Fluid-flow solutions in PEPA to the state space explosion problem

Achieving the appropriate performance requirements for computer-communication systems is as important as the correctness of the end-result. This is particularly difficult in the case of massively parallel computer systems such as the clusters of PCs behind the likes of Google and peer-to-peer filesharing networks such as Bittorrent. Measuring the performance of such systems using a mathematical model is invariably computationally intensive. Formal modelling techniques make possible the derivation of such performance measures but currently suffer from the state-space explosion problem, that is, models become intractably large even for systems of apparently modest complexity. This work develops a novel class of techniques aimed at addressing this problem by approximating a representation of massive state spaces as more computationally-tractable real variables (fluid-flow analysis)

A Hierarchy of Scheduler Classes for Stochastic Automata

Stochastic automata are a formal compositional model for concurrent stochastic timed systems, with general distributions and non-deterministic choices. Measures of interest are defined over schedulers that resolve the nondeterminism. In this paper we investigate the power of various theoretically and practically motivated classes of schedulers, considering the classic complete-information view and a restriction to non-prophetic schedulers. We prove a hierarchy of scheduler classes w.r.t. unbounded probabilistic reachability. We find that, unlike Markovian formalisms, stochastic automata distinguish most classes even in this basic setting. Verification and strategy synthesis methods thus face a tradeoff between powerful and efficient classes. Using lightweight scheduler sampling, we explore this tradeoff and demonstrate the concept of a useful approximative verification technique for stochastic automata

Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions

Performance modelling for system-level design

xii+208hlm.;24c

Mean field for performance models with generally distributed-timed transitions

In this paper we extend the mean-field limit of a class of stochastic models with exponential and deterministic delays to include exponential and generally-distributed delays. Our main focus is the rigorous proof of the mean-field limit

Mean field for performance models with generally distributed-timed transitions

In this paper we extend the mean-field limit of a class of stochastic models with exponential and deterministic delays to include exponential and generally-distributed delays. Our main focus is the rigorous proof of the mean-field limit

Practical Statistics for Particle Physics

This is the write-up of a set of lectures given at the Asia Europe Pacific School of High Energy Physics in Quy Nhon, Vietnam in September 2018, to an audience of PhD students in all branches of particle physics They cover the different meanings of 'probability', particularly frequentist and Bayesian, the binomial, Poisson and Gaussian distributions, hypothesis testing, estimation, errors (including asymmetric and systematic errors) and goodness of fit. Several different methods used in setting upper limits are explained, followed by a discussion on why 5 sigma are conventionally required for a 'discovery'

Location-Aware Quality of Service Measurements for Service-Level Agreements

We add specifications of location-aware measurements to performance models in a compositional fashion, promoting precision in performance measurement design. Using immediate actions to send control signals between measurement components we are able to obtain more accurate measurements from our stochastic models without disturbing their structure. A software tool processes both the model and the measurement specifications to give response time distributions and quantiles, an essential calculation in determining satisfaction of service-level agreements (SLAs)