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Performance Evaluation Process Algebra (PEPA) is astochasticprocess algebra designed for modelling computer and communication systems introduced byJane Hillston in the 1990s.^[1] The language extends classical process algebras such asMilner'sCCS andHoare'sCSP by introducing probabilistic branching and timing of transitions.

Rates are drawn from theexponential distribution and PEPA models are finite-state and so give rise to astochastic process, specifically acontinuous-time Markov process (CTMC). Thus the language can be used to study quantitative properties of models of computer and communication systems such asthroughput, utilisation andresponse time as well as qualitative properties such as freedom fromdeadlock. The language is formally defined using a structuredoperational semantics in the style invented byGordon Plotkin.

As with most process algebras, PEPA is a parsimonious language. It has only four combinators,prefix,choice,co-operation andhiding. Prefix is the basic building block of a sequential component: the process (a,r).P performs activitya at rater before evolving to behave as componentP. Choice sets up a competition between two possible alternatives: in the process (a,r).P + (b,s).Q eithera wins the race (and the process subsequently behaves asP) orb wins the race (and the process subsequently behaves asQ).

The co-operation operator requires the two "co-operands" to join for those activities which are specified in the co-operation set: in the processP <a,b>Q the processesP andQ must co-operate on activitiesa andb, but any other activities may be performed independently. Thereversed compound agent theorem gives a set of sufficient conditions for a co-operation to have aproduct form stationary distribution.

Finally, the processP/{a} hides the activitya from view (and prevents other processes from joining with it).

Given a set of action names, the set of PEPA processes is defined by the followingBNF grammar:

${\displaystyle P::=(a,\lambda ).P|P+Q|P\stackrel{▹◃}{L}Q|P/L|A}$

The parts of the syntax are, in the order given above

action

the process${\displaystyle (a,\lambda ).P}$ can perform an actiona at rate${\displaystyle \lambda }$ and continue as the processP.

choice

the processP+Q may behave as either the processP or the processQ.

cooperation

processesP andQ exist simultaneously and behave independently for actions whose names do not appear inL. For actions whose names appear inL, the action must be carried out jointly and a race condition determines the time this takes.

hiding

the processP behaves as usual for action names not inL, and performs a silent action${\displaystyle \tau }$ for action names that appear inL.

process identifier

write${\displaystyle A\stackrel{\underset{\mathrm{d}\mathrm{e}\mathrm{f}}{}}{=}P}$ to use the identifierA to refer to the processP.

• PEPA Plug-in^[2] forEclipse^[3]
• ipc: the imperial PEPA compiler^[4][5]
• GPAnalyser^[6] for fluid analysis of massively parallel systems^[7]

• PEPA: Performance Evaluation Process Algebra

• Process calculi
• Theoretical computer science

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