system remains operational as long as a connected group of I processing elements (PES) and J meniory modules (MMs) is available for the execution of a task. We develop two simple M(:s for the processors and me1rioric.s and solve them using a soft,ware packagcb, called HARP. Thi.; gives the probabilities of 1. PES and j MMs working at, any time t, denoted as P,(t) and PJ(t). Thc..dfcct, of the MIN is captured in the model by finding thc niimlwr of switchcs required for the connection of z PES and .j MMs. We, then, solvc, a third MC for the switches to find thc probability t,hat thc MIN provides the required connrction. Multiplying this term with Pj(t) and P3(t), the probability of an (z Y j) working group is obtained. Using this approach, we compute the availability of 16-aode, 64-nodc, and 256-node Butterfly configurations and validate t,he results through simulation. 1. Introductjon