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Markovian process algebras, such as PEPA and stochastic π-calculus, bring a powerful compositional approach to the performance modelling of complex systems. However, the models generated by process algebras , as with other interleaving formalisms, are susceptible to the state space explosion problem. Models with only a modest number of process algebra terms… (More)

—We extend the mean-field (a.k.a. fluid-analysis) approach for massively-parallel continuous-time Markov chains (CTMCs) to models with both Markovian and deterministically-timed transitions. We introduce a new low-level formalism for specifying massively-parallel models with generally-timed transitions , the population generalised semi-Markov process… (More)

Recent developments in the analysis of large Markov models facilitate the fast approximation of transient characteristics of the underlying stochastic process. Fluid analysis makes it possible to consider previously intractable models whose underlying discrete state space grows exponentially as model components are added. In this work, we show how… (More)

We present a new tool, GPA, that can generate key performance measures for very large systems. Based on solving systems of ordinary differential equations (ODEs), this method of performance analysis is far more scalable than stochastic simulation. The GPA tool is the first to produce higher moment analysis from differential equation approximation, which is… (More)

Capturing energy consumption directly from a stochastic behavioural model is a computationally expensive process. Using a so-called fluid analysis technique we are able to access accumulated reward measures in much larger scale stochastic systems than has been previously possible.These accumulated rewards are ideal for deriving energy and power consumption… (More)

—Recent ordinary differential equation (ODE) based techniques allow efficient analysis of Markovian population models with extremely large state spaces. In most cases of realistic scale, they provide the only alternative to stochastic simulation. Moreover, numerical solution of the ODEs is cheaper computationally than simulation by orders of magnitude. We… (More)

—Rapid and accessible performance evaluation of complex software systems requires two critical features: the ability to specify useful performance metrics easily and the capability to analyse massively-distributed architectures, without recourse to large compute clusters. We present the unified stochastic probe, a performance specification mechanism for… (More)

Fluid modelling is a next-generation technique for analysing massive performance models. Passive cooperation is a popular cooperation mechanism frequently used by performance engineers. Therefore having an accurate translation of passive cooperation into a fluid model is of direct practical application. We compare different existing styles of fluid model… (More)

Recent developments in the analysis of stochastic process algebra models allow for transient measures of very large models to be extracted. By performing so-called fluid analysis of stochastic process algebra models, it is now feasible to analyse systems of size 10 1000 states and beyond. This paper seeks to extend the type of measure that can be extracted… (More)

We consider a generic mean-field scenario, in which a sequence of population models, described by discrete-time Markov chains (DTMCs), converges to a deterministic limit in discrete time. Under the assumption that the limit has a globally attracting equilibrium, the steady states of the sequence of DTMC models converge to the point-mass distribution… (More)