Congruence Properties for a Timed Extension of the π-Calculus

We propose equivalences and preorders with congruence properties for a timed extension of the π-calculus. We present a timed extension of syntax and basic operational semantics to the π-calculus. The derived timed bisimulation relations are shown to be non-input congruent. The timed bisimilarities equalize the bisimilar processes not only in actions but also in timing of the actions. For the purpose of modeling hard deadlines, we propose a more relaxed bisimulation, calleddelay time orderthat relates a process behaves ‘faster’ in action to a process with the same communication capability. We show that the delay time orders are non-input congruent as well where the ‘time-insensitive’ composition is allowed. We illustrate our timed extension by a simple example of a streaming server and a player client where the network configuration may change dynamically.