5,323 research outputs found

    Reachability of Communicating Timed Processes

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    We study the reachability problem for communicating timed processes, both in discrete and dense time. Our model comprises automata with local timing constraints communicating over unbounded FIFO channels. Each automaton can only access its set of local clocks; all clocks evolve at the same rate. Our main contribution is a complete characterization of decidable and undecidable communication topologies, for both discrete and dense time. We also obtain complexity results, by showing that communicating timed processes are at least as hard as Petri nets; in the discrete time, we also show equivalence with Petri nets. Our results follow from mutual topology-preserving reductions between timed automata and (untimed) counter automata.Comment: Extended versio

    Preemptive D-timed Petri nets, timeouts, modeling and analysis of communication protocols

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    Preemptive D-timed Petri nets are Petri nets with deterministic firing times and with generalized inhibitor arcs to interrupt firing transitions. A formalism is presented which represents the behavior of free-choice D-timed Petri nets by discrete-space discrete-time semi-Markov processes. Stationary probabilities of states can thus be determined by standard techniques used for analysis of Markov chains. A straightforward application of timed Petri nets is modelling and analysis of systems of asynchronous communicating processes, and in particular communication protocols. Places of Petri nets model queues of messages, transitions represent delays in communication networks, interrupt arcs conveniently model timeout mechanisms, and probabilities associated with free-choice classes correspond to relative frequencies of random events. Simple protocols are used as an illustration of modelling and analysis

    M-timed Petri nets, priorities, preemptions, and performance evaluation of systems

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    In M-timed Petri nets, firing times are exponentially distributed random variables associated with transitions of a net. Several classes of M-timed Petri nets are discussed in this paper to show increasing “modelling power” of different nets. Conflict-free nets can model M- and E k -type queueing systems. Free-choice nets can also represent H k -type systems. Systems with several classes of users and with service priorities assigned to user classes require nets with inhibitor arcs. Preemption of service can be represented by extended nets with escape (or generalized inhibitor) arcs. Finally, to provide flexible modelling of scheduling and decision strategies, enhanced Petri nets are introduced with two classes of transitions, immediate and timed ones, and with (exponentially distributed) firing times associated with the timed transitions. It is shown that the behavior of bounded M-timed Petri nets can be represented by finite “state” graphs which are finite-state continuous-time homogeneous Markov processes. Stationary probabilities of states can thus be obtained by standard techniques used for analysis of Markov chains, and then operational analysis can be applied for performance evaluation. Simple models of interactive systems are used as an illustration of modelling

    Modeling and analysis of semiconductor manufacturing processes using petri nets

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    This thesis addresses the issues in modeling and analysis of multichip module (MCM) manufacturing processes using Petri nets. Building such graphical and mathematical models is a crucial step to understand MCM technologies and to enhance their application scope. In this thesis, the application of Petri nets is presented with top-down and bottom-up approaches. The theory of Petri nets is summarized with its basic notations and properties at first. After that, the capability of calculating and analyzing Petri nets with deterministic timing information is extended to meet the requirements of the MCM models. Then, using top-down refining and system decomposition, MCM models are built from an abstract point to concrete systems with timing information. In this process, reduction theory based on a multiple-input-single-output modules for deterministic Petri nets is applied to analyze the cycle time of Petri net models. Besides, this thesis is of significance in its use of the reduction theory which is derived for timed marked graphs - an important class of Petri nets

    Timed Basic Parallel Processes

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    Timed basic parallel processes (TBPP) extend communication-free Petri nets (aka. BPP or commutative context-free grammars) by a global notion of time. TBPP can be seen as an extension of timed automata (TA) with context-free branching rules, and as such may be used to model networks of independent timed automata with process creation. We show that the coverability and reachability problems (with unary encoded target multiplicities) are PSPACE-complete and EXPTIME-complete, respectively. For the special case of 1-clock TBPP, both are NP-complete and hence not more complex than for untimed BPP. This contrasts with known super-Ackermannian-completeness and undecidability results for general timed Petri nets. As a result of independent interest, and basis for our NP upper bounds, we show that the reachability relation of 1-clock TA can be expressed by a formula of polynomial size in the existential fragment of linear arithmetic, which improves on recent results from the literature

    Extending the Petri box calculus with time

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    PBC (Petri Box Calculus) is a process algebra where real parallelism of concurrent systems can be naturally expressed. One of its main features is the definition of a denotational semantics based on Petri nets, which emphasizes the structural aspects of the modelled systems. However, this formal model does not include temporal aspects of processes, which are necessary when considering real-time systems. The aim of this paper is to extend the existing calculus with those temporal aspects. We consider that actions are not instantaneous, that is, their execution takes time. We present an operational semantics and a denotational semantics based on timed Petri nets. Finally, we discuss the introduction of other new features such as time-outs and delays. Throughout the paper we assume that the reader is familiar with both Petri nets and PBC

    Modified D-timed Petri nets, timeouts, and modelling of communication protocols

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    Modified D-timed Petri nets are Petri nets with ”spe- cial” arcs to interrupt firing transitions, and with deter- ministic firing times; these special arcs are called ”in- terrupt” arcs. It is shown that the behaviour of simple modified bounded free-choice D-timed Petri nets can be represented by finite probabilistic state graphs, stationary probabilities of states can thus be obtained by standard techniques used for analysis of Markov chains. An imme- diate application of such a model is performance analysis of systems of interacting asynchronous processes, and in particular communication protocols. Places of Petri nets model queues of messages, transitions represent events in communication networks, interrupt arcs conveniently model timeouts, and probabilities associated with free- choice classes correspond to relative frequencies of random events. A simple protocol based on unnumbered messages and acknowledgements is used as an illustration of analy- sis

    Towards a Notion of Distributed Time for Petri Nets

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    We set the ground for research on a timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. The novelty is that, rather than a single global clock, we use a set of unrelated clocks --- possibly one per place --- allowing a local timing as well as distributed time synchronisation. We give a formal definition of the model and investigate properties of local versus global timing, including decidability issues and notions of processes of the respective models

    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
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