90,618 research outputs found
The Conversion of Dynamic Fault Trees to Stochastic Petri Nets, as a case of Graph Transformation
AbstractA model-to-model transformation from Dynamic Fault Trees to Stochastic Petri Nets, by means of graph transformation rules, is presented in this paper. Dynamic Fault Trees (DFT) are used for the reliability analysis of complex and large systems and represent by means of gates, how combinations or sequences of component failure events, lead to the failure of the system. DFTs need the state space solution which can be obtained by converting a DFT to a Stochastic Petri Net: this task is expressed by means of graph transformation rules, and is applied to a case of system
Model-based Simulation of VoIP Network Reconfigurations using Graph Transformation Systems
We address the modelling and validation of P2P networks with
special attention for problems related to VoIP services, focusing particularly
on Skype. We use generalised stochastic graph transformation systems
and associated stochastic simulation techniques based on generalised semi-
Markov processes
Stochastic Graph Transformation with Regions
Graph transformation can be used to implement stochastic simulation of dynamic systems based on semi-Markov processes, extending the standard approach based on Markov chains. The result is a discrete event system, where states are graphs, and events are rule matches associated to general distributions, rather than just exponential ones. We present an extension of this model, by introducing a hierarchical notion of event location, allowing for stochastic dependence of higher-level events on lower-level ones
Synthesis of Stochastic Flow Networks
A stochastic flow network is a directed graph with incoming edges (inputs)
and outgoing edges (outputs), tokens enter through the input edges, travel
stochastically in the network, and can exit the network through the output
edges. Each node in the network is a splitter, namely, a token can enter a node
through an incoming edge and exit on one of the output edges according to a
predefined probability distribution. Stochastic flow networks can be easily
implemented by DNA-based chemical reactions, with promising applications in
molecular computing and stochastic computing. In this paper, we address a
fundamental synthesis question: Given a finite set of possible splitters and an
arbitrary rational probability distribution, design a stochastic flow network,
such that every token that enters the input edge will exit the outputs with the
prescribed probability distribution.
The problem of probability transformation dates back to von Neumann's 1951
work and was followed, among others, by Knuth and Yao in 1976. Most existing
works have been focusing on the "simulation" of target distributions. In this
paper, we design optimal-sized stochastic flow networks for "synthesizing"
target distributions. It shows that when each splitter has two outgoing edges
and is unbiased, an arbitrary rational probability \frac{a}{b} with a\leq b\leq
2^n can be realized by a stochastic flow network of size n that is optimal.
Compared to the other stochastic systems, feedback (cycles in networks)
strongly improves the expressibility of stochastic flow networks.Comment: 2 columns, 15 page
Rate Equations for Graphs
In this paper, we combine ideas from two different scientific traditions: 1)
graph transformation systems (GTSs) stemming from the theory of formal
languages and concurrency, and 2) mean field approximations (MFAs), a
collection of approximation techniques ubiquitous in the study of complex
dynamics. Using existing tools from algebraic graph rewriting, as well as new
ones, we build a framework which generates rate equations for stochastic GTSs
and from which one can derive MFAs of any order (no longer limited to the
humanly computable). The procedure for deriving rate equations and their
approximations can be automated. An implementation and example models are
available online at https://rhz.github.io/fragger. We apply our techniques and
tools to derive an expression for the mean velocity of a two-legged walker
protein on DNA.Comment: to be presented at the 18th International Conference on Computational
Methods in Systems Biology (CMSB 2020
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