PEPA

Performance Evaluation Process Algebra (PEPA) is a stochastic process algebra designed for modelling computer and communication systems introduced by Jane Hillston in the 1990s. The language extends classical process algebras such as Milner's CCS and Hoare's CSP by introducing probabilistic branching and timing of transitions.
Rates are drawn from the exponential distribution and PEPA models are finite-state and so give rise to a stochastic process, specifically a continuous-time Markov process (CTMC). Thus the language can be used to study quantitative properties of models of computer and communication systems such as throughput, utilisation and response time as well as qualitative properties such as freedom from deadlock. The language is formally defined using a structured operational semantics in the style invented by Gordon Plotkin.
As with most process algebras, PEPA is a parsimonious language. It has only four combinators, "prefix", "choice", "co-operation" and "hiding". Prefix is the basic building block of a sequential component: the process ("a", "r")."P" performs activity "a" at rate "r" before evolving to behave as component "P". Choice sets up a competition between two possible alternatives: in the process ("a", "r")."P" + ("b", "s")."Q" either "a" wins the race (and the process subsequently behaves as "P") or "b" wins the race (and the process subsequently behaves as "Q").
The co-operation operator requires the two "co-operands" to join for those activities which are specified in the co-operation set: in the process "P" < "a", "b"> "Q" the processes "P" and "Q" must co-operate on activities "a" and "b", but any other activities may be performed independently. The reversed compound agent theorem gives a set of sufficient conditions for a co-operation to have a product form stationary distribution.
Finally, the process "P"/{"a"} hides the activity "a" from view (and prevents other processes from joining with it).
Syntax.
Given a set of action names, the set of PEPA processes is defined by the following BNF grammar:
The parts of the syntax are, in the order given above