Abstract
Abstract Stochastic bigraphical reactive systems (SBRS) is a recent formalism for modelling systems that evolve in time and space. However, the underlying spatial model is based on sets of trees and thus cannot represent spatial locations that are shared among several entities in a simple or intuitive way. We adopt an extension of the formalism, SBRS with sharing , in which the topology is modelled by a directed acyclic graph structure. We give an overview of SBRS with sharing, we extend it with rule priorities, and then use it to develop a model of the 802.11 CSMA/CA RTS/CTS protocol with exponential backoff, for an arbitrary network topology with possibly overlapping signals. The model uses sharing to model overlapping connectedness areas, instantaneous prioritised rules for deterministic computations, and stochastic rules with exponential reaction rates to model constant and uniformly distributed timeouts and constant transmission times. Equivalence classes of model states modulo instantaneous reactions yield states in a CTMC that can be analysed using the model checker PRISM. We illustrate the model on a simple example wireless network with three overlapping signals and we present some example quantitative properties.
Highlights
Systems of mobile devices and wireless networks evolve in both time and space
Stochastic bigraphical reactive systems (SBRS) [Mil[09], KMT08] is a recent formalism for modelling the temporal and spatial evolution of computation: it should be ideally suited to this domain
We have adopted SBRS with sharing to exploit a locality model based on Directed Acyclic Graphs (DAG) and we illustrated the extended formalism with a model of the IEEE 802.11 Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) RTS/CTS protocol
Summary
Systems of mobile devices and wireless networks evolve in both time and space. Stochastic bigraphical reactive systems (SBRS) [Mil[09], KMT08] is a recent formalism for modelling the temporal and spatial evolution of computation: it should be ideally suited to this domain. The authors assume a fixed network topology consisting of two senders and two receivers In their model there is exactly one shared signal, and each station can sense any other station. The model we present here differs in the following significant ways: support for arbitrary network topologies, and explicit representation of potentially overlapping wireless signals for all the stations in the network. These features are essential to represent networks in which two or more stations transmit to the same receiver and they cannot sense each other, causing a transmission collision.
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