Scalable performance analysis of massively parallel stochastic systems
The accurate performance analysis of large-scale computer and communication systems is di- rectly inhibited by an exponential growth in the state-space of the underlying Markovian per- formance model. This is particularly true when considering massively-parallel architectures such as cloud or grid computing infrastructures. Nevertheless, an ability to extract quanti- tative performance measures such as passage-time distributions from performance models of these systems is critical for providers of these services. Indeed, without such an ability, they remain unable to o er realistic end-to-end service level agreements (SLAs) which they can have any con dence of honouring. Additionally, this must be possible in a short enough period of time to allow many di erent parameter combinations in a complex system to be tested. If we can achieve this rapid performance analysis goal, it will enable service providers and engineers to determine the cost-optimal behaviour which satis es the SLAs. In this thesis, we develop a scalable performance analysis framework for the grouped PEPA stochastic process algebra. Our approach is based on the approximation of key model quantities such as means and variances by tractable systems of ordinary di erential equations (ODEs). Crucially, the size of these systems of ODEs is independent of the number of interacting entities within the model, making these analysis techniques extremely scalable. The reliability of our approach is directly supported by convergence results and, in some cases, explicit error bounds. We focus on extracting passage-time measures from performance models since these are very commonly the language in which a service level agreement is phrased. We design scalable analy- sis techniques which can handle passages de ned both in terms of entire component populations as well as individual or tagged members of a large population. A precise and straightforward speci cation of a passage-time service level agreement is as im- portant to the performance engineering process as its evaluation. This is especially true of large and complex models of industrial-scale systems. To address this, we introduce the uni ed stochastic probe framework. Uni ed stochastic probes are used to generate a model augmenta- tion which exposes explicitly the SLA measure of interest to the analysis toolkit. In this thesis, we deploy these probes to de ne many detailed and derived performance measures that can be automatically and directly analysed using rapid ODE techniques. In this way, we tackle applicable problems at many levels of the performance engineering process: from speci cation and model representation to e cient and scalable analysis.