Richard A. Hayden

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Markovian process algebras, such as PEPA and stochastic π-calculus, bring a powerful compositional ap-<lb>proach to the performance modelling of complex systems. However, the models generated by process alge-<lb>bras, as with other interleaving formalisms, are susceptible to the state space explosion problem. Models<lb>with only a modest number of process(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 deterministicallytimed transitions. We introduce a new low-level formalism for specifying massively-parallel models with generally-timed transitions, the population generalised semi-Markov process (PGSMP).(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 consider a generic mean-field scenario, in which a sequence of population models, described by discretetime 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)
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)
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 analyze massively distributed architectures, without recourse to large compute clusters. We present the unified stochastic probe, a performance specification mechanism for(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 states and beyond. This paper seeks to extend the type of measure that can be extracted from(More)
We present a tool called Grouped PEPA Analyser (GPA) that allows fast analysis of large scale models described in the stochastic process algebra PEPA. GPA employs the techniques for approximations of transient moments in PEPA models with ordinary differential equations (ODEs), which allow analysis of systems with state spaces far beyond the limits of(More)