Jane Hillston

A compositional approach to performance modelling

1. Introduction 2. Background 3. Performance evaluation process algebra 4. Modelling study: multi-server multi-queue systems 5. Notions of equivalence 6. Isomorphism and weak isomorphism 7. Strong bisimilarity 8. Strong equivalence 9. Conclusions Bibliography Index.

Bio-PEPA: A framework for the modelling and analysis of biological systems

In this work we present Bio-PEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use of general kinetic laws. Bio-PEPA may be seen as an intermediate, formal, compositional representation of biological systems, on which different kinds of analyses can be carried out. Bio-PEPA is enriched with some notions of equivalence. Specifically, the isomorphism and strong bisimulation for PEPA have been considered and extended to our language. Finally, we show the translation of a biological model into the new language and we report some analysis results.

The PEPA workbench: a tool to support a process algebra-based approach to performance modelling

In this paper we present a new technique for performance modelling and a tool supporting this approach. Performance Evaluation Process Algebra (PEPA) [1] is an algebraic language which can be used to build models of computer systems which capture information about the performance of the system. The PEPA language serves two purposes as a formal description language for computer system models. The performance-related information in the model may be used to predict the performance of the system whereas the behavioural information in the model may be exploited when reasoning about the functional behaviour of the system (e.g. when finding deadlocks or when exhibiting equivalences between sub-components). In this paper we concentrate on the performance aspects of the language.

Fluid flow approximation of PEPA models

In this paper we present a novel performance analysis technique for large scale systems modelled in the stochastic process algebra PEPA. In contrast to the well-known approach of analysing via continuous time Markov chains, our underlying mathematical representation is a set of coupled ordinary differential equations (ODEs). This analysis process supports all of the comhinators of the PEPA algebra and is well suited to systems with large numbers of replicated components. The paper presents an elegant procedure for the generation of the ODEs and compares the results of this analysis with more conventional methods.

Flexible skeletal programming with eskel

We present an overview of eSkel, a library for skeletal parallel programming. eSkel aims to maximise the conceptual flexibility afforded by its component skeletons and to facilitate dynamic selection of skeleton compositions. We present simple examples which illustrate these properties, and discuss the implementation challenges which the model poses.

Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA

This paper examines the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway [5] through modelling in a Markovian process algebra, PEPA [11]. Two models of the system are presented, a reagent-centric view and a pathway-centric view. The models capture functionality at the level of subpathway, rather than at a molecular level. Each model affords a different perspective of the pathway and analysis. We demonstrate the two models to be formally equivalent using the timing-aware bisimulation defined over PEPA models and discuss the biological significance.

Specifying Performance Measures for PEPA

Stochastic process algebras such as PEPA provide ample support for the component-based construction of models. Tools compute the numerical solution of these models; however, the stochastic process algebra methodology lacks support for the specification and calculation of complex performance measures. This paper addresses that problem by presenting a performance specification language which supports high level reasoning about PEPA models, allowing the description of equilibrium (steady-state) measures. The meaning of the specification language can be made formal by examining its foundations in a stochastic modal logic. A case-study is presented to illustrate the approach.

Compositional Markovian Modelling Using a Process Algebra

We introduce a stochastic process algebra, PEPA, as a high-level modelling paradigm for continuous time Markov chains (CTMC). Process algebras are mathematical theories which model concurrent systems by their algebra and provide apparatus for reasoning about the structure and behaviour of the model. Recent extensions of these algebras, associating random variables with actions, make the models also amenable to Markovian analysis. A compositional structure is inherent in the PEPA language. As well as the clear advantages that this offers for model construction, we demonstrate how this compositionality may be exploited to reduce the state space of the CTMC. This leads to an exact aggregation based on lumpability.

PEPA Nets: A Structured Performance Modelling Formalism

In this paper we describe a formalism which uses the stochastic process algebra PEPA as the inscription language for labelled stochastic Petri nets. Viewed in another way, the net is used to provide a structure for combining related PEPA systems. The combined modelling language naturally represents such applications as mobile code systems where the PEPA terms are used to model the program code which moves between network hosts (the places in the net). We describe the implementation of a tool to support this modelling formalism and apply this to model a peer-to-peer filestore.

An efficient algorithm for aggregating PEPA models

Performance Evaluation Process Algebra (PEPA) is a formal language for performance modeling based on process algebra. It has previously been shown that, by using the process algebra apparatus, compact performance models can be derived which retain the essential behavioral characteristics of the modeled system. However, no efficient algorithm for this derivation was given. We present an efficient algorithm which recognizes and takes advantage of symmetries within the model and avoids unnecessary computation. The algorithm is illustrated by a multiprocessor example.