On the Transient Analysis of Stiff Markov Chains

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.