Obtaining performance models, like Markov chains and queueing networks, for systems of significant complexity and magnitude is a di#cult task that is usually tackled using human intelligence and experience. This holds in particular for performance models of a highly irregular nature. In this paper we argue by means of a non-trivial example --- a plain-old telephone system (POTS) --- that a stochastic extension of process algebra can diminish these problems by permitting an automatic generation of Markov chains. We introduce a stochastic process algebra that separates the advance of time and action occurrences. For the sake of specification convenience we incorporate an elapse operator that allows the modular description of time constraints where delays are described by continuous phase-type distributions. Using this language we provide a formal specification of the POTS and show how a stochastic process of more than 10 7 states is automatically obtained from this system description. ...

In order to reason about the correctness of asynchronous circuit implementations and specifications, Dill has developed a variant of trace theory[ 1]. Tracetheory describes the behavior of an asynchronous circuit by representing its possible executions as strings called"traces". A useful relation defined in this theory is called conformance, which holds when one tracespecification can be safely substituted for another. We propose a new relation in the context of Dill's trace theory, called strong conformance. We show that this relation is capable of detecting certain errors in asynchronouscircuits that cannot bedetectedthrough conformance. Strong conformance also helps to justify circuit optimization rules whereacomponent is replaced by another component having extra capabilities (e.g.,itcan accept more inputs). The structural operators of Dill's tracetheory --- compose, rename and hide --- are shown to be monotonic with respect to strong conformance. Experiments arepresented using a modified version of Dill's tracetheory verifier which implements the check for strong conformance.