Modelling Real-Time Behaviour with an Interval Time Calculus

We present an extension of Milner's CCS [Mil89] with interval time. The notion of time is introduced in terms of time intervals which specify when actions are allowed to occur. We define three equivalences: strong, timed weak, and weak bisimulation equivalence. The strong bisimulation equivalence refines the corresponding relation in CCS by requiring strongly bisimilar processes to have the same timing behavior, the weak bisimulation equivalence is in essence the weak bisimulation equivalence of CCS, while the timed weak equivalence lays strictly between strong and weak equivalence, since it in addition to weak bisimularity also considers the timing of observable actions.