A formal algebraic approach for the quantitative modeling of connectors in architectures

In this paper we propose an algebraic formalization of connectors in the quantitative setting in order to address the performance issues related with the architectures of component-based systems. For this, we firstly introduce a weighted Algebra of Interactions over a set of ports and a commutative and idempotent semiring. The algebra serves sufficiently for modeling well-known coordination schemes in the weighted setup. In turn, we introduce and study a weighted Algebra of Connectors over a set of ports and a commutative and idempotent semiring, which extends the weighted Algebra of Interactions with types that express two different modes of synchronization, in particular, Rendezvous and Broadcast. We show the expressiveness of the algebra by modeling several weighted connectors. Moreover, we derive two subalgebras, namely the weighted Algebra of Synchrons and of Triggers, and study their properties. Finally, we introduce a weighted congruence relation for connectors and provide conditions for proving congruence between distinct weighted connectors.