Susanna Donatelli

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.

Superposed Generalized Stochastic Petri Nets: Definition and Efficient Solution

In a previous paper we have defined Superposed Stochastic Automata (SSA) [13], a class of Stochastic Petri Nets (SPN) whose solution can be efficiently computed since it never requires the construction of the complete Markov chain of the underlying Markovian process. The efficient solution of SSA is based on a method proposed by Plateau in [23] for the analysis of stochastic processes generated by the composition of stochastic automata. Efficient analysis is there achieved (both in terms of space and time) with a technique based on Kronecker (tensor) algebra for matrices.

Superposed stochastic automata: a class of stochastic Petri nets with parallel solution and distributed state space

Abstract Stochastic processes generated by the composition of stochastic automata can be analyzed efficiently (both in terms of space and time) with a technique based on Kronecker (tensor) algebra for matrices, as shown by Plateau. The technique is applied in this paper to the analysis of a class of Stochastic Petri nets (SPN) that is named Superposed Stochastic Automata (SSA) an it is used to solve nets of hundreds of thousands states. The evaluation of the steady state probability distribution for this class of models was implemented with sequential as well as parallel algorithms. Although SSA are a rather restricted subclass of SPN, the extension of the analysis methodology to a more general setting appears to be feasible.

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 compositional semantics for UML state machines aimed at performance evaluation

Unified Modeling Language (UML) is gaining acceptance to describe the behaviour of systems. It has attracted the attention of researchers that are interested in deriving, automatically, performance evaluation models from systems descriptions. A required step to automatically produce a performance model (as any executable model) is that the semantics of the description language is formally defined. Among the UML diagrams, we concentrate on state machines (SMs) and we build a semantics for a significant subset of them in terms of generalized stochastic Petri nets (GSPNs). The paper shows how to derive an executable GSPN model from a description of a system, expressed as a set of SMs. The semantics is compositional since the executable GSPN model is obtained by composing, using standard Petri net operators, the GSPN models of the single SMs, and each GSPN model is obtained by composition of submodels for SM basic features.

Petri Nets in Performance Analysis: An Introduction

In this tutorial paper, the authors discuss the motivations that led to the adoption of Petri nets for performance evaluation, define the class of Petri nets that is most frequently used for performance analysis, and present the subclasses that allow a simpler derivation of performance metrics. Definitions and discussions are paralleled with examples, thus visualizing the strong and weak points of the different alternatives.

State-of-the-art fusion-finder algorithms sensitivity and specificity.

Background. Gene fusions arising from chromosomal translocations have been implicated in cancer. RNA-seq has the potential to discover such rearrangements generating functional proteins (chimera/fusion). Recently, many methods for chimeras detection have been published. However, specificity and sensitivity of those tools were not extensively investigated in a comparative way. Results. We tested eight fusion-detection tools (FusionHunter, FusionMap, FusionFinder, MapSplice, deFuse, Bellerophontes, ChimeraScan, and TopHat-fusion) to detect fusion events using synthetic and real datasets encompassing chimeras. The comparison analysis run only on synthetic data could generate misleading results since we found no counterpart on real dataset. Furthermore, most tools report a very high number of false positive chimeras. In particular, the most sensitive tool, ChimeraScan, reports a large number of false positives that we were able to significantly reduce by devising and applying two filters to remove fusions not supported by fusion junction-spanning reads or encompassing large intronic regions. Conclusions. The discordant results obtained using synthetic and real datasets suggest that synthetic datasets encompassing fusion events may not fully catch the complexity of RNA-seq experiment. Moreover, fusion detection tools are still limited in sensitivity or specificity; thus, there is space for further improvement in the fusion-finder algorithms.

On the Product Form Solution for Stochastic Petri Nets

The combinatorial explosion of the state space of Stochastic Petri Nets (SPNs) is a well known problem that inhibits the exact solution of large SPNs, and therefore a broad use of this kind of Petri Nets as a modelling tool. The same problem exists also for other modelling formalisms like for example Queueing Networks (QNs). In [13, 3] a class of QNs whose solution can be computed in an easy way was defined. For this class of models the solution can be factorized into terms that refer to each single queue of the network. This solution is known as Product Form Solution (PFS).

Application and Theory of Petri Nets 1999

This talk will present two detailed examples of hybrid systems, covering design, simulation and implementation. The first concerns an Automated Highway System. The second application deals with a collection of autonomous unmanned aircraft. The paper provides a background about hybrid systems. 1 What Is a Hybrid System A hybrid system or automaton comprises two interacting components: one component evolves in continuous time and has state variables x ∈ R, the other is event-driven and has finitely many states q ∈ Q. With each discrete state q is associated a differential inclusion ẋ ∈ F (q, x). Here F (q, x) ⊂ R. Associated with each pair (q, q′) is an “enabling zone” or “guard” G(q, q′) ⊂ R (if the guard is empty the discrete transition q → q′ is infeasible), and a “reset” relation R(q, q′) ⊂ R × R. Suppose the system starts in state (q0, x0) at time t0. The continuous state evolves during the time interval [t0, t1) according to the inclusion ẋ(t) ∈ F (q0, x(t)), x(t0) = x0 until a time t1 is reached when x(t1−) ∈ G(q0, q1) for some q1. Because the guard of the transition q0 → q1 is now satisfied, the discrete state changes instantaneously from q0 to q1, and the continuous state is reset from x(t1−) to x1 where (x(t1−), x1) ∈ R(q0, q1). (If another guard is satisfied following the reset, there may be another discrete transition.) The continuous state now evolves during [t1, t2) according to ẋ(t) ∈ F (q1, x(t)), x(t1) = x1 until at t2 another guard is satisfied and the system makes a discrete transition and resets the continuous state as before. Thus a system trajectory evolves in two phases. In the first phase, the discrete state is unchanged, time progresses and the continuous state evolves. In the ? Research supported by National Science Foundation and Office of Naval Research. S. Donatelli, J. Kleijn (Eds.): ICATPN’99, LNCS 1639, pp. 1–5, 1999. c