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A compositional, collaborative performance pipeline

Ashok Argent-Katwala

PhD Thesis
Department of Computing, Imperial College London, University of London
November, 2006

Realistic performance models of complex systems are typically too large to design or analyse directly. At the conceptual level, people have difficulty understanding and modelling systems; they also find it hard to pose meaningful queries about them. At the computational level, large systems cannot be analysed by considering their global state spaces.

We can ease these problems with a compositional approach to performance modelling throughout the design and analysis process. Higher level models help people structure their problems, and can be converted into appropriate formalisms for solution. Publishing models, queries and results allows a broad community to collaborate and solve bigger problems. Automatically identifying and applying appropriate compositional techniques enables large systems to be solved.

This thesis provides a separable approach at each stage along the performance analysis pipeline – in modelling, in posing performance questions, and in quantitatively answering those questions. First, we introduce the PEPA Queues formalism – combining queueing networks with a stochastic process algebra to describe localised behaviour – to aid building higher level models. Then we provide an open networked store of models, queries and results via a database-backed Semantic Web service, PEPAdb. We propose action-centric queries for asking a variety of performance questions in a uniform fashion. Queries are composed with the model being measured, so can be reused across different models.

PEPAdb also forms the foundation for our tool that derives many steady-state product-form results automatically in a single, coherent formalism using the Reversed Compound Agent Theorem (RCAT). We automatically detect when we can apply RCAT to generate a full description of the reverse process. Using symbolic manipulation of model specifications that have a regular, possibly infinite, state space, we use RCAT to calculate the steady-state probabilities of the whole model in terms of those of its cooperating components. We illustrate the combination of all our tools in several case studies, exploiting the compositional approach throughout.

Process Algebra
Stochastic Modelling
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