Direct methods for sparse matrices
Direct methods for sparse matrices
A decomposition approach for stochastic reward net models
Performance Evaluation
Computer architecture (2nd ed.): a quantitative approach
Computer architecture (2nd ed.): a quantitative approach
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
A survey of out-of-core algorithms in numerical linear algebra
External memory algorithms
Multi-Terminal Binary Decision Diagrams: An Efficient DataStructure for Matrix Representation
Formal Methods in System Design
Advances in Model Representations
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
An Efficient Disk-Based Tool for Solving Very Large Markov Models
Proceedings of the 9th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
PRISM: Probabilistic Symbolic Model Checker
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
A Data Structure for the Efficient Kronecker Solution of GSPNs
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
On the Use of Model Checking Techniques for Dependability Evaluation
SRDS '00 Proceedings of the 19th IEEE Symposium on Reliable Distributed Systems
ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS
ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS
Efficient Solution of GSPNs Using Canonical Matrix Diagrams
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
Markovian analysis of large finite state machines
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Journal of Parallel and Distributed Computing
Distributed disk-based algorithms for model checking very large Markov chains
Formal Methods in System Design
Tackling large state spaces in performance modelling
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Improving GPU sparse matrix-vector multiplication for probabilistic model checking
SPIN'12 Proceedings of the 19th international conference on Model Checking Software
Self-adaptive containers: building resource-efficient applications with low programmer overhead
Proceedings of the 8th International Symposium on Software Engineering for Adaptive and Self-Managing Systems
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Many physical or computer systems can be modelled as Markov chains. A range of solution techniques exist to address the state-space explosion problem, encountered while analysing such Markov models. However, numerical solution of these Markov chains is impeded by the need to store the probability vector(s) explicitly in the main memory. In this paper, we extend the earlier out-of-core methods for the numerical solution of large Markov chains and introduce an algorithm which uses a disk to hold the probability vector as well as the matrix. We give experimental results of the implementation of the algorithm for a Kanban manufacturing system and a flexible manufacturing system. Next, we describe how the algorithm can be modified to exploit sparsity structure of a model, leading to better performance. We discuss two models, a cyclic server polling system and a workstation cluster system, in this context and present results for the polling models. We also introduce a new sparse matrix storage format which can provide 30% or more saving over conventional schemes.