Well-formed Nets Research Articles

Free-choice Nets with Home Clusters are Lucent

A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. Characterizing the class of systems that are lucent is a foundational and also challenging question. However, little research has been done on the topic. In this paper, it is shown that all free-choice nets having a home cluster are lucent. These nets have a so-called home marking such that it is always possible to reach this marking again. Such a home marking can serve as a regeneration point or as an end-point. The result is highly relevant because in many applications, we want the system to be lucent and many “well-behaved” process models fall into the class identified in this paper. Unlike previous work, we do not require the marked Petri net to be live and stronglyconnected. Most of the analysis techniques for free-choice nets are tailored towards well-formed nets. The approach presented in this paper provides a novel perspective enabling new analysis techniques for free-choice nets that do not need to be well-formed. Therefore, we can also model systems and processes that are terminating and/or have an initialization phase.

On Liveness and Reversibility of Equal-Conflict Petri Nets

Weighted Petri nets provide convenient models of many man-made systems. Real applications are often required to possess the fundamental Petri net properties of liveness and reversibility, as liveness preserves all the functionalities (fireability of all transitions) of the system and reversibility lets the system return to its initial state (marking) using only internal operations. Characterizations of both behavioral properties, liveness and reversibility, are known for well-formed weighted Choice-Free and ordinary Free-Choice Petri nets, which are special cases of Equal-Conflict Petri nets. However, reversibility is not well understood for this larger class, where choices must share equivalent preconditions, although characterizations of liveness are known. In this paper, we provide the first characterization of reversibility for all live Equal-Conflict Petri nets by extending, in a weaker form, a known condition that applies to the Choice-Free and Free-Choice subclasses. We deduce the monotonicity of reversibility in the live Equal-Conflict class. We also give counter-examples for other classes where the characterization does not hold. Finally, we focus on well-formed Equal-Conflict Petri nets, for which we offer the first polynomial sufficient conditions for liveness and reversibility, contrasting with the previous exponential time conditions.

Structured performance analysis for component-based systems

The component-based system (CBS) paradigm is now largely used to design software systems. In addition, performance and behavioural analysis remains a required step for the design and the construction of efficient systems. This is especially the case of CBS, which involve interconnected components running concurrent processes. This paper proposes a compositional method for modelling and structured performance analysis of CBS. Modelling is based on stochastic well-formed nets (SWNs), a high level model of stochastic Petri nets, widely used for dependability analysis of concurrent systems. Starting from the definition of the system given in a suitable architecture description language, and from the definition of the elementary components, we build an SWN of the global system together with a set of SWNs modelling the components of the CBS and their connections. From these models, we derive performances of the system thanks to a structured analysis induced by the structure of the CBS. We describe the application of our method through an example designed in the framework of the CORBA component model.

An Approach to Predict Performance of Component-based Software with the Palladio Component Model and Stochastic Well-formed Nets

This paper describes which information about a component is needed to enable relevant analyses and emphasizes that prediction feedback should not based on internal models, but based on models which the domain experts understand. This paper proposes a new approach with the Palladio Component Model and Stochastic Well-formed Nets to provide performance predictions of distributed systems throughout the whole development lifecycle.

An Approach to Predict Performance of Component-based Software with the Palladio Component Model and Stochastic Well-formed Nets

This paper describes which information about a component is needed to enable relevant analyses and emphasizes that prediction feedback should not based on internal models, but based on models which the domain experts understand. This paper proposes a new approach with the Palladio Component Model and Stochastic Well-formed Nets to provide performance predictions of distributed systems throughout the whole development lifecycle.

Simplified proof of the blocking theorem for free-choice Petri nets

Every cluster in a bounded and live free-choice system has a unique blocking marking. It can be reached by firing an occurrence sequence, which avoids any transition of the cluster. This theorem is due to Gaujal, Haar and Mairesse. We will give a short proof using standard results on CP-subnets of well-formed free-choice nets.

The GreatSPN tool

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.

Performance evaluation of UML design with Stochastic Well-formed Nets

The paper presents a method to compute performance metrics ( response time, sojourn time, throughput) on Unified Modeling Language design. The method starts with UML design annotated according to the UML Profile for Schedulability, Performance and Time. The UML design is transformed into a performance model where to compute the referred metrics. Being the performance model a Stochastic Well-formed Net, the method is enabled to analyze systems where the object identities are relevant as well as those where they are not. A complete case study reveals how to apply the method and its usefulness.

Using a Stochastic Well-formed Net model for assessing a decentralized approach to configuration management

Traditional support tools for software engineers, normally based on a client–server architecture, are unsuitable to deal with the new issues emerging from the current (and future) cooperative work scenarios (where connectivity is intrinsically transient, the number of interacting partners dynamically changes, etc.). This paper presents a quantitative assessment of a fully decentralized, peer-to-peer, cooperative infrastructure. Stochastic Well-formed Nets (SWNs) modeling the new peer-to-peer architecture, and a traditional (client–server) one, are developed and analyzed: we used SWNs for their ability to directly exploit the symmetries intrinsically present in the modeled systems in order to reduce the complexity of analysis/simulation. The goal is to compare the impact of the two alternative protocols on the collaborative work. The paper focuses on methodological issues concerning choice of an appropriate model abstraction level, adoption of a compositional modeling approach, and mainly, management of model solution complexity. Some performance figures of interest (selected among a number) are also presented and discussed.

Quantitative Assessment of a Peer-to-peer Cooperative Infrastructure Using Stochastic Well-Formed Nets

Traditional support tools for software engineers, normally based on a client-server architecture, are unsuitable to deal with the new issues emerging from the current (and future) cooperative work scenarios (where connectivity is intrinsically transient, the number of interacting partners dynamically changes, etc.). This paper presents a quantitative assessment of a fully decentralized, peer-to-peer, cooperative infrastructure. Stochastic Well-Formed Nets (SWNs) modelling the new peer-to-peer architecture, and a traditional (client-server) one, are developed and analysed: we used SWNs for their ability to directly exploit the symmetries intrinsically present in the modelled systems, thus greatly reducing the complexity of the analysis. The main goal is to compare the impact of the two alternative protocols on the collaborative work. Together with the performance figures of interest, methodological issues concerning the choice of the most appropriate model abstraction level, the adoption of a compositional modelling approach, and the management of the model complexity are also discussed.

Exploiting partial symmetries in well-formed nets for the reachability and the linear time model checking problems

Taking advantage of the symmetries of a system is an efficient way to cope with the combinatory explosion involved by the verification process. Whereas numerous algorithms and tools efficiently deal with the verification of a symmetrical formula on a symmetrical model, the management of partial symmetries is still an open research topic. In this work, We present the design and the evaluation of two methods applicable on coloured Petri nets. These two methods are extensions of the symbolic reachability graph construction for the well-formed Petri nets. The first algorithm, called the extended symbolic reachability graph construction, tackles the reachability problem. The second one called the symbolic synchronized product, checks a partially symmetric linear time formula on a net. The evaluations show that these two methods outperform the previous approaches dealing with partial symmetries. Furthermore they are complementary ones since the former while being less general gives better results than the latter when applied to the reachability problem.

An application example of symbolic calculus for SWN structural relations

Structural analysis techniques allow system properties to be efficiently verified, and may significantly improve the effectiveness of state-space based analysis. Symbolic approaches have been proposed to extend in an effective way structural analysis results from ordinary Petri nets to high level Petri nets but they apply to restricted sub-classes of high level Petri nets (e.g. Unary Regular nets). In the paper some salient points of a symbolic calculus of Stochastic Well-formed Nets structural relations are presented using an example.

On the performance analysis of ABR in ATM LANs with Stochastic Petri Nets

In this paper we use Generalized Stochastic Petri Nets (GSPNs) and Stochastic Well-formed Nets (SWNs) for the performance analysis of Asynchronous Transfer Mode (ATM) Local Area Networks (LANs) that adopt the Available Bit Rate (ABR) service category in its Relative Rate Marking (RRM) version. We also consider a peculiar version of RRM ABR called Stop & Go ABR; this is a simplified ABR algorithm designed for the provision of best-effort services in low-cost ATM LANs, according to which sources can transmit only at two different cell rates, the Peak Cell Rate (PCR) and Minimum Cell Rate (MCR). Results obtained from the solution of GSPN models of simple ATM LAN setups comprising RRM or Stop & Go ABR users, as well as Unspecified Bit Rate (UBR) users, are first validated through detailed simulations, and then used to show that Stop & Go ABR is capable of providing good performance and fairness in a number of different LAN configurations. We also develop SWN models of homogeneous ABR LANs, that efficiently and automatically exploit system symmetries allowing the investigation of larger LAN configurations.

Double categories: a modular model of multiplicative linear logic

We construct a double category [Dscr ] of proof-nets in multiplicative linear logic (MLL). Its horizontal arrows are MLL modules (subnets of well-formed nets), its vertical arrows model side-effects, and its double cells interpret the cut-elimination procedure. The categorical model is modular in the sense that every computation of a composite module (π1; π2) factors out as the separate and interacting computations of the two subcomponents π1 and π2. This enables us to trace MLL modules in the course of cut-elimination, and analyze their behaviour in time.

Implementing compositionality for stochastic Petri nets

An implementation of compositionality for stochastic well-formed nets (SWN) and, consequently, for generalized stochastic Petri nets (GSPN) has been recently included in the GreatSPN tool. Given two SWNs and a labelling function for places and transitions, it is possible to produce a third one as a superposition of places and transitions of equal label. Colour domains and arc functions of SWNs have to be treated appropriately. The main motivation for this extension was the need to evaluate a library of fault-tolerant “mechanisms” that have been recently defined, and are now under implementation, in a European project called TIRAN. The goal of the TIRAN project is to devise a portable software solution to the problem of fault tolerance in embedded systems, while the goal of the evaluation is to provide evidence of the efficacy of the proposed solution. Modularity being a natural “must” for the project, we have tried to reflect it in our modelling effort. In this paper, we discuss the implementation of compositionality in the GreatSPN tool, and we show its use for the modelling of one of the TIRAN mechanisms, the so-called local voter.

On the use of partial symmetries for lumping Markov chains

In this paper a method is proposed, to exploit partially symmetric behavior of systems for efficient performance evaluation. The method works on performance models described with the Stochastic Well-Formed Nets (SWN) formalism: it allows to automatically discover partial symmetries in the model behavior, and directly derive a lumped Markov chain from it, suitable for performance analysis purposes. With respect to previous works on automatic exploitation of symmetries in SWNs, the proposed approach allows a significantly higher reduction of the state space size in many practical cases.

Modeling ATM systems with GSPNs and SWNs

This paper overviews the work of the authors in the field of modeling and analysis of Asynchronous Transfer Mode (ATM) networks using Generalized Stochastic Petri Nets (GSPN) and a special class of high-level stochastic Petri nets known as Stochastic Well-formed Nets (SWN). These formalisms are first shown to be adequate tools for the development of models of ATM systems, provided that only one timed transition is used, together with many immediate transitions. The only timed transition in the GSPN and SWN models represents the ATM systems cell time, while immediate transitions implement the ATM systems behavior. The firing time distribution of the only timed transition is irrelevant for the computation of several interesting performance indices. The results, as well as the problems, derived from the analysis of ATM switches and Local Area Networks (LAN) that adopt the Available Bit Rate (ABR) service category are summarized and discussed, providing references to the works containing the technical details.

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.

Efficient discrete-event simulation of colored Petri nets

Colored Petri nets are a powerful formalism for the description of complex, asynchronous distributed systems. They can express in a very concise way the behavior of very large systems, especially in case these systems are composed of many replications of a few basic components that individually behave in a similar way. The simulation of such models is, however, difficult to perform in a computationally efficient way. For the specific class of stochastic well-formed nets (SWNs), we present a set of optimizations that allow a very efficient implementation of the event-driven simulation technique. Three approaches are followed to improve simulation efficiency: first, an efficient algorithm for the computation of the occurrences of a transition in a given marking; second, reduction of the amount of work needed to schedule or preempt the occurrence of a transition as a consequence of a marking change, taking into account the restrictions on color functions for the SWN formalism; third, reduction of the average length of the event list in the case of symmetric models where the so-called symbolic simulation technique applies. The approach is validated by performance measurements on several large SWN models taken from the literature.

Compositional Construction of SWN models

In this paper we investigate how a Petri net based formalism can take advantage of the notion of compositional construction of systems borrowed from Stochastic Process Algebras. A set of operators for the compositional construction of Stochastic Petri net models is presented, using Stochastic Well-formed Nets to take advantage of their reduced representation and solution of the system modelled.