Tight Steady-State Availability Bounds Using the Failure Distance Concept

Continuous-time Markov chains are commonly used for dependability modeling of repairable fault-tolerant computer systems. Realistic models of non-trivial fault-tolerant systems often have very large state spaces. An attractive approach for dealing with the largeness problem is the use of pruning methods with error bounds. Several such methods for computing steady-state availability bounds have been proposed recently. This paper presents a new method which exploits the failure distance concept to bound more efficiently the behavior in the non-generated state space. It is proved that the bounding method gives tighter bounds than previous methods. Numerical analysis shows that the new bounds can be significantly tighter.