A unified framework for the performability evaluation of fault-tolerant computer systems

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