Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets
Performance Evaluation
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
IEEE Transactions on Software Engineering
Turning back time in Markovian process algebra
Theoretical Computer Science
Performance Model Interchange Format (PMIF 2.0): XML Definition and Implementation
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Separable equilibrium state probabilities via time reversal in Markovian process algebra
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
A general performance model interchange format
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Deficiency Zero Petri Nets and Product Form
PETRI NETS '09 Proceedings of the 30th International Conference on Applications and Theory of Petri Nets
Element Based Semantics in Multi Formalism Performance Models
MASCOTS '10 Proceedings of the 2010 IEEE International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems
Synthesis and Analysis of Product-form Petri Nets
Fundamenta Informaticae - Applications and Theory of Petri Nets and Other Models of Concurrency, 2011
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Stochastic Petri nets (SPNs) provide a convenient, diagrammatic description of concurrent systems, such as computer and communication networks, and can represent quantitative (or performance) aspects such as mean response times and probability of failure. Such models can be supported by performance modelling interchange formats (PMIFs), facilitating sharing and model interoperability. We propose a hierarchical method for constructing a large class of Petri nets, which preserves efficient product-form solutions when they exist. This scalable approach greatly improves the efficiency of finding steady state probabilities in a wide range of SPNs, making much larger SPNs feasible. An existing PMIF is extended by including a new type of node that describes a particular type of small Petri net, called a "building block", the synchronisation primitives for which can be used to specify task-spawning and task-gathering, whilst retaining product-form solutions under specified conditions. When there is no product-form, the whole network is translated into a Petri net and solved directly - either by a Markov chain solver or by simulation. The extended PMIF and the proposed methodology are applied to a model of a computer system with RAID storage.