  We focus on the realizability problem of Message Sequence Graphs (MSG), i.e.
the problem whether a given MSG specification is correctly distributable among
parallel components communicating via messages. This fundamental problem of MSG
is known to be undecidable. We introduce a well motivated restricted class of
MSG, so called controllable-choice MSG, and show that all its models are
realizable and moreover it is decidable whether a given MSG model is a member
of this class. In more detail, this class of MSG specifications admits a
deadlock-free realization by overloading existing messages with additional
bounded control data. We also show that the presented class is the largest
known subclass of MSG that allows for deadlock-free realization.
