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Keywords
(7)
Continuous Time Markov Chain
Fluid Flow
Large Scale System
Ordinary Differential Equation
Performance Analysis
State Space
Process Algebra
Related Publications
(18)
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Fluid Flow Approximation of PEPA models
Fluid Flow Approximation of PEPA models,10.1109/QEST.2005.12,Jane Hillston
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Fluid Flow Approximation of PEPA models
(
Citations: 107
)
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Jane Hillston
In this paper we present a novel
performance analysis
technique for largescale systems modelled in the stochas tic
process algebra
PEPA. In contrast to the wellknown ap proach of analysing via continuous time Markov chains, our underlying mathematical representation is a set of coupled ordinary differential equations (ODEs). This analysis pro cess supports all of the combinators of the PEPA algebra and is wellsuited to systems with large numbers of repli cated components. The paper presents an elegant procedure for the generation of the ODEs and compares the results of this analysis with more conventional methods. gebra such as PEPA. The approach is based on two shifts from the usual perspective: • Firstly, we do not aim to calculate the probability dis tribution over the entire
state space
of the model. We choose a more abstract state representation in terms of state variables, quantifying the types of behaviour evi dent in the model.
Conference:
Quantitative Evaluation of Systems  QEST
, pp. 3343, 2005
DOI:
10.1109/QEST.2005.12
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Citation Context
(89)
...The model can be translated to give a populationbased model in terms of MFEs (McCaig et al. 2008;
Hillston 2005;
Cardelli 2008b)...
Chris McCaigMike
,
et al.
A rigorous approach to investigating common assumptions about disease ...
...Such semantics are based on the generation of sets of ordinary differential equations (ODE) [
12
,4,7]...
Mieke Massink
,
et al.
Modelling Nonlinear Crowd Dynamics in BioPEPA
...Lastly, and perhaps most importantly, this validation study offers a comparative evaluation of the accuracy against the competing approximate deterministic solution based on ordinary differential equations (ODEs) [
13
], [14]...
Mirco Tribastone
.
Approximate Mean Value Analysis of Process Algebra Models
...In the last few years, there has been a growing interest in techniques that tackle the state space explosion by treating continuously the numerousness of each system’s component, thus approximating Markov processes with deterministic dynamical system, usually described by means of an ordinary differential equation (ODE 1 , [
4
], [5])...
...In particular, in this paper we deal with deterministic approximation of Continuous Time Markov Chains, a technique usually known as fluidflow approximation [
4
]...
...2 Fluid approximation has been applied in particular as an analysis tool for the collective behavior of Stochastic Process Algebra (SPA) based models of large populations of interacting agents [
4
], [6], [7], [8]...
...The first works on fluidflow approximation showed in many cases a very good agreement between the behavior of a SPA model and of its fluid ODE [
4
]...
Luca Bortolussi
.
Hybrid Limits of Continuous Time Markov Chains
...Among those, PEPA [
60
] is a basic markovian PA in which basic components are sequential processes (finite automata), while parallel composition is only supported at top level; its fluidflow approximation consider large scale models of massively repeated sequential components...
...Following that line of thinking, in [
60
] a numerically aggregated representation scheme is defined for PEPA expressions with replicated components...
Manuel Silva
,
et al.
Fluidization and fluid views of discrete event systems
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The Computer Journal  CJ
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A Compositional Approach to Performance Modelling
(
Citations: 784
)
Jane Hillston
Published in 1996.
Sort by:
Citations
(107)
A rigorous approach to investigating common assumptions about disease transmission
(
Citations: 1
)
Chris McCaigMike
,
Mike Begon
,
Rachel Norman
,
Carron Shankland
Journal:
Theory in Biosciences  THEOR BIOSCI
, vol. 130, no. 1, pp. 1929, 2011
Fluid analysis of energy consumption using rewards in massively parallel markov models
(
Citations: 1
)
Anton Stefanek
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Richard A. Hayden
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Jeremy T. Bradley
Published in 2011.
Modelling Nonlinear Crowd Dynamics in BioPEPA
Mieke Massink
,
Diego Latella
,
Andrea Bracciali
,
Jane Hillston
Conference:
Fundamental Approaches to Software Engineering  FASE
, pp. 96110, 2011
Approximate Mean Value Analysis of Process Algebra Models
Mirco Tribastone
Conference:
Modeling, Analysis, and Simulation On Computer and Telecommunication Systems  MASCOTS
, pp. 369378, 2011
Hybrid Limits of Continuous Time Markov Chains
Luca Bortolussi
Conference:
Quantitative Evaluation of Systems  QEST
, 2011