ACM Transactions on Computer Systems (TOCS)
Communicating sequential processes
Communicating sequential processes
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Numerical transient analysis of Markov models
Computers and Operations Research
Distributed algorithms and protocols
Distributed algorithms and protocols
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Design and validation of computer protocols
Design and validation of computer protocols
SIAM Journal on Scientific and Statistical Computing
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
A theoretical overview of Krylov subspace methods
Applied Numerical Mathematics - Special issue on iterative methods for linear equations
An efficient disk-based tool for solving large Markov models
Performance Evaluation - Special issue on tools for performance evaluation
Hypergraph-Partitioning-Based Decomposition for Parallel Sparse-Matrix Vector Multiplication
IEEE Transactions on Parallel and Distributed Systems
A probabilistic dynamic technique for the distributed generation of very large state spaces
Performance Evaluation - Special issue on modelling techniques and tools for performance evaluation
Space/time trade-offs in hash coding with allowable errors
Communications of the ACM
Passage time distributions in large Markov chains
SIGMETRICS '02 Proceedings of the 2002 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Communication and Concurrency
Out-of-Core Solution of Large Linear Systems of Equations Arising from Stochastic Modelling
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
An analysis of bistate hashing
Proceedings of the Fifteenth IFIP WG6.1 International Symposium on Protocol Specification, Testing and Verification XV
Towards Performance Evaluation with General Distributions in Process Algebras
CONCUR '98 Proceedings of the 9th International Conference on Concurrency Theory
Improved probabilistic verification by hash compaction
CHARME '95 Proceedings of the IFIP WG 10.5 Advanced Research Working Conference on Correct Hardware Design and Verification Methods
Reliable Hashing without Collosion Detection
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
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
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
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
On Observability in Timed Continuous Petri Net Systems
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Queueing Networks and Markov Chains
Queueing Networks and Markov Chains
Fluid Flow Approximation of PEPA models
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
EXPLODE: a lightweight, general system for finding serious storage system errors
OSDI '06 Proceedings of the 7th symposium on Operating systems design and implementation
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Stochastic performance models provide a powerful way of capturing and analysing the behaviour of complex concurrent systems. Traditionally, performance measures for these models are derived by generating and then analysing a (semi-)Markov chain corresponding to the model's behaviour at the state-transition level. However, and especially when analysing industrial-scale systems, workstation memory and compute power is often overwhelmed by the sheer number of states. This chapter explores an array of techniques for analysing stochastic performance models with large state spaces. We concentrate on explicit techniques suitable for unstructured state spaces and show how memory and run time requirements can be reduced using a combination of probabilistic algorithms, disk-based solution techniques and communication-efficient parallelism based on hypergraph-partitioning. We apply these methods to different kinds of performance analysis, including steady-state and passage-time analysis, and demonstrate them on case study examples.