Compositional Asymmetric Cooperations for Process Algebras with Probabilities, Priorities, and Time

The modeling and analysis experience with process algebras has shown the necessity of extending them with priority, probabilistic internal/external choice, and time in order to be able to faithfully model the behavior of real systems and capture the properties of interest. An important open problem in this scenario is how to obtain semantic compositionality in the presence of all these features, to allow for an efficient analysis. Starting from a Markovian process algebra, i.e. a process algebra incorporating exponentially distributed durations, the objective of this paper is to show how to add the expressive features above while preserving compositionality. Theoretically speaking, we argue that, when abandoning the classical nondeterministic setting by considering the features above, a natural solution is to break the symmetry of the roles of the processes participating in a synchronization. We accomplish this by distinguishing between master actions -- the choice among which is carried out generatively according to their priorities/probabilities or exponentially distributed durations -- and slave actions -- the choice among which is carried out reactively according to their priorities/probabilities -- and by imposing that a master action can synchronize with slave actions only. We show that such an asymmetric cooperation mechanism is natural and easy to understand by means of the novel cooperation structure model. Technically speaking, we define EMPA_gr, a Markovian process algebra extended with probabilities, priorities, zero durations, and the generative master-reactive slaves synchronization mechanism. Then, we prove that the synchronization mechanism in EMPA_gr is correct w.r.t. the cooperation structure model, we show that the Markovian bisimulation equivalence is a congruence w.r.t. all the operators of EMPA_ as well as recursion, and we present a sound and complete axiomatization of the Markovian bisimulation equivalence for nonrecursive process terms. As far as the Markovian bisimulation equivalence is concerned, we introduce a new notion of Markovian bisimulation up to Markovian bisimulation equivalence, which improves the previous definitions given in the literature, and a new proof technique for showing congruence w.r.t. recursion in Markovian process algebras, which repairs some inaccuracies in the proofs previosly proposed in the literature.