On Dependability Evaluation of Mesh Connected Multiprocessors*

Analytical techniques for reliability and availability prediction of mesh connected systems are proposed in this paper. The models are based on the submesh requirements. First, a reliability model is proposed assuming that a submesh can be always recognized if it exits. Analysis of the linear consecutive n-out-of-N system is extended using an expanding row/column technique to evaluate the submesh reliability. An alternative approach called row folding is also discussed. Due to the high complexity involved in computing the exact reliability, both of these techniques use approximation to estimate lower bounds. Next, the submesh reliability is computed based on two diierent allocation policies, known as the two-dimensional buddy system (TDBS), and the frame sliding (FS). The model with the TDBS is further extended to estimate the reliability of multiple working submeshes which is useful in a multiuser environment. Availability analysis for a submesh of the required size is conducted using a Markov chain (MC). State truncation is used to reduce the computation time, and the MC is solved using HARP. Validation of the analytical models is done through extensive simulation. Issues, such as, reliability comparison based on allocation policies, and methods for improving system reliability are addressed using the analytical models.