A Symbolic Approach to the Analysis of Multi-Formalism Markov Reward Models

Abstract

When modelling large systems, modularity is an important concept, as it aids modellers to master the complexity of their model. Moreover, employing different modelling formalisms within the same modelling project has the potential to ease the description of various parts or aspects of the overall system. In the area of performability modelling, formalisms such as stochastic reward nets, stochastic process algebras, stochastic automata, or stochastic UML state charts are often used, and several of these may be employed within one modelling project. This chapter presents an approach for efficiently constructing a symbolic representation in the form of a zero-suppressed Binary Decision Diagram (BDD), which represents the Markov Reward Model underlying a multi-formalism high-level model. In this approach, the interaction between the submodels may be established either by the sharing of state variables or by the synchronisation of common activities. It is shown that the Decision Diagram data structure and the associated algorithms enable highly efficient state space generation and different forms of analysis of the underlying Markov Reward Model (e.g. calculation of reward measures or asserting non-functional system properties by means of model checking techniques).

Self-organized Data Redundancy Management for Peer-to-Peer Storage Systems

“…Since our comparison is in terms of bandwidth costs, we only take the impulse rewards into account. The impulse reward during the time interval [t, t + Δt] is calculated as follows, see for example [21]:…”