Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks
Performance Evaluation
PEPA nets: a structured performance modelling formalism
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Structured analysis techniques for large Markov chains
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Triangular and skew-symmetric splitting method for numerical solutions of Markov chains
Computers & Mathematics with Applications
A Bootstrap Algebraic Multilevel Method for Markov Chains
SIAM Journal on Scientific Computing
| Hi-index | 0.00 |
In this paper, a new analysis approach for continuous time Markov chains (CTMCs) with a multidimensional structure is introduced. The presented solution technique employs the multidimensional structure to define aggregated CTMCs that can be analyzed more efficiently. Generator matrices of aggregated CTMCs are described in a compact form by exploiting the Kronecker structure of the generator matrix of a structured CTMC. The solution of aggregated systems is used to improve the solution of the original system. This idea of a multilevel solution is motivated by multigrid methods, which are efficient solvers for partial differential equations. The technique can be combined with different iterative solution techniques. It usually improves the convergence of these techniques significantly. Numerical results are given to illustrate that the new solution technique allows the fast and accurate analysis of very large CTMCs.