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

Performance modeling of e-procurement workflow using Generalised Stochastic Petri net (GSPN)

This paper proposes a Generalised Stochastic Petri net (GSPN) model representing a generic e-procurement workflow process. The model displays the dynamic behaviour of the system and shows the inter relationship of process activities. An analysis based on matrix equation approach enabled users to analyse the critical system's states, and thus justify the process performance. The results obtained allow users for better decision making in improving e-procurement workflow performance

Modelling, reduction and analysis of Markov automata (extended version)

Markov automata (MA) constitute an expressive continuous-time compositional modelling formalism. They appear as semantic backbones for engineering frameworks including dynamic fault trees, Generalised Stochastic Petri Nets, and AADL. Their expressive power has thus far precluded them from effective analysis by probabilistic (and statistical) model checkers, stochastic game solvers, or analysis tools for Petri net-like formalisms. This paper presents the foundations and underlying algorithms for efficient MA modelling, reduction using static analysis, and most importantly, quantitative analysis. We also discuss implementation pragmatics of supporting tools and present several case studies demonstrating feasibility and usability of MA in practice

Stepwise reduction and approximation method for performance analysis of generalized stochastic petri nets

This thesis delves into the performance analysis of generalized stochastic Petri net (GSPN) model by using an approximation method: the Stepwise Reduction and Approximation (SRA) Method. The key point is that we are able to analyze a subnet in isolation by keeping its token flow direction and its sub-throughput equivalent with all the possible tokens entering into the subnet. The thesis first defines various kinds of potentially reducible subnets, subnet selection rules, approximation subnet construction rules, and reduction evaluation rules. Then corresponding to the possible subnets, the approximation method is used stepwisely until the interested measures are found with the global state space reduced. Two GSPN model examples from the literature are analyzed by using the proposed method. The approximation errors are given and discussed. Finally, the conclusions are drawn and future research is discussed

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 $(E \vdash MC^2$)

An approach to modelling and analysing reliability of Breeze/ADL-based software architecture

Breeze/architecture description language (ADL), is an eXtensible markup language (XML) based architecture description language which is used to model software systems at the architecture level. Though Breeze/ADL provides an appropriate basis for architecture modelling, it can neither analyse nor evaluate the architecture reliability. In this paper, we propose a Breeze/ADL based strategy which, by combining generalized stochastic Petri net (GSPN) and tools for reliability analysis, supports architecture reliability modelling and evaluation. This work expands the idea in three directions: Firstly, we give a Breeze/ADL reliability model in which we add error attributes to Breeze/ADL error model for capturing architecture error information, and at the same time perform the system error state transition through the Breeze/ADL production. Secondly, we present how to map a Breeze/ADL reliability model to a GSPN model, which in turn can be used for reliability analysis. The other task is to develop a Breeze/ADL reliability analysis modelling tool–EXGSPN (Breeze/ADL reliability analysis modelling tool), and combine it with platform independent petri net editor 2 (PIPE2) to carry out a reliability assessment