For asynchronous and open distributed systems, dynamicity, openness, and stringent quality of service requirements post grand challenges to model and develop such systems. The Actor-Role-Coordinator (ARC) model was previously proposed to address these challenges. The role concept in the model attends to the dynamicity and openness issues by providing abstractions of actor behaviors. In this paper, we focus on coordinating actors and roles through message manipulations based on synchronous event-based timing constraints. In addition, different types of timing constraints are generalized into a semiring-based constraint structure; and the all-pairs extremal paths algorithm on closed semirings is applied to derive the most stringent constraints which are logical implications of the original set of constraints. The derived implicit constraints are further used to test constraint inclusions and decide intersections between feasible regions of timing constraint sets. The integration of the ARC model and the semiring-based timing constraint models is prototyped through Maude, a rewriting logic language. We further use the approach to solve the Restaurant for Dining Philosophers problem and illustrate the expressiveness of the ARC and the semiring-based timing constraint models for exogenous and composable coordination of open systems.