ACM Transactions on Computer Systems (TOCS)
ACM Transactions on Mathematical Software (TOMS)
Stochastic Automata Network of Modeling Parallel Systems
IEEE Transactions on Software Engineering
A compositional approach to performance modelling
A compositional approach to performance modelling
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
An Efficient Kronecker Representation for PEPA Models
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
Efficient Reachability Set Generation and Storage Using Decision Diagrams
Proceedings of the 20th International Conference on Application and Theory of Petri Nets
Superposed Generalized Stochastic Petri Nets: Definition and Efficient Solution
Proceedings of the 15th International Conference on Application and Theory of Petri Nets
INFORMS Journal on Computing
Efficient Solution of GSPNs Using Canonical Matrix Diagrams
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
On the benefits of using functional transitions and Kronecker algebra
Performance Evaluation
Modular Analytical Performance Models for Ad Hoc Wireless Networks
WIOPT '05 Proceedings of the Third International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
Formal techniques for performance analysis: blending SAN and PEPA
Formal Aspects of Computing
Exploiting interleaving semantics in symbolic state-space generation
Formal Methods in System Design
PEPS2007 - Stochastic Automata Networks Software Tool
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
Split: a flexible and efficient algorithm to vector-descriptor product
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Reachable State Space Generation for Structured Models which Use Functional Transitions
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
GTAexpress: A Software Package to Handle Kronecker Descriptors
QEST '09 Proceedings of the 2009 Sixth International Conference on the Quantitative Evaluation of Systems
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Performance Models For Master/Slave Parallel Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
Analytical Modeling for Operating System Schedulers on NUMA Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Kronecker products and shuffle algebra
IEEE Transactions on Computers
Performance evaluation of OpenMP-based algorithms for handling Kronecker descriptors
Journal of Parallel and Distributed Computing
A Structured Stochastic Model for Prediction of Geological Stratal Stacking Patterns
Electronic Notes in Theoretical Computer Science (ENTCS)
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The description of large state spaces through stochastic structured modeling formalisms like stochastic Petri nets, stochastic automata networks and performance evaluation process algebra usually represent the infinitesimal generator of the underlying Markov chain as a Kronecker descriptor instead of a single large sparse matrix. The best known algorithms used to compute iterative solutions of such structured models are: the pure sparse solution approach, an algorithm that can be very time efficient, and almost always memory prohibitive; the Shuffle algorithm which performs the product of a descriptor by a probability vector with a very impressive memory efficiency; and a newer option that offers a trade-off between time and memory savings, the Split algorithm. This paper presents a comparison of these algorithms solving some examples of structured Kronecker represented models in order to numerically illustrate the gains achieved considering each model's characteristics.