Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Numerical methods in Markov chain modeling
Operations Research
A multi-level solution algorithm for steady-state Markov chains
SIGMETRICS '94 Proceedings of the 1994 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
On generating a hierarchy for GSPN analysis
ACM SIGMETRICS Performance Evaluation Review - Special issue on Stochastic Petri Nets
An efficient disk-based tool for solving large Markov models
Performance Evaluation - Special issue on tools for performance evaluation
"On-the-Fly" Solution Techniques for Stochastic Petri Nets and Extensions
IEEE Transactions on Software Engineering
Using the exact state space of a Markov model to compute approximate stationary measures
Proceedings of the 2000 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Structured analysis approaches for large Markov chains
Applied Numerical Mathematics
Comparison of Partitioning Techniques for Two-Level Iterative Solvers on Large, Sparse Markov Chains
SIAM Journal on Scientific Computing
Multilevel Solutions for Structured Markov Chains
SIAM Journal on Matrix Analysis and Applications
Structured Solution of Asynchronously Communicating Stochastic Modules
IEEE Transactions on Software Engineering
Hierarchical Structuring of Superposed GSPNs
IEEE Transactions on Software Engineering
Storage Alternatives for Large Structured State Spaces
Proceedings of the 9th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
On the Exact and Approximate Analysis of Hierarchical Discrete Time Queueing Networks
MMB '95 Proceedings of the 8th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation: Quantitative Evaluation of Computing and Communication Systems
INFORMS Journal on Computing
The Möbius state-level abstract functional interface
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Adaptive decomposition and approximation for the analysis of stochastic petri nets
Performance Evaluation - Dependable systems and networks-performance and dependability symposium (DSN-PDS) 2002: Selected papers
INFORMS Journal on Computing
Approximate Computation of Transient Results for Large Markov Chains
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
PRISM 2.0: A Tool for Probabilistic Model Checking
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
SMART: The Stochastic Model checking Analyzer for Reliability and Timing
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Block SOR Preconditioned Projection Methods for Kronecker Structured Markovian Representations
SIAM Journal on Scientific Computing
Validation of Stochastic Systems: A Guide to Current Research (Lecture Notes in Computer Science)
Validation of Stochastic Systems: A Guide to Current Research (Lecture Notes in Computer Science)
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Compositionality for Markov reward chains with fast and silent transitions
Performance Evaluation
Location Prediction Based on a Sector Snapshot for Location-Based Services
Journal of Network and Systems Management
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Analysis of large and realistic Markov models suffers mainly from the so-called state space explosion. Large systems of equations have to be solved to obtain the result measures. The limiting factors of a solution are space and time. Apart from using more powerful computers for the solution, sophisticated data structures have been used for a compact storage of huge Markov chains and new efficient analysis techniques have been developed recently to exploit structure in the model for a more efficient analysis of the Markov chains. This paper gives an overview of analysis techniques based on model structure, describes the availability of these new techniques and outlines future research directions in the field.