Abstract:
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Markov models are commonly used to asses the
dependability/performability of fault-tolerant systems. Computation of many dependability/performability measures for
repairable fault-tolerant systems requires the transient analysis of irreducible Markov models. Examples of such measures are the unavailability at time t and the expected interval unavailability
at time t. Randomization (also called uniformization) is a well-known Markov transient analysis method and has good properties: numerical stability, well-controlled computation error, and ability to specify the computation error in advance. However, the randomization method is computationally expensive when
the model is stiff, as is the case for Markov models of repairable fault-tolerant systems when the mission time of interest is large.
Steady-state detection is a technique recently proposed to speedup randomization when the model is irreducible. This paper points out that another method, regenerative randomization, which
has the same good properties as randomization, also covers irreducible models, and compares, for the important class of irreducible failure/repair models with exponential failure and repair time distributions and repair in every state with failed components, the efficiency of the regenerative randomization method with that of randomization with steady-state detection.
In the frequent case in which the initial state is the state without failed components the regenerative randomization method can be
faster than randomization with steady-state detection, specially when the model is large and the failure rates are much smaller
than the repair rates. For other initial probability distributions, the regenerative randomization method seems to perform worse
than randomization with steady-state detection. |