On the instantaneous availability and performability evaluation of fault-tolerant computer systems

The problem of evaluating the performability and instantaneous availability of gracefully degradable computer systems is considered. The key to the development of a unifying mathematical framework is the introduction of two related performability processes: 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. Using the techniques of partial differential equations, it is shown that the joint distribution of the forward performability and configuration states satisfies a linear, hyperbolic partial differential equation (PDE) running forward in time, while the performability-to-go process satisfies a similar PDE running in reverse time. The method includes nonhomogeneous Markov models of the configuration mode. A numerical method for solving the PDEs is presented and illustrated with examples. Practical implications of the reverse-time equations for the sensitivity analysis of instantaneous availability is discussed