Modelling Probabilistic Wireless Networks

Abstract

Abstract. We propose a process calculus to model high level wireless systems, where the topology of a network is described by a digraph. The calculus enjoys features which are proper of wireless networks, namely broadcast communication and probabilistic behaviour.We first focus on the problem of composing wireless networks, then we present a compositional theory based on a probabilistic generalisation of the well known may-testing and must-testing preorders. Also, we define an extensional semantics for our calculus, which will be used to define both simulation and deadlock simulation preorders for wireless networks. We prove that our simulation preorder is sound with respect to the may-testing preorder; similarly, the deadlock simulation preorder is sound with respect to the musttesting preorder, for a large class of networks. We also provide a counterexample showing that completeness of the simulation preorder, with respect to the may testing one, does not hold. We conclude the paper with an application of our theory to probabilistic routing protocols.

Modelling MAC-Layer Communications in Wireless Systems

“…In [3] a calculus is proposed for describing the probabilistic behaviour of wireless networks. There is an explicit representation of the underlying network, in terms of a connectivity graph.…”

Characterising Testing Preorders for Broadcasting Distributed Systems

“…Extension of Systems Following the approach of [3] we focus on a specific class of systems and how they can be extended to obtain larger systems.…”

“…In this paper we focus on a sub-calculus of that of [3,2] in which the station code is non-probabilistic. From these papers we also borrow the (non-trivial) partial operator M > N for composing systems to form larger ones.…”

“…It can be shown that all composable systems can be generated by atomic systems, which contain only one node, using the operator >. As explained in [3,2], the composite system M > N may be viewed as N extending M by adding new stations and adding code to execute at the interface nodes of M; it may also be viewed as N blackbox testing the system M by placing probing code at its interface.…”

“…The calculus is presented in §2. In §3 we recall the theory of composition for networks of [3], upon which we define the testing preorders may , must . In §4 we explain the extensional semantics, and define both the sets of traces and deadlock traces of systems.…”