Proceedings 9th International Workshop on Petri Nets and Performance Models

The construction of the reachability graph presents the problem that its size may grow exponentially with respect to the size of the Petri-net model. For this reason, all available tools suffer restrictions due to the limitation of the available computational resources. We present a new, efficient algorithm based on a data structure that encodes canonical firing count vectors starting from the ini... View full abstract»

This paper discusses and formalises the benefits of using multiple enabled transitions for extensions of Petri nets having quantitative notions of time. It also points out that what could be thought as a straightforward extension actually implies some subtle underlying semantic choices. As an example, a complete semantics for Merlin's (1974) time Petri nets is defined, based on the threshold notio... View full abstract»

In this paper we present a stochastic extension of finite PBC, sPBC in which actions have a stochastic delay associated, which is taken from a negative exponential distribution. We define for the language both an operational and a denotational semantics, using a class of labelled stochastic Petri net as supporting values. In this paper we restrict our attention to finite sPBC, i.e. we consider nei... View full abstract»

This paper presents some transformation techniques from bounded SPN systems to corresponding SPA models, preserving concurrency. Initially, a simple algorithm is introduced, showing that the obtained SPA models simulate the net systems. Then the algorithm is improved in order to keep more of the net structure, when possible. For the case of non ordinary net systems the SPA language is extended by ... View full abstract»

Concurrent generalized Petri nets (CGPNs) are a subclass of Markov regenerative stochastic Petri nets, characterized by timed transitions with general distributed firing times (GEN transitions), that become enabled simultaneously while no other GEN transitions can be activated during their enabling periods. In their original definition, CGPNs were identified through a study of their state space; h... View full abstract»

Petri nets and stochastic Petri nets have been widely adopted as one of the best tools to model the logical and timing behavior of discrete-state systems. However, their practical applicability is limited by the state-space explosion problem. We survey some of the techniques that have been used to cope with large state spaces, starting from early explicit methods, which require data structures of ... View full abstract»

Equivalence is a basic concept in many modeling formalisms to compare different realizations of a system or to compute for a given system a minimal equivalent representation. We present two different equivalence relations for a class of generalized stochastic Petri nets (GSPNs) with labeled transitions (LGSPNs), namely trace equivalence and bisimulation equivalence. In contrast to most other appro... View full abstract»

Despite the development of many modeling formalisms and model solution methods, most tool implementations support only a single formalism. Furthermore, models expressed in the chosen formalism cannot be combined with models expressed in other formalisms. This monolithic approach both limits the usefulness of such tools to practitioners, and hampers modeling research, since it is difficult to compa... View full abstract»

The case-study presented in this paper is aimed at assessing the dependability of a Programmable Logic Controller (PLC) devoted to safety functions. This case study has been brought to our attention by a national environmental agency and has been partially abstracted and anonymized to protect proprietary information. The PLC consists of a triplicated channel with a (2:3) majority voting logic and ... View full abstract»

State-space explosion is one of the main problems in the area of the performance evaluation of Petri net models. This problem prevents the exact numerical analysis of complex real-life systems. To overcome the limitation of state spaces that are too large, many methods have been proposed in which the whole system is divided into small analysable parts. This paper presents one of these so-called de... View full abstract»

We show that a particular class of Generalized Stochastic Petri Nets have stationary probabilities that exhibit a product form. Efficient solution algorithms can be developed for the computation of the performance indices of such Product-Form GSPNs. These algorithms avoid the generation of the underlying state space. Hence, large PF-GSPN models can now be effectively studied View full abstract»

We consider a monoclass threshold queue with hysteresis. Many applications of such a system can be found in the transport protocols of communication networks. Thresholds help to smooth the variations of delay and throughput, and hysteresis limits the number of (expensive) switches of the control mechanism. The queues are modeled and analysed by means of Stochastic Petri Nets (SPNs), a powerful par... View full abstract»

The first aim of this paper is to characterize marking reachability within scenarios defined on t-time Petri nets. This reachability can be structural (does not depend on the enabling durations), necessary (for all the possible values of the enabling durations within some given enabling intervals) or possible (for some values of the enabling durations). This approach is based on the computation of... View full abstract»

Mobius is an extensible framework and tool for performance and dependability modeling, and supports multiple modeling formalisms and solvers. As a framework, Mobius must be sufficiently general to capture the various formalism behaviors. Specifically, the Mobius execution policy must be flexible enough to accommodate the execution policies of all formalisms implemented in the framework. We know of... View full abstract»

In this paper we model a wireless Internet access system based on the GSM/GPRS (Global System for Mobile communications/General Packet Radio Service) technology, with three different Petri net-based paradigms: Generalized Stochastic Petri Nets (GSPNs), Deterministic and Stochastic Petri Nets (DSPNs), and Fluid Stochastic Petri Nets (FSPNs). We show that all three Petri net-based paradigms provide ... View full abstract»

This paper gives an overview of the Mobius framework, and gives a formal specification for defining atomic models within the framework. The framework is designed to be capable of incorporating multiple modeling formalisms, including atomic models (e.g, SPNs), composition formalisms (e.g., Replicate/Join), measure specification formalisms, connection formalisms, and solvers. We focus on atomic mode... View full abstract»

In this paper, we describe the experience in modeling contact centers through stochastic well-formed net (SWN) models in an industry-driven project. The paper describes the problem and shows some of the questions that SWN models could answer, but it also highlights some limitations of the formalism and of the tools used for the analysis. It then discusses the work done to rationalize the model con... View full abstract»

The solution of a generalized stochastic Petri net (GSPN) is severely restricted by the size of its underlying continuous-time Markov chain. In recent work (G. Ciardo and A.S. Miner, 1999), matrix diagrams built from a Kronecker expression for the transition rate matrix of certain types of GSPNs were shown to allow for more efficient solution; however, the GSPN model requires a special form, so th... View full abstract»

Markov chain based analysis of GSPNs suffers from the state space explosion problem. In this paper we combine ideas from two different other approaches to analyze systems with very large state spaces. First, we represent the generator matrix as a sum of Kronecker products of small component matrices. Second, we use an extension of probabilistic decision graphs to represent probability vectors. The... View full abstract»

Fluid (or hybrid) Petri nets with flush-out arcs are Petri net based models with two classes of places: discrete places that carry a natural number of distinct objects (tokens), and fluid places that hold a positive amount of fluid, represented by a real number. For this kind of formalism, equations can be automatically derived from the model. Such equations, however, are often too complex to be s... View full abstract»

An important feature of the next generation Internet will be the ubiquitous access of mobile users dealing with real-time applications. A recently introduced architecture, called USAIA by J. Sokol and J. Widmer (2001), is considered to provide both for realtime traffic, fast handoffs and a high probability for QoS support during movement of the mobile nodes. This paper examines the performance of ... View full abstract»

The time domain analysis of non-Markovian stochastic Petri nets (NMSPNs) with preemptive repeat identical (pri) type transitions is considered in this paper. The set of time domain equations describing the evolution of the marking process is provided. The relation of the time domain and the formerly available transform domain description is discussed. Based on the time domain description of the pr... View full abstract»

This paper presents a general framework for modeling distributed computing environments for performance analysis by means of Timed Hierarchical Coloured Petri Nets. The proposed framework was used to build and analyze a Coloured Petri Net model of a HTTP web server. Analysis of the performance of the web server model reveals how the web server will respond to changes in the arrival rate of request... View full abstract»