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)

Integrated performance evaluation of extended queueing network models with line

Despite the large literature on queueing theory and its applications, tool support to analyze these models ismostly focused on discrete-event simulation and mean-value analysis (MVA). This circumstance diminishesthe applicability of other types of advanced queueing analysis methods to practical engineering problems,for example analytical methods to extract probability measures useful in learning and inference. In this toolpaper, we present LINE 2.0, an integrated software package to specify and analyze extended queueingnetwork models. This new version of the tool is underpinned by an object-oriented language to declarea fairly broad class of extended queueing networks. These abstractions have been used to integrate in acoherent setting over 40 different simulation-based and analytical solution methods, facilitating their use inapplications

Process algebraic non-product-forms

AbstractA generalization of the Reversed Compound Agent Theorem of Markovian process algebra is derived that yields separable, but non-product-form solutions for collections of interacting processes such as arise in multi-class queueing networks with Processor Sharing servers. It is based on an analysis of the minimal cycles in the state space of a multi-agent cooperation, which can be simply identified. The extended methodology leads to what we believe are new separable solutions and, more generally, the results represent a viable practical application of the theory of Markovian process algebras in stochastic modelling

Reverse Bisimilarity vs. Forward Bisimilarity

Reversibility is the capability of a system of undoing its own actions starting from the last performed one, in such a way that a past consistent state is reached. This is not trivial for concurrent systems, as the last performed action may not be uniquely identifiable. There are several approaches to address causality-consistent reversibility, some including a notion of forward-reverse bisimilarity. We introduce a minimal process calculus for reversible systems to investigate compositionality properties and equational characterizations of forward-reverse bisimilarity as well as of its two components, i.e., forward bisimilarity and reverse bisimilarity, so as to highlight their differences. The study is conducted not only in a nondeterministic setting, but also in a stochastic one where time reversibility and lumpability for Markov chains are exploited

Applying Reversibility Theory for the Performance Evaluation of Reversible Computations

Reversible computations have been widely studied from the functional point of view and energy consumption. In the literature, several authors have proposed various formalisms (mainly based on process algebras) for assessing the correctness or the equivalence among reversible computations. In this paper we propose the adoption of Markovian stochastic models to assess the quantitative properties of reversible computations. Under some conditions, we show that the notion of time-reversibility for Markov chains can be used to efficiently derive some performance measures of reversible computations. The importance of time-reversibly relies on the fact that, in general, the process’s stationary distribution can be derived efficiently by using numerically stable algorithms. This paper reviews the main results about time-reversible Markov processes and discusses how to apply them to tackle the problem of the quantitative evaluation of reversible computationsReversible computations have been widely studied from the functional point of view and energy consumption. In the literature, several authors have proposed various formalisms (mainly based on process algebras) for assessing the correctness or the equivalence among reversible computations. In this paper we propose the adoption of Markovian stochastic models to assess the quantitative properties of reversible computations. Under some conditions, we show that the notion of time-reversibility for Markov chains can be used to efficiently derive some performance measures of reversible computations. The importance of time-reversibly relies on the fact that, in general, the process's stationary distribution can be derived efficiently by using numerically stable algorithms. This paper reviews the main results about time-reversible Markov processes and discusses how to apply them to tackle the problem of the quantitative evaluation of reversible computations