Time-Sensitive Distributed Systems (TSDS), such as applications using autonomous drones, achieve goals under possible environment interference (e.g., winds). Moreover, goals are often specified using explicit time constraints which must be satisfied by the system perpetually. For example, drones carrying out the surveillance of some area must always have recent pictures, i.e., at most M time units old, of some strategic locations. We propose a Multiset Rewriting language with explicit time for specifying and analysing TSDSes. We introduce two properties, realizability (some trace is good) and survivability (where, in addition, all admissible traces are good). A good trace is an infinite trace in which goals are perpetually satisfied. The transition to properties over infinite traces leads to many challenges as one can easily fall into undecidability fragments of verification problems. The main challenge is to identify the syntatical conditions on specifications so that the survivability and feasibility problems fall into a decidable fragment, and at the same time, that interesting examples can be specified. Also, the notion that a system satisfies a property perpetually implies that the desired property should be valid at all time instances independent of environment interference. Another issue is that systems should not be allowed to perform an unbounded number of actions in a single time instance, a problem similar to the Zeno paradox. We propose a class of systems called progressive timed systems (PTS), where intuitively only a finite number of actions can be carried out in a bounded time period. We define a language for specifying realizability and suvivability properties which allows the specification of many interesting problems in TSDS. 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. |