IEEE Transactions on Computers - Special issue on fault-tolerant computing
Passage time distributions in large Markov chains
SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Model-Checking Algorithms for Continuous-Time Markov Chains
IEEE Transactions on Software Engineering
QBDs with Marked Time Epochs: a Framework for Transient Performance Measures
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Model checking infinite-state markov chains
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
CSL model checking algorithms for QBDs
Theoretical Computer Science
Performability assessment by model checking of Markov reward models
Formal Methods in System Design
CSL model checking algorithms for infinite-state structured Markov chains
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
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A large variety of computer and communication systems can be modeled adequately as infinite-state continuous-time Markov chains (CTMCs). A highly structured class of such infinite-state CTMCs is the class of Quasi-Birth-Death processes (QBDs), on which we focus in this paper. We present an efficient variant of uniformization for computing the transient probability Vi,j(t) of being in each state j of the QBD for any possible initial state i at time t. Note that both the set of starting states and the set of goal states have infinite size. All the probabilities Vi,j(t) are needed in the context of probabilistic model checking. The key idea of our algorithm is to split the infinite set of starting states into a finite part and an infinite (repeating) part. The transient probabilities for the infinite part are then computed using the new notion of representatives. We present the required data structures and algorithm, as well as an application-dependent optimal stopping criterion. In a simple case study we show the feasibility of our approach, as well as the efficiency gain due to the optimal stopping criterion.