Compositional Theories of Qualitative and Quantitative Behaviour

The integrated modelling and analysis of functional and non-functional aspects of system behaviour is one of the important challenges in the field of formal methods today. Our ever-increasing dependence upon of all sorts of critical applications of networked and/or embedded systems, often including sophisticated multi-media features, lends this intellectual challenge also great practical relevance. In this talk we will report on work in this area in the past decade or so on the use of techniques from so-called formal methods in the area of performance modelling and analysis, and in particular on the theory of stochastic process algebra (SPA) and its application. Traditional performance models like Markov chains and queueing networks are widely accepted as simple but effective models in different areas, yet they lack the notion of hierarchical system (de)composition that has proved so useful for conquering the complexity of systems in the domain of funtional system properties. Compositional, hierarchical description and analysis of functional system behaviour is the domain process algebra [24,3,17]. It offers a mathematically well-elaborated framework for reasoning about the structure and behaviour of reactive and distributed systems in a compositional way, including abstraction mechanisms that allow for the treatment of system components as black boxes, encapsulating their internal structure. Process algebras are typically equipped with a formally defined structured operational semantics (SOS [26]) that maps process algebra terms onto labelled transition systems in a compositional manner. Such labelled transition systems consist of a set of states and a transition relation that describes how the system evolves from one state to another. These transitions are labelled with action names that represent the (inter)actions that may cause the transitions to occur. Such transition systems can be visualised by drawing states as nodes of a graph and transitions as directed edges (labelled with action names) between them. The labelled transition model is very close to the usual representation of Markov chains as transition systems or automata. Also there system states are connected