We present a real-time extension to the π-calculus and use it to study a notion of time-bounded equivalence. We introduce the notion of timed compositionality and the associated timed congruence which are useful to reason about the timed behaviour of processes under hard constraints. In addition to this meta-theory we develop an abstract machine for our calculus based on event-scheduling and establish its soundness w.r.t. the given operational semantics. We have built an implementation for a realistic language called kiltera based on this machine.