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<p>The problem of evaluating the performability density and distribution of degradable computer systems is considered. A generalized model of performability is considered, wherein the dynamics of configuration modes are modeled as a nonhomogeneous Markov process, and the performance rate in each configuration mode can be time dependent. The key to the development of a unifying mathematical framework is the introduction of two related performability processes: the forward performability process over the interval (0,t), and the performability-to-go process over the interval (t,T), where T is the mission time. Stochastic differential equations techniques show that the joint density of the forward performability and configuration states satisfies a linear, hyperbolic partial differential equation (PDE) with time-dependent coefficients that runs forward in time, while the performability-to-go process satisfies an adjoint PDE running reverse in time. A numerical method for solving the PDEs is presented and is illustrated with examples.</p>
performability evaluation; fault-tolerant computer systems; performability density; degradable computer systems; configuration modes; nonhomogeneous Markov process; mathematical framework; forward performability process; performability-to-go; mission time; differential equations; hyperbolic partial differential equation; fault tolerant computing; Markov processes; partial differential equations; performance evaluation.
K.R. Pattipati, H.A.P. Blom, Y. Li, "A Unified Framework for the Performability Evaluation of Fault-Tolerant Computer Systems", IEEE Transactions on Computers, vol. 42, no. , pp. 312-326, March 1993, doi:10.1109/12.210174
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