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Quantitative Modelling with Process Algebras

Stochastic process algebras, providing high-level descriptions of dynamic systems, amenable to rigorous mathematical analysis through formal semantics.

The PEPA project began in Edinburgh in 1991 and has developed a modelling language and associated tools to predict the performance of software and hardware systems.  The PEPA language (Performance Evaluation Process Algebra) is a compact modelling language which models systems as compositions of sequential components which performance timed activities either individually or in cooperation with other components.  PEPA models are analysed by compilation into Continuous-time Markov Chains (CTMCs) or other mathematical structures.

Research projects on the language include extending the software tools which support it, and improving their analysis capabilities, and applying the language to modelling real-world performance problems in hardware and software systems.  For example, two topics of particular interest currently are development of sophisticated techniques for interrogating models and guiding analysis to explore scientific questions about the system, and analysis techniques to investigate the power-performance trade-off in large, flexible systems such as those found in cloud computing.

 Bio-PEPA is a closely related which has been specifically designed for modelling biochemical reactions, motivated by problems in systems biology.  It has been used to model a variety of intracellular biological processes including circadian rhythms in plants and algi, and rRNA synthesis.  However, it has also found applications in other domains such as crowd dynamics.  Unlike PEPA, Bio-PEPA models adaptive behaviour through functional rates and incorporates representation of the spatial organisation of a system and how it impacts the dynamics of behaviour.  Research projects on Bio-PEPA include extending the language to have a better representation of binding sites, investigating the analysis and interrogation techniques which can be applied to models, and developing verification techniques to ensure the quality of models, particularly for users who are not familiar with formal languages.  Here again there is scope for research on the efficient implementation of tools, particularly for example on visualisation of results, and on case studies exploring the capabilities of the language.

Prospective Supervisors

Jane Hillston

Stephen Gilmore


Further information

PEPA language



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