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Fluid Flow Approximation of PEPA models

Fluid Flow Approximation of PEPA models,10.1109/QEST.2005.12,Jane Hillston

Fluid Flow Approximation of PEPA models   (Citations: 107)
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In this paper we present a novel performance analysis technique for large-scale systems modelled in the stochas- tic process algebra PEPA. In contrast to the well-known 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 well-suited 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. 33-43, 2005
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    • ...The model can be translated to give a population-based model in terms of MFEs (McCaig et al. 2008; Hillston 2005; Cardelli 2008b)...

    Chris McCaigMikeet 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 Massinket al. Modelling Non-linear Crowd Dynamics in Bio-PEPA

    • ...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 fluid-flow 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 fluid-flow 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 fluid-flow 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 Silvaet al. Fluidization and fluid views of discrete event systems

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