Giuliana Franceschinis

Modelling with Generalized Stochastic Petri Nets

From the Publisher: This book presents a unified theory of Generalized Stochastic Petri Nets (GSPNs) together with a set of illustrative examples from different application fields. The continuing success of GSPNs and the increasing interest in using them as a modelling paradigm for the quantitative analysis of distributed systems suggested the preparation of this volume with the intent of providing newcomers to the field with a useful tool for their first approach. Readers will find a clear and informal explanation of the concepts followed by formal definitions when necessary or helpful. The largest section of the book however is devoted to showing how this methodology can be applied in a range of domains.

GreatSPN 1.7: graphical editor and analyzer for timed and stochastic Petri nets

This paper describes the GreatSPN 1.7 package for the modeling, validation, and performance evaluation of distributed systems using Generalized Stochastic Petri Nets and their colored extension. The tool provides a friendly framework to experiment with timed Petri net based modeling techniques. It implements efficient analysis algorithms to allow its use on “real” applications, not only toy examples. Developed in a university for non-profit purposes, it is distributed free of charge to other universities for educational and research purposes. An overview of the complete architecture of the package is given together with examples of its application. Then the various analysis and simulation modules are described.

On Well-Formed Coloured Nets and Their Symbolic Reachability Graph

The new class of Well Formed Coloured Nets (WN) is formally defined as an extension of Regular Nets (RN), together with an extended Symbolic Reachability Graph (SRG) construction algorithm. WNs allow the representation of any colour function in a structured form, so that they have the same modelling power as general coloured nets (CPN). In particular, with respect to RN, WNs allow the use of non-symmetric initial markings, of repeated occurrences of the same basic class in the Cartesian product defining the colours for transitions and places, and of the “constant” and “successor” functions as arc labels. The SRG allows colour symmetries to be exploited to reduce the space and time complexity of the analysis by reachability graph. The advantage of using WNs instead of unconstrained CPNs is that the detection of symmetries to construct the SRG is totally algorithmic, and requires no special heuristics.

Multi-path continuous media streaming: what are the benefits?

Quality of service (QoS) in delivery of continuous media (CM) over the Internet is still relatively poor and inconsistent. Although many such applications can tolerate some degree of missing information, significant losses degrade an applications QoS. In this paper, we investigate the potential benefits of mitigating this problem through the exploitation of multiple paths existing in the network between a set of senders and a receiver of CM. Our focus in this work is on providing a fundamental understanding of the benefits of using multiple paths to deliver CM over best-effort wide-area networks. Specifically, we consider pre-recorded CM applications and use the following metrics in evaluating the performance of multi-path streaming as compared to single-path streaming: (a) data loss rate, (b) conditional error burst length distribution, and (c) lag1-autocorrelation. The results of this work can be used in guiding the design of multi-path CM systems streaming data over best-effort wide-area networks.

The GreatSPN tool: recent enhancements

GreatSPN is a tool that supports the design and the qualitative and quantitative analysis of Generalized Stochastic Petri Nets (GSPN) and of Stochastic Well-Formed Nets (SWN). The very first version of GreatSPN saw the light in the late eighties of last century: since then two main releases where developed and widely distributed to the research community: GreatSPN1.7 [13], and GreatSPN2.0 [8]. This paper reviews the main functionalities of GreatSPN2.0 and presents some recently added features that significantly enhance the efficacy of the tool.

An introduction to generalized stochastic Petri nets

Abstract The paper decribes the GSPN approach to the performance evaluation of distributed systems. The structural properties and temporal specifications of GSPN are summarized, and application examples are then illustrated, trying to emphasize the methodology to be followed in the model development and validation, rather than the numerical results that can be obtained from the specific models developed in the paper.

A symbolic reachability graph for coloured Petri nets

Coloured Petri nets are well suited to the modelling of symmetric systems. Model symmetries can be usefully exploited for the sake of analysis efficiency as well as for modelling convenience. We present a reduced reachability graph called symbolic reachability graph that enjoys the following properties: (1) it can be constructed directly by an efficient algorithm without considering the actual state space of the model; (2) it can be substantially smaller than the ordinary reachability graph; (3) its analysis provides equivalent results as the analysis of the ordinary reachability graph. The construction procedure for the symbolic reachability graph is completely effective in the case of a syntactically restricted class of coloured nets called “well-formed nets”, while for the unrestricted case of coloured nets some procedures may not be easily implementable in algorithmic form.

The OsMoSys approach to multi-formalism modeling of systems

Analysis and simulation of complex systems are facilitated by the availability of appropriate modeling formalisms and tools. In many cases, no single analysis and modeling method can successfully cope with all aspects of a complex system: a multi-formalism multi-solution approach is very appealing, since it offers the possibility of applying the most suitable formalisms and solution techniques to model and analyze different components or aspects of a system. Another important feature that a successfull modeling approach should include is the possibility of reusing (sub)models: by composing parameterized submodels and then instantiating the parameters, complete models of different scenarios can be obtained and analyzed.This paper introduces an innovative approach to multi-formalism modeling of systems that is part of the OsMoSys (Object-based multi-formaliSm MOdeling of SYStems) framework. OsMoSys uses the proposed modeling approach to build multi-formalism models, and workflow management to achieve multi-solution. Our modeling approach is based on meta-modeling, allowing to easily define and integrate different formalisms, and on some concepts from object orientation. Its main objectives are the interoperability of different formalisms and the definition of mechanisms to guarantee the flexibility and the scalability of the modeling framework.

Parametric fault tree for the dependability analysis of redundant systems and its high-level Petri net semantics

In order to cope efficiently with the dependability analysis of redundant systems with replicated units, a new, more compact fault-tree formalism, called Parametric Fault Tree (PFT), is defined. In a PFT formalism, replicated units are folded and indexed so that only one representative of the similar replicas is included in the model. From the PFT, a list of parametric cut sets can be derived, where only the relevant patterns leading to the system failure are evidenced regardless of the actual identity of the component in the cut set. The paper provides an algorithm to convert a PFT into a class of High-Level Petri Nets, called SWN. The purpose of this conversion is twofold: to exploit the modeling power and flexibility of the SWN formalism, allowing the analyst to include statistical dependencies that could not have been accommodated into the corresponding PFT and to exploit the capability of the SWN formalism to generate a lumped Markov chain, thus alleviating the state explosion problem. The search for the minimal cut sets (qualitative analysis) can be often performed by a structural T-invariant analysis on the generated SWN. The advantages that can be obtained from the translation of a PFT into a SWN are investigated considering a fault-tolerant multiprocessor system example.

Repairable fault tree for the automatic evaluation of repair policies

Fault trees are a well known mean for the evaluation of dependability of complex systems. Many extensions have been proposed to the original formalism in order to enhance the advantages of fault tree analysis for the design and assessment of systems. In this paper we propose an extension, repairable fault trees, which allows the designer to evaluate the effects of different repair policies on a repairable system: this extended formalism has been integrated in a multi-formalism multi-solution framework, and it is supported by a solution technique which transparently exploits generalized stochastic Petri nets (GSPN)for modelling the repairing process. The modelling technique and the solution process are illustrated through an example.