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

Abstract

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.

A method of reasoning about PEPA models proceeds by considering the derivation graph obtained from the model using the underlying operational semantics of the PEPA language. The derivation graph is systematically reduced to a form where it can be treated as the state transition diagram of the underlying stochastic (in fact, Markovian) process. From this can be obtained the infinitesimal generator matrix of the Markov process. A steady state probability distribution for the system can then be obtained, if it exists.

We have implemented a prototype tool which supports this methodology from the initial checking of the well-formedness of the PEPA model through the creation of the state transition diagrams to the calculation of performance measures based on the infinitesimal generator matrix. The tool is implemented in Standard ML [2] and provides an interface to the Maple Symbolic Algebra package [3] for the solution of matrix equations.