08. Stochastic Process Algebra

08. Stochastic Process Algebra - CS4 Modelling and...

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CS4 Modelling and Simulation LN-8 8 Stochastic Process Algebra In this lecture note we consider another class of performance modelling paradigms— stochastic extensions of process algebras . Like queueing networks and stochastic Petri nets, and their variants, these formal languages can be regarded as high-level model spec- iFcation languages for low-level stochastic models. As we will see, the development of SPA has been very similar to that of SPN: in both cases an untimed formalism, used for studying the correct functional behaviour of systems, is extended by associating expo- nential delays with actions and reachability analysis is used to construct a corresponding Markov process. The advantages of SPAs are that they incorporate the attractive features of process algebras and thus bring to the area of performance modelling several attributes which are not o±ered by the existing formalisms. Perhaps the most important such fea- ture is the compositionality which is inherent in the models and can be exploited during their analysis. In this note we present some simple examples which illustrate this and several other aspects of the SPA approach to performance modelling. Several stochastic process algebras have appeared in the literature but they are all broadly similar. Here we will concentrate on PEPA (Performance Evaluation Process Algebra). 8.1 Process Algebras Process algebras are abstract languages used for the speciFcation and design of concurrent systems. The most widely used process algebras are Milner’s Calculus of Communicating Systems (CCS) and Hoare’s Communicating Sequential Processes (CSP) and the SPAs take inspiration from both these formalisms. Models in CCS and CSP have been used extensively to establish the correct behaviour of complex systems by deriving qualitative properties such as freedom from deadlock or livelock . In the process algebra approach systems are modelled as collections of entities, called agents , which execute atomic actions . These actions are the building blocks of the lan- guage and they are used to describe sequential behaviours which may run concurrently, and synchronisations or communications between them. In CCS two agents communicate when one performs an action, a say, while the other performs the complementary action a . The resulting communication action is regarded as an internal action that is invisible to the environment. Agents may proceed with their internal actions simultaneously but it is important to note that the semantics given to the language imposes an interleaving on such concurrent behaviour, i.e. it is not possible for two actions to occur simultaneously. The grammar of the language makes it possible to construct an agent which has a designated Frst action (preFx); has a choice over alternatives (choice); or has concurrent possibilities (composition).
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08. Stochastic Process Algebra - CS4 Modelling and...

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