Computation of Bounds for Transient Measures of Large Rewarded Markov Models using Regenerative Randomization

Abstract

In this paper we generalize a method (called regenerative randomization) for the transient solution of continuous time Markov models. The generalized method allows to compute two transient measures (the expected transient reward rate and the expected averaged reward rate) for rewarded continuous time Markov models with a structure covering bounding models which are useful when a complete, exact model has unmanageable size. The method has the same good properties as the well-known (standard) randomization method: numerical stability, well-controlled computation error, and ability to specify the computation error in advance, and, for large enough models and long enough times, is significantly faster than the standard randomization method. The method requires the selection of a regenerative state and its performance depends on that selection. For a class of models, class C', including typical failure/repair models with exponential failure and repair time distributions and repair in every state with failed components, a natural selection for the regenerative state exists, and results are available assessing approximately the performance of the method for that natural selection in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be significantly faster than standard randomization for models in that class. The potentially superior e6ciency ofthe regenerative randomization method compared to standard randomization for models not in class C' is illustrated using a large performability model of a fault-tolerant multiprocessor system.