'Closed interval process algebra' versus 'Interval process algebra'

In this paper we extend the theory of processes with durational actions tha t has been proposed in [1,2] to describe and reason about the performance o f systems. We associate basic actions with lower and upper time bounds, tha t specify their possible different durations. Depending on how the lower an d upper time bounds are fixed, eager actions (those which happen as soon as they can), lazy actions (those which can wait arbitrarily long before firi ng) as well as patient actions (those which can be delayed for a while) can be modelled. Processes are equipped with a (soft) operational semantics wh ich is consistent with the original one and is well-timed (observation trac es are ordered with respect to time). The bisimulation-based equivalence de fined on top of the new operational semantics, timed equivalence, turns out to be a congruence and, within the lazy fragment of the algebra, refines u ntimed equivalences. Decidability and automatic checking of timed equivalen ce are also stated by resorting to a finite alternative characterization wh ich is amenable to an automatic treatment by using standard algorithms. The relationships with other timed calculi and equivalences proposed in the li terature are also established.