Topics in matrix analysis
Computing Poisson probabilities
Communications of the ACM
Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
The uniformed power method for transient solutions of Markov processes
Computers and Operations Research
Error-minimizing Krylov subspace methods
SIAM Journal on Scientific Computing
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
A numerical study of large sparse matrix exponentials arising in Markov chains
Computational Statistics & Data Analysis
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
Model Checking Dependability Attributes of Wireless Group Communication
DSN '04 Proceedings of the 2004 International Conference on Dependable Systems and Networks
Safe On-The-Fly Steady-State Detection for Time-Bounded Reachability
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Sliding Window Abstraction for Infinite Markov Chains
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Efficient Probabilistic Model Checking on General Purpose Graphics Processors
Proceedings of the 16th International SPIN Workshop on Model Checking Software
Quantitative Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
The Ins and Outs of the Probabilistic Model Checker MRMC
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
A numerical aggregation algorithm for the enzyme-catalyzed substrate conversion
CMSB'06 Proceedings of the 2006 international conference on Computational Methods in Systems Biology
Symmetry reduction for probabilistic model checking
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
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The predominant technique for computing the transient distribution of a Continuous Time Markov Chain (CTMC) exploits uniformization, which is known to be stable and efficient for non-stiff to mildly-stiff CTMCs. On stiff CTMCs however, uniformization suffers from severe performance degradation. In this paper, we report on our observations and analysis of an alternative technique using Krylov subspaces. We implemented a Krylov-based extension to MRMC (Markov Reward Model Checker) and conducted extensive experiments on five case studies from different application domains. The results reveal that the Krylov-based technique is an order of magnitude faster on stiff CTMCs.