A Timed calculus of wireless systems

We propose a timed broadcasting process calculus for wireless systems where time-consuming communications are exposed to 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 deter- ministic; (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. We use our calculus to model and study MAC-layer protocols with a special emphasis on collisions and security. 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 laws.