  The notion of quiescence - the absence of outputs - is vital in both
behavioural modelling and testing theory. Although the need for quiescence was
already recognised in the 90s, it has only been treated as a second-class
citizen thus far. This paper moves quiescence into the foreground and
introduces the notion of quiescent transition systems (QTSs): an extension of
regular input-output transition systems (IOTSs) in which quiescence is
represented explicitly, via quiescent transitions. Four carefully crafted rules
on the use of quiescent transitions ensure that our QTSs naturally capture
quiescent behaviour.
  We present the building blocks for a comprehensive theory on QTSs supporting
parallel composition, action hiding and determinisation. In particular, we
prove that these operations preserve all the aforementioned rules.
Additionally, we provide a way to transform existing IOTSs into QTSs, allowing
even IOTSs as input that already contain some quiescent transitions. As an
important application, we show how our QTS framework simplifies the fundamental
model-based testing theory formalised around ioco.
