Markovian Processes Go Algebra

We propose a calculus MPA for reasoning about random behaviour through time. In contrast to classical calculi each atomic action is supposed to happen after a delay that is characterized by a certain exponentially distributed random variable. The operational semantics of the calculus deenes markovian labelled transition systems as a combination of classical action-oriented transition systems and markovian processes, especially continuous time markov chains. This model allows to calculate performance measures (e.g. response times), as well as purely functional statements (e.g. occurences of deadlocks). In order to reeect diierent behavioural aspects we deene a hierarchy of bisimulation equivalences and show that they are all congruences. Finally we present syntactic laws characterizing markovian bisimulation equivalence, our central notion of equivalence , and show that these laws form a sound and complete axiomatization for nite processes.