A timed calculus for wireless systems

We propose a timed process calculus for wireless systems exposed to communication collisions. The operational semantics of our calculus is given in terms of a labelled transition system. The calculus enjoys a number of desirable time properties such as (i) time determinism: the passage of time is deterministic; (ii) patience: devices will wait indefinitely until they can communicate; (iii) maximal progress: data transmissions cannot be delayed, they must occur as soon as a possibility for communication arises. As a case study we use our calculus to model the Carrier Sense Multiple Access (CSMA) scheme.The main behavioural equality of our calculus is a timed variant of barbed congruence, a standard branching-time and contextually-defined program equivalence. As an efficient proof method for timed barbed congruence we define a labelled bisimilarity. We then apply our bisimulation proof-technique to prove a number of algebraic properties.