Dependable Computing for Critical Applications 3 pp 137-160 | Cite as

# On the Transient Analysis of Stiff Markov Chains

## Abstract

Dependability and performability analysis commonly requires the transient analysis of Markov chains. Because most of these models involve rates of different orders of magnitude, they lead to *stiff* Markov chains, which are ill-conditioned in a computational sense for conventional numerical methods. In this paper the well-known randomization technique is adapted to cope with a special class of stiff models. Then we present a class of models wich remain computational intractable. This leads to an appropriate new characterization of stiff Markov chains. For this model class the recently proposed implicit ODE-solvers are also computational infeasible, if they use iterative numerical techniques. A modified step size control and iterative aggregation/disaggregation techniques are proposed to improve the solver performance. The composite usage of both techniques yields large computational gains, especially for higher order methods.

## Keywords

Algebraic System Transient Analysis Ordinary Differential Equation Stiffness Index Continuous Time Markov Chain## Preview

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