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Compositionality for Markov reward chains with fast transitions. (English) Zbl 1149.68320

Wolter, Katinka (ed.), Formal methods and stochastic models for performance evaluation. Fourth European performance engineering workshop, EPEW 2007, Berlin, Germany, September 27–28, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-75210-3/pbk). Lecture Notes in Computer Science 4748, 18-32 (2007).
Summary: A parallel composition is defined for Markov reward chains with fast transitions and for discontinuous Markov reward chains. In this setting, compositionality with respect to the relevant aggregation preorders is established. For Markov reward chains with fast transitions the preorders are \(\tau \)-lumping and \(\tau \)-reduction. Discontinuous Markov reward chains are ‘limits’ of Markov reward chains with fast transitions, and have related notions of lumping and reduction. In total, four compositionality results are shown. In addition, the two parallel operators are related by a continuity property.
For the entire collection see [Zbl 1142.68012].

MSC:

68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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