10,149 research outputs found

    Matrix-geometric solution of infinite stochastic Petri nets

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    We characterize a class of stochastic Petri nets that can be solved using matrix geometric techniques. Advantages of such on approach are that very efficient mathematical technique become available for practical usage, as well as that the problem of large state spaces can be circumvented. We first characterize the class of stochastic Petri nets of interest by formally defining a number of constraints that have to be fulfilled. We then discuss the matrix geometric solution technique that can be employed and present some boundary conditions on tool support. We illustrate the practical usage of the class of stochastic Petri nets with two examples: a queueing system with delayed service and a model of connection management in ATM network

    Dependability Analysis of Control Systems using SystemC and Statistical Model Checking

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    Stochastic Petri nets are commonly used for modeling distributed systems in order to study their performance and dependability. This paper proposes a realization of stochastic Petri nets in SystemC for modeling large embedded control systems. Then statistical model checking is used to analyze the dependability of the constructed model. Our verification framework allows users to express a wide range of useful properties to be verified which is illustrated through a case study

    Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets

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    Two formal stochastic models are said to be bisimilar if their solutions as a stochastic process are probabilistically equivalent. Bisimilarity between two stochastic model formalisms means that the strengths of one stochastic model formalism can be used by the other stochastic model formalism. The aim of this paper is to explain bisimilarity relations between stochastic hybrid automata, stochastic differential equations on hybrid space and stochastic hybrid Petri nets. These bisimilarity relations make it possible to combine the formal verification power of automata with the analysis power of stochastic differential equations and the compositional specification power of Petri nets. The relations and their combined strengths are illustrated for an air traffic example.Comment: 15 pages, 4 figures, Workshop on Formal Methods for Aerospace (FMA), EPTCS 20m 201

    Structural characterization of decomposition in rate-insensitive stochastic Petri nets

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    This paper focuses on stochastic Petri nets that have an equilibrium distribution that is a product form over the number of tokens at the places. We formulate a decomposition result for the class of nets that have a product form solution irrespective of the values of the transition rates. These nets where algebraically characterized by Haddad et al.~as SΠ2S\Pi^2 nets. By providing an intuitive interpretation of this algebraical characterization, and associating state machines to sets of TT-invariants, we obtain a one-to-one correspondence between the marking of the original places and the places of the added state machines. This enables us to show that the subclass of stochastic Petri nets under study can be decomposed into subnets that are identified by sets of its TT-invariants

    MathMC: A mathematica-based tool for CSL model checking of deterministic and stochastic Petri nets

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    Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discreteevent systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. CSL (Continuous Stochastic Logic) is a (branching) temporal logic developed to express probabilistic properties in continuous time Markov chains (CTMCs). In this paper we present a Mathematica-based tool that implements recent developments for model checking CSL style properties on DSPNs. Furthermore, as a consequence of the type of process underlying DSPNs (a superset of Markovian processes), we are also able to check CSL properties of Generalized Stochastic Petri Nets (GSPNs) and labeled CTMCs

    About the Approximation of Stochastic Petri Nets by Continuous Petri Nets: Several Regions

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    Reliability analysis is often based on stochastic discrete event models like Markov models or stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. Moreover, the convergence of stochastic estimators is slow. For these reasons, fluidification can be investigated to estimate the asymptotic behaviour of stochastic processes with timed continuous Petri nets. The contribution of this paper is to point out the limits of the fluidification in the context of the stochastic steady state approximation. Unfortunately, the asymptotic mean marking of stochastic and continuous Petri nets with same structure and same initial marking are mainly often different. This paper shows that this difficulty is related to the partition in regions of the reachability state space and the existence of critical region

    Modelling and Simulation of Queuing Models through the concept of Petri Nets

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    In recent years Petri Nets has been in demand due to its visual depiction. Petri Nets are used as an effective method for portraying synchronization, a concurrency between different system activities. In queuing models Petri networks are used to represent distributed modeling of the system and thus evaluate their performance. By specifying suitable stochastic Petri Nets models, the authors concentrate on representing multi-class queuing systems of various queuing disciplines. The key idea is to define SPN models that simulate a given queue discipline 's behavior with some acceptable random choice. Authors have find system queuing with both a single server and multiple servers with load-dependent service rate. Petri networks in the queuing model have enhanced scalability by combining queuing and modeling power expressiveness of 'petri networks.' Examples of application of SPN models to performance evaluation of multiprocessor systems demonstrate the utility and effectiveness of this modeling method. In this paper, authors have made use of Stochastic Petri nets in queuing models to evaluate the performance of the system

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

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    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