Analysing reward measures of LARES performability models by discontinuous Markov chains

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 continuoustime 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.