  Time-Sensitive Distributed Systems (TSDS), such as applications using
autonomous drones, achieve goals under possible environment interference (\eg,
winds). Moreover, goals are often specified using explicit time constraints
which must be satisfied by the system \emph{perpetually}. For example, drones
carrying out the surveillance of some area must always have \emph{recent
pictures}, \ie, at most $M$ time units old, of some strategic locations. This
paper proposes a Multiset Rewriting language with explicit time for specifying
and analysing TSDSes. We introduce two properties, \emph{realizability} (some
trace is good) and \emph{survivability} (where, in addition, all admissible
traces are good). A good trace is an infinite trace in which goals are
perpetually satisfied. We propose a class of systems called \emph{progressive
timed systems} (PTS), where intuitively only a finite number of actions can be
carried out in a bounded time period. We prove that for this class of systems
both the realizability and the survivability problems are PSPACE-complete.
Furthermore, if we impose a bound on time (as in bounded model-checking), we
show that for PTS, realizability becomes NP-complete, while survivability is in
the $\Delta_2^p$ class of the polynomial hierarchy. Finally, we demonstrate
that the rewriting logic system Maude can be used to automate time bounded
verification of PTS.
