Modelling IEEE 802.11 CSMA/CA RTS/CTS with stochastic bigraphs with sharing

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

BigraphER: rewriting and analysis engine for bigraphs

BigraphER is a suite of open-source tools providing an effi- cient implementation of rewriting, simulation, and visualisation for bigraphs, a universal formalism for modelling interacting systems that evolve in time and space and first introduced by Milner. BigraphER consists of an OCaml library that provides programming interfaces for the manipulation of bigraphs, their constituents and reaction rules, and a command-line tool capable of simulating Bigraphical Reactive Systems (BRSs) and computing their transition systems. Other features are native support for both bigraphs and bigraphs with sharing, stochastic reaction rules, rule priorities, instantiation maps, parameterised controls, predicate checking, graphical output and integration with the probabilistic model checker PRISM

Fuzzy Bigraphs: An Exercise in Fuzzy Communicating Agents

Bigraphs and their algebra is a model of concurrency. Fuzzy bigraphs are a generalization of birgraphs intended to be a model of concurrency that incorporates vagueness. More specifically, this model assumes that agents are similar, communication is not perfect, and, in general, everything is or happens to some degree.Comment: 11 pages, 3 figure

Stochastic Bigraphs

In this paper we present a stochastic semantics for Bigraphical Reactive Systems. A reduction and a labelled stochastic semantics for bigraphs are defined. As a sanity check, we prove that the two semantics are consistent with each other. We illustrate the expressiveness of the framework with an example of membrane budding in a biological system

Process algebra for event-driven runtime verification: a case study of wireless network management

Runtime verification is analysis based on information extracted from a running system. Traditionally this involves reasoning about system states, for example using trace predicates. We have been investigating runtime verification for event-driven systems and in that context we propose a higher level of abstraction can be useful, namely reasoning at the level of user-perceived system events. And when considering events, then the natural formalism for verification is a form of process algebra

Modelling and Verification of Large-Scale Sensor Network Infrastructures

Large-scale wireless sensor networks (WSN) are increasingly deployed and an open question is how they can support multiple applications. Networks and sensing devices are typically heterogeneous and evolving: topologies change, nodes drop in and out of the network, and devices are reconfigured. The key question we address is how to verify that application requirements are met, individually and collectively, and can continue to be met, in the context of large-scale, evolving network and device configurations. We define a modelling and verification framework based on Bigraphical Reactive Systems (BRS) for modelling, with bigraph patterns and temporal logic properties for specifying application requirements. The bigraph diagrammatic notation provides an intuitive representation of concepts such as hierarchies, communication, events and spatial relationships, which are fundamental to WSNs. We demonstrate modelling and verification through a real-life urban environmental monitoring case-study. A novel contribution is automated online verification using BigraphER and replay of real-life sensed data streams and network events by the Cooja network simulator. Performance results for verification of two application properties running on a WSN with up to 200 nodes indicate our framework is capable of handling WSNs of that scale

On Designing Multicore-aware Simulators for Biological Systems

The stochastic simulation of biological systems is an increasingly popular technique in bioinformatics. It often is an enlightening technique, which may however result in being computational expensive. We discuss the main opportunities to speed it up on multi-core platforms, which pose new challenges for parallelisation techniques. These opportunities are developed in two general families of solutions involving both the single simulation and a bulk of independent simulations (either replicas of derived from parameter sweep). Proposed solutions are tested on the parallelisation of the CWC simulator (Calculus of Wrapped Compartments) that is carried out according to proposed solutions by way of the FastFlow programming framework making possible fast development and efficient execution on multi-cores.Comment: 19 pages + cover pag

Bigraphs with sharing

Bigraphical Reactive Systems (BRS) were designed by Milner as a universal formalism for modelling systems that evolve in time, locality, co-locality and connectivity. But the underlying model of location (the place graph) is a forest, which means there is no straightforward representation of locations that can overlap or intersect. This occurs in many domains, for example in wireless signalling, social interactions and audio communications. Here, we define bigraphs with sharing, which solves this problem by an extension of the basic formalism: we define the place graph as a directed acyclic graph, thus allowing a natural representation of overlapping or intersecting locations. We give a complete presentation of the theory of bigraphs with sharing, including a categorical semantics, algebraic properties, and several essential procedures for computation: bigraph with sharing matching, a SAT encoding of matching, and checking a fragment of the logic BiLog. We show that matching is an instance of the NP-complete sub-graph isomorphism problem and our approach based on a SAT encoding is also efficient for standard bigraphs. We give an overview of BigraphER (Bigraph Evaluator & Rewriting), an efficient implementation of bigraphs with sharing that provides manipulation, simulation and visualisation. The matching engine is based on the SAT encoding of the matching algorithm. Examples from the 802.11 CSMA/CA RTS/CTS protocol and a network management support system illustrate the applicability of the new theory