A sequence diagram sounds like a convenient way to try to represent the
duration of an activity, but I think there are some subtler issues
involved.  Another way to look at your scenario is to say that you are
trying to track two changes of state in your Worker instance, from not
working to working and from working to not working.  Also, is the Worker
still in the working state when he sends the Completed message, or is he
out of the working state?  Philosophically, I would say he is in the
non-working state, which means the Completed message should begin its own
focus of control.

As has been pointed out, asynchronous activity is difficult to interpret on
a sequence diagram.  That is because focus of control in a sequence diagram
isn't meant to depict chronological duration.  For example, when your
Worker sends the Completed message, this may start a chain of events in
which the Worker isn't involved.  Perhaps these take two pages of sequence
diagram to complete.  In the meantime, the instant after the Worker sends
the Completed message, he starts the GoHome activity.  Because you are
dealing with asynchronous activity, it means he doesn't have to wait until
the other two pages worth of activity is completed until he goes home.
Therefore, GoHome would again begin its own focus of control, but you can't
interpret the distance between Completed and GoHome as time.  (If the
Worker couldn't GoHome until all of the ancillary Completed activities had
occurred, then GoHome should be in the same focus of control as Completed.)
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