172,635 research outputs found
Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations
We propose diffusion-like equations with time and space fractional
derivatives of the distributed order for the kinetic description of anomalous
diffusion and relaxation phenomena, whose diffusion exponent varies with time
and which, correspondingly, can not be viewed as self-affine random processes
possessing a unique Hurst exponent. We prove the positivity of the solutions of
the proposed equations and establish the relation to the Continuous Time Random
Walk theory. We show that the distributed order time fractional diffusion
equation describes the sub-diffusion random process which is subordinated to
the Wiener process and whose diffusion exponent diminishes in time (retarding
sub-diffusion) leading to superslow diffusion, for which the square
displacement grows logarithmically in time. We also demonstrate that the
distributed order space fractional diffusion equation describes super-diffusion
phenomena when the diffusion exponent grows in time (accelerating
super-diffusion).Comment: 11 pages, LaTe
Correlated continuous-time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics
Standard continuous time random walk (CTRW) models are renewal processes in
the sense that at each jump a new, independent pair of jump length and waiting
time are chosen. Globally, anomalous diffusion emerges through action of the
generalized central limit theorem leading to scale-free forms of the jump
length or waiting time distributions. Here we present a modified version of
recently proposed correlated CTRW processes, where we incorporate a power-law
correlated noise on the level of both jump length and waiting time dynamics. We
obtain a very general stochastic model, that encompasses key features of
several paradigmatic models of anomalous diffusion: discontinuous, scale-free
displacements as in Levy flights, scale-free waiting times as in subdiffusive
CTRWs, and the long-range temporal correlations of fractional Brownian motion
(FBM). We derive the exact solutions for the single-time probability density
functions and extract the scaling behaviours. Interestingly, we find that
different combinations of the model parameters lead to indistinguishable shapes
of the emerging probability density functions and identical scaling laws. Our
model will be useful to describe recent experimental single particle tracking
data, that feature a combination of CTRW and FBM properties.Comment: 25 pages, IOP style, 5 figure
Compositional Performance Modelling with the TIPPtool
Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations
Towards an HLA Run-time Infrastructure with Hard Real-time Capabilities
Our work takes place in the context of the HLA standard and its application in real-time systems context. The HLA standard is inadequate for taking into consideration the different constraints involved in real-time computer systems. Many works have been invested in order to providing real-time capabilities to Run Time Infrastructures (RTI) to run real time simulation. Most of these initiatives focus on major issues including QoS guarantee, Worst Case Transit Time (WCTT) knowledge and scheduling services provided by the underlying operating systems. Even if our ultimate objective is to achieve real-time capabilities for distributed HLA federations executions, this paper describes a preliminary work focusing on achieving hard real-time properties for HLA federations running on a single computer under Linux operating systems. Our paper proposes a novel global bottom up approach for designing real-time Run time Infrastructures and a formal model for validation of uni processor to (then) distributed real-time simulation with CERTI
CSP channels for CAN-bus connected embedded control systems
Closed loop control system typically contains multitude of sensors and actuators operated simultaneously. So they are parallel and distributed in its essence. But when mapping this parallelism to software, lot of obstacles concerning multithreading communication and synchronization issues arise. To overcome this problem, the CT kernel/library based on CSP algebra has been developed. This project (TES.5410) is about developing communication extension to the CT library to make it applicable in distributed systems. Since the library is tailored for control systems, properties and requirements of control systems are taken into special consideration. Applicability of existing middleware solutions is examined. A comparison of applicable fieldbus protocols is done in order to determine most suitable ones and CAN fieldbus is chosen to be first fieldbus used. Brief overview of CSP and existing CSP based libraries is given. Middleware architecture is proposed along with few novel ideas
Practical applications of probabilistic model checking to communication protocols
Probabilistic model checking is a formal verification technique for the analysis of systems that exhibit stochastic behaviour. It has been successfully employed in an extremely wide array of application domains including, for example, communication and multimedia protocols, security and power management. In this chapter we focus on the applicability of these techniques to the analysis of communication protocols. An analysis of the performance of such systems must successfully incorporate several crucial aspects, including concurrency between multiple components, real-time constraints and randomisation. Probabilistic model checking, in particular using probabilistic timed automata, is well suited to such an analysis. We provide an overview of this area, with emphasis on an industrially relevant case study: the IEEE 802.3 (CSMA/CD) protocol. We also discuss two contrasting approaches to the implementation of probabilistic model checking, namely those based on numerical computation and those based on discrete-event simulation. Using results from the two tools PRISM and APMC, we summarise the advantages, disadvantages and trade-offs associated with these techniques
A Modeling Framework for Schedulability Analysis of Distributed Avionics Systems
This paper presents a modeling framework for schedulability analysis of
distributed integrated modular avionics (DIMA) systems that consist of
spatially distributed ARINC-653 modules connected by a unified AFDX network. We
model a DIMA system as a set of stopwatch automata (SWA) in UPPAAL to analyze
its schedulability by classical model checking (MC) and statistical model
checking (SMC). The framework has been designed to enable three types of
analysis: global SMC, global MC, and compositional MC. This allows an effective
methodology including (1) quick schedulability falsification using global SMC
analysis, (2) direct schedulability proofs using global MC analysis in simple
cases, and (3) strict schedulability proofs using compositional MC analysis for
larger state space. The framework is applied to the analysis of a concrete DIMA
system.Comment: In Proceedings MARS/VPT 2018, arXiv:1803.0866
Evaluation of A Resilience Embedded System Using Probabilistic Model-Checking
If a Micro Processor Unit (MPU) receives an external electric signal as
noise, the system function will freeze or malfunction easily. A new resilience
strategy is implemented in order to reset the MPU automatically and stop the
MPU from freezing or malfunctioning. The technique is useful for embedded
systems which work in non-human environments. However, evaluating resilience
strategies is difficult because their effectiveness depends on numerous,
complex, interacting factors.
In this paper, we use probabilistic model checking to evaluate the embedded
systems installed with the above mentioned new resilience strategy. Qualitative
evaluations are implemented with 6 PCTL formulas, and quantitative evaluations
use two kinds of evaluation. One is system failure reduction, and the other is
ADT (Average Down Time), the industry standard. Our work demonstrates the
benefits brought by the resilience strategy. Experimental results indicate that
our evaluation is cost-effective and reliable.Comment: In Proceedings ESSS 2014, arXiv:1405.055
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