Modelling MAC-Layer Communications in Wireless Systems

TL;DR

This paper introduces a formal timed process calculus for modeling wireless network communications, including message broadcasting, reception, and collisions, with a proof methodology for system equivalence based on bisimulation.

Contribution

It develops a novel calculus and proof techniques for analyzing wireless network behaviors, including collision handling and external observability, with completeness results.

Findings

A formal semantics for wireless broadcast and collision modeling

A sound and complete proof method for system equivalence

Illustrative examples demonstrating the proof methodology

Abstract

We present a timed process calculus for modelling wireless networks in which individual stations broadcast and receive messages; moreover the broadcasts are subject to collisions. Based on a reduction semantics for the calculus we define a contextual equivalence to compare the external behaviour of such wireless networks. Further, we construct an extensional LTS (labelled transition system) which models the activities of stations that can be directly observed by the external environment. Standard bisimulations in this LTS provide a sound proof method for proving systems contextually equivalence. We illustrate the usefulness of the proof methodology by a series of examples. Finally we show that this proof method is also complete, for a large class of systems.