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In a previous work, we introduced an input/output variant of stochasticautomata (IOSA) that, once the model is closed (i.e., all synchronizations areresolved), the resulting automaton is fully stochastic, that is, it does notcontain non-deterministic choices. However, such variant is not sufficientlyversatile for compositional modelling. In this article, we extend IOSA withurgent actions. This extension greatly increases the modularization of themodels, allowing to take better advantage on compositionality than itspredecessor. However, this extension introduces non-determinism even in closedmodels. We first show that confluent models are weakly deterministic in thesense that, regardless the resolution of the non-determinism, the stochasticbehaviour is the same. In addition, we provide sufficient conditions to ensurethat a network of interacting IOSAs is confluent without the need to obtain thecomposed IOSA.

Input/Output Stochastic Automata with Urgency: Confluence and weak determinism