Title: Analysing reward measures of LARES performability models by discontinuous Markov chains

Authors: Alexander Gouberman; Martin Riedl; Markus Siegle

Addresses: Institut für Technische Informatik, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85579 Neubiberg, Germany ' Institut für Technische Informatik, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85579 Neubiberg, Germany ' Institut für Technische Informatik, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85579 Neubiberg, Germany

Abstract: This paper presents a new method for specifying and analysing Markovian performability models. An extension of the LARES modelling language is considered which offers both delayed and immediate transitions, as well as rate and impulse rewards on whose basis different types of reward measures can be defined. The paper describes the evaluation path, starting from the modular and hierarchical LARES description and leading via a flat labelled transition system to the underlying stochastic model. The latter is a continuous-time Markov chain with fast transitions which, by taking the limit of the fast transition rates, can be interpreted as a CTMC with stochastic discontinuities. Finally, by continuisation of impulse rewards and an aggregation process, a standard Markov reward model is obtained.

Keywords: performability; Markov reward model; MRM; impulse reward; CTMC with stochastic discontinuities; immediate transition; LARES.

DOI: 10.1504/IJCCBS.2017.084062

International Journal of Critical Computer-Based Systems, 2017 Vol.7 No.1, pp.22 - 42

Published online: 09 May 2017 *

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