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Modeling and Analysis of Timed Petri Nets Using Heaps of Pieces
, 1997
"... We show that safe timed Petri nets can be represented by special automata over the (max,+) semiring, which compute the height of heaps of pieces. This extends to the timed case the classical representation a la Mazurkievicz of the behavior of safe Petri nets by trace monoids and trace languages. Fo ..."
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Cited by 56 (18 self)
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We show that safe timed Petri nets can be represented by special automata over the (max,+) semiring, which compute the height of heaps of pieces. This extends to the timed case the classical representation a la Mazurkievicz of the behavior of safe Petri nets by trace monoids and trace languages. For a subclass including all safe Free Choice Petri nets, we obtain reduced heap realizations using structural properties of the net (covering by safe state machine components). We illustrate the heapbased modeling by the typical case of safe jobshops. For a periodic schedule, we obtain a heapbased throughput formula, which is simpler to compute than its traditional timed event graph version, particularly if one is interested in the successive evaluation of a large number of possible schedules. Keywords Timed Petri nets, automata with multiplicities, heaps of pieces, (max,+) semiring, scheduling. I. Introduction The purpose of this paper 1 is to prove the following result: Timed safe Pe...
Markov Nets: Probabilistic Models for distributed and concurrent systems
 IEEE Transactions on Automatic Control
, 2001
"... For distributed systems, i.e. large networked complex systems, there is a drastic difference between a local view and knowledge of the system, and its global view. Distributed systems have local state and time, but do not possess global state and time in the usual sense. In this paper, motivated by ..."
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Cited by 39 (17 self)
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For distributed systems, i.e. large networked complex systems, there is a drastic difference between a local view and knowledge of the system, and its global view. Distributed systems have local state and time, but do not possess global state and time in the usual sense. In this paper, motivated by the monitoring of distributed systems and in particular of telecommunications networks, we develop Markov nets as an extension of Markov chains and hidden Markov models (Hmm) for distributed and concurrent systems. By a concurrent system, we mean a system in which components may evolve independently, with sparse synchronizations. We follow a socalled true concurrency approach, in which neither global state nor global linear time are available. Instead, we use only local states in combination with a partial order model of time. Our basic mathematical tool is that of Petri net unfoldings. Keywords : discrete event systems, stochastic Petri nets, unfoldings. 1 Motivations Distributed network...
Blocking a Transition in a Free Choice Net, and what it tells about its throughput
 in "Journal of Computer and System Sciences
"... In a live and bounded Free Choice Petri net, pick a nonconflicting transition. Then there exists a unique reachable marking in which no transition is enabled except the selected one. For a routed live and bounded Free Choice net, this property is true for any transition of the net. Consider now a l ..."
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Cited by 20 (7 self)
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In a live and bounded Free Choice Petri net, pick a nonconflicting transition. Then there exists a unique reachable marking in which no transition is enabled except the selected one. For a routed live and bounded Free Choice net, this property is true for any transition of the net. Consider now a live and bounded stochastic routed Free Choice net, and assume that the routings and the firing times are independent and identically distributed. Using the above results, we prove the existence of asymptotic firing throughputs for all transitions in the net. Furthermore, the vector of the throughputs at the different transitions is explicitly computable up to a multiplicative constant. 1.
Algebraic techniques for timed systems
 in CONCUR'98 Concurrency Theory, 9th International Conference
, 1998
"... A b s t r a c t. Performance evaluation is a central issue in the design of complex realtime systems. In this work, we propose an extension of socalled "MaxPlus " algebraic techniques to handle more realistic types of realtime systems. In particular, our framework encompasses g ..."
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Cited by 6 (2 self)
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A b s t r a c t. Performance evaluation is a central issue in the design of complex realtime systems. In this work, we propose an extension of socalled &quot;MaxPlus &quot; algebraic techniques to handle more realistic types of realtime systems. In particular, our framework encompasses graph or partial order automata, and more generally abstract models of realtime computations (including synchronous programs running over distributed architectures). To achieve this, we introduce a new dioid of partially commutative power series (transductions), whose elements encode timed behaviors. This formalism extends the traditional representation of timed event graphs by (rational) commutative transfer series with coefficients in the MaxPlus semiring. We sketch how this framework can be used to symbolically solve several problems of interest, related to realtime systems. Then we illustrate the use of this framework to encode a nontrivial mixed formalism of dataliow diagrams and automata. 1 M o t i v a t i o n s
Probabilistic Cluster Unfoldings
 FUNDAMENTA INFORMATICAE
"... This article introduces probabilistic cluster branching processes, a probabilistic unfolding semantics for untimed Petri nets, with no structural or safety assumptions, giving probability measures for concurrent runs. The unfolding is constructed by local choices on each cluster (conflict closed sub ..."
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Cited by 5 (3 self)
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This article introduces probabilistic cluster branching processes, a probabilistic unfolding semantics for untimed Petri nets, with no structural or safety assumptions, giving probability measures for concurrent runs. The unfolding is constructed by local choices on each cluster (conflict closed subnet), while the authorization for cluster actions is governed by a stochastic trace, the policy, that authorizes cluster actions. We introduce and characterize stopping times for these models, and prove a strong Markov property. Particularly adaquate probability measures for the choice of step in a cluster, as well as for the policy, are obtained by constructing Markov Fields from suitable markingdependent Gibbs potentials.
A Model Driven Approach to Represent Sequence Diagrams as Free Choice Petri Nets
 in 12th International IEEE Enterprise Distributed Object Computing Conference (EDOC). 2008
"... Model Driven Development (MDD) aims to promote the role of modeling in Software Engineering. Enterprise systems and architectures are often modeled via multiple representations. For example UML models are widely used by the designers to capture various viewpoint of the system; while formal models us ..."
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Cited by 5 (2 self)
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Model Driven Development (MDD) aims to promote the role of modeling in Software Engineering. Enterprise systems and architectures are often modeled via multiple representations. For example UML models are widely used by the designers to capture various viewpoint of the system; while formal models using languages such as CSP, Z and Petri Nets are suitable for the analysis. Model transformation techniques developed as a part of MDD can be applied to generate one model from another model automatically. This allows benefiting from the tools and techniques developed and used in multiple languages. This paper presents a method of applying MDD model transformation from UML 2.0 Sequence Diagrams to Petri Nets. The paper shows that the model transformation results in Free Choice Petri Nets. As a result, the low complexity of analysis and the synthesis techniques can be applied to the models of enterprise systems which are captured in UML Sequence Diagrams. 1.
Properties of untimed Routed Petri Nets
, 1999
"... In this paper, we study the properties of routing functions in nontimed Petri nets with respect to the nets' semantics. We consider two types of routing (origin dependent and origin independent) which are not mutually representable, and describe the net semantics induced. For unequivocal routi ..."
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Cited by 2 (1 self)
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In this paper, we study the properties of routing functions in nontimed Petri nets with respect to the nets' semantics. We consider two types of routing (origin dependent and origin independent) which are not mutually representable, and describe the net semantics induced. For unequivocal routing, the process behavior denable only in the origin dependent case is shown to be unique up to isomorphism. We show that every routed net is weakly routing place bisimilar to a Free Choice net. This fact, in turn, facilitates the subsequent study of fairness properties, which are characterized by the local equitability of the routing functions.
Automated Synthesis Of Liveness Enforcing Supervisors Using Petri Nets
, 2000
"... Given an arbitrary Petri net structure, which may have uncontrollable and unobservable transitions, the liveness enforcement procedure presented here determines a set of linear inequalities on the marking of a Petri net. When the Petri net is supervised so that its markings satisfy these inequalitie ..."
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Cited by 2 (2 self)
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Given an arbitrary Petri net structure, which may have uncontrollable and unobservable transitions, the liveness enforcement procedure presented here determines a set of linear inequalities on the marking of a Petri net. When the Petri net is supervised so that its markings satisfy these inequalities, the supervised net is proved to be live for all initial markings that satisfy the supervision constraints. Also the supervision is proved to be maximally permissive for a large class of Petri nets, which includes the fully controllable and observable Petri nets. Moreover, the supervisor supports specifications requiring only some of the Petri net transitions to be live. The maximal permissivity also applies for this case. The procedure allows automated synthesis of the supervisors. The sufficient conditions for which our theoretical results are guaranteed to apply can also be automatically verified.
Networked Conflicting Timed Event Graphs Representation in (Max,+) Algebra
, 2013
"... Abstract: Timed Event Graphs (TEGs) are a specific class of Petri nets that have been thoroughly studied given their useful linear state representation in (Max,+) algebra. Unfortunately, TEGs are generally not suitable for modeling systems displaying resources sharing (or conflicts). In this paper, ..."
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Abstract: Timed Event Graphs (TEGs) are a specific class of Petri nets that have been thoroughly studied given their useful linear state representation in (Max,+) algebra. Unfortunately, TEGs are generally not suitable for modeling systems displaying resources sharing (or conflicts). In this paper, we show that if a system with conflicts is modeled using a NCTEG (Networked Conflicting Timed Event Graphs), it is quite possible to obtain an equivalent (Max,+) representation. More precisely, we prove that the evolution of a NCTEG satisfies linear timevarying (Max,+) equations. In case of cyclic NCTEGs, which are a natural model of many repetitive systems, we provide a standard timeinvariant (Max,+) representation. As an application of the proposed approach to exhibit its interest, we consider the case of Jobshops. We first propose a generic NCTEGbased model of these systems and subsequently apply the corresponding (Max,+) representation to evaluate some of their performances.