Stepwise refinement of sequence diagrams with soft real-time constraints

UML sequence diagrams and similar notations are much used to specify and analyze computer systems and their requirements. Probabilities are often essential, in particular for capturing soft real-time constraints. It is also important to be able to specify systems at different levels of abstraction. Refinement is a means to relate abstract specifications to more concrete specifications in such a way that constraints and analysis results are preserved through the transition. In order to allow soft real-time constraints to be included as an integral part of sequence diagram specifications, this paper presents an approach to extend UML 2.x sequence diagrams to capture probabilistic choice in general and soft real-time constraints in particular. The approach is supported by formal semantics and pragmatic refinement relations with mathematical properties that allow stepwise and modular development of specifications. An example focusing on communication is provided to demonstrate the language and refinement relations.