  We introduce the model of communicating timed automata (CTA) that extends the
classical models of finite-state processes communicating through FIFO perfect
channels and timed automata, in the sense that the finite-state processes are
replaced by timed automata, and messages inside the perfect channels are
equipped with clocks representing their ages. In addition to the standard
operations (resetting clocks, checking guards of clocks) each automaton can
either (1) append a message to the tail of a channel with an initial age or (2)
receive the message at the head of a channel if its age satisfies a set of
given constraints. In this paper, we show that the reachability problem is
undecidable even in the case of two timed automata connected by one
unidirectional timed channel if one allows global clocks (that the two automata
can check and manipulate). We prove that this undecidability still holds even
for CTA consisting of three timed automata and two unidirectional timed
channels (and without any global clock). However, the reachability problem
becomes decidable (in $\mathsf{EXPTIME}$) in the case of two automata linked
with one unidirectional timed channel and with no global clock. Finally, we
consider the bounded-context case, where in each context, only one timed
automaton is allowed to receive messages from one channel while being able to
send messages to all the other timed channels. In this case we show that the
reachability problem is decidable.
