Stochastic process algebras as a tool for performance and dependability modelling

Abstract

The stochastic process-algebra modelling paradigm has been introduced recently as an extension of classical process algebras with timing information aiming mainly at the integration of functional design with quantitative analysis of computer systems. Time is represented by exponentially distributed random variables that are assigned to each activity in the model. Thus, the semantic model of a stochastic process-algebra model can easily be transformed into a continuous time Markov chain which is suitable for computing performance measures as well as dependability measures. The main problem that one encounters frequently in Markov based modelling is the problem of having to solve a huge and stiff Markov chain. In dependability modelling, largeness is caused by lots of detailed and sometimes surplus information stored in the high level model. Stiff Markov chains result when one uses performance related activities together with reliability events in the same model. Various methods to tackle these problems are known, among them the concept of lumpability and decomposition techniques. Recent results in the area of stochastic process algebras have shown that their theoretical foundations can be related to these concepts. This makes it possible to provide access to these powerful techniques to modellers without requiring a very deeply technical knowledge. >