Construction and Verification of Performance and Reliability Models

Over the last two decades formal methods have been extended towards performance and reliability evaluation. This paper tries to provide a rather intuitive explanation of the basic concepts and features in this area. Instead of striving for mathematical rigour, the intention is to give an illustrative introduction to the basics of stochastic models, to stochastic modelling using process algebra, and to model checking as a technique to analyse stochastic models

On Probabilistic Parallel Programs with Process Creation and Synchronisation

We initiate the study of probabilistic parallel programs with dynamic process creation and synchronisation. To this end, we introduce probabilistic split-join systems (pSJSs), a model for parallel programs, generalising both probabilistic pushdown systems (a model for sequential probabilistic procedural programs which is equivalent to recursive Markov chains) and stochastic branching processes (a classical mathematical model with applications in various areas such as biology, physics, and language processing). Our pSJS model allows for a possibly recursive spawning of parallel processes; the spawned processes can synchronise and return values. We study the basic performance measures of pSJSs, especially the distribution and expectation of space, work and time. Our results extend and improve previously known results on the subsumed models. We also show how to do performance analysis in practice, and present two case studies illustrating the modelling power of pSJSs.Comment: This is a technical report accompanying a TACAS'11 pape

Derivation of passage-time densities in PEPA models using ipc: the imperial PEPA compiler

We present a technique for defining and extracting passage-time densities from high-level stochastic process algebra models. Our high-level formalism is PEPA, a popular Markovian process algebra for expressing compositional performance models. We introduce ipc, a tool which can process PEPA-specified passage-time densities and models by compiling the PEPA model and passage specification into the DNAmaca formalism. DNAmaca is an established modelling language for the low-level specification of very large Markov and semi-Markov chains. We provide performance results for ipc/DNAmaca and comparisons with another tool which supports PEPA, PRISM. Finally, we generate passage-time densities and quantiles for a case study of a high-availability web server. 1

Approximate performability and dependability analysis using generalized stochastic Petri Nets

Since current day fault-tolerant and distributed computer and communication systems tend to be large and complex, their corresponding performability models will suffer from the same characteristics. Therefore, calculating performability measures from these models is a difficult and time-consuming task.\ud \ud To alleviate the largeness and complexity problem to some extent we use generalized stochastic Petri nets to describe to models and to automatically generate the underlying Markov reward models. Still however, many models cannot be solved with the current numerical techniques, although they are conveniently and often compactly described.\ud \ud In this paper we discuss two heuristic state space truncation techniques that allow us to obtain very good approximations for the steady-state performability while only assessing a few percent of the states of the untruncated model. For a class of reversible models we derive explicit lower and upper bounds on the exact steady-state performability. For a much wider class of models a truncation theorem exists that allows one to obtain bounds for the error made in the truncation. We discuss this theorem in the context of approximate performability models and comment on its applicability. For all the proposed truncation techniques we present examples showing their usefulness

A general framework for quantifying the effects of land-use history on ecosystem dynamics

Land-use legacies are important for explaining present-day ecological patterns and processes. However, an overarching approach to quantify land-use history effects on ecosystem properties is lacking, mainly due to the scarcity of high-quality, complete and detailed data on past land use. We propose a general framework for quantifying the effects of land-use history on ecosystem properties, which is applicable (i) to different ecological processes in various ecosystem types and across trophic levels; and (ii) when historical data are incomplete or of variable quality. The conceptual foundation of our framework is that past land use affects current (and future) ecosystem properties through altering the past values of resources and conditions that are the driving variables of ecosystem responses. We describe and illustrate how Markov chains can be applied to derive past time series of driving variables, and how these time series can be used to improve our understanding of present-day ecosystem properties. We present our framework in a stepwise manner, elucidating its general nature. We illustrate its application through a case study on the importance of past light levels for the contemporary understorey composition of temperate deciduous forest. We found that the understorey shows legacies of past forest management: high past light availability lead to a low proportion of typical forest species in the understorey. Our framework can be a useful tool for quantifying the effect of past land use on ecological patterns and processes and enhancing our understanding of ecosystem dynamics by including legacy effects which have often been ignored

A Markov Chain Model Checker

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen Twente Markov Chain Checker $(E \vdash MC^2$), where properties are expressed in appropriate extensions of CTL. We illustrate the general bene ts of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of $(E \vdash MC^2$)

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