Compositionality for Markov reward chains with fast transitions

Authors:
J. Markovski;A. Sokolova;N. Trčka;E. P. De Vink
Affiliations:
Technische Universiteit Eindhoven, Formal Methods Group, AZ, Eindhoven, The Netherlands;University of Salzburg, Computational Systems Group, Salzburg, Austria;Technische Universiteit Eindhoven, Formal Methods Group, AZ, Eindhoven, The Netherlands;Technische Universiteit Eindhoven, Formal Methods Group, AZ, Eindhoven, The Netherlands
Venue:
EPEW'07 Proceedings of the 4th European performance engineering conference on Formal methods and stochastic models for performance evaluation
Year:
2007

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Abstract

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 τ -lumping and τ -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.