Abstract
In this paper, we consider the problem of evaluating the performability density and distribution of degradable computer systems. 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: forward performability process over the interval [ O , t ] , and the performability-to-go process over the interval [t, TI, where T is the mission time. Using the techniques of stochastic differential equations, we 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. The concept of performability-to-go allows us to subsume previous results on moment recursions and performability evaluation. A numerical method for solving the PDE’s is presented and is illustrated with examples.
Original language | English |
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Article number | 0018-9340/93 |
Pages (from-to) | 312-326 |
Number of pages | 15 |
Journal | IEEE Transactions on Computers |
Volume | 42 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1993 |
Externally published | Yes |
Keywords
- Adjoint equations, availability, fault tolerance, hyperbolic partial differential equations, Markov reward models, nonhomogenous Markov processes, numerical method of lines, performability, performability-to-go