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Ergodicity and Throughput Bounds of Petri Nets with Unique Consistent Firing Count Vector
 IEEE Transactions on Software Engineering
, 1991
"... This paper addresses ergodicity and throughput bounds characterizations for a subclass of timed and stochastic Petri nets, interleaving qualitative and quantitative theories. The considered nets represent an extension of the well known subclass of marked graphs, defined as having a unique consistent ..."
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Cited by 35 (14 self)
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This paper addresses ergodicity and throughput bounds characterizations for a subclass of timed and stochastic Petri nets, interleaving qualitative and quantitative theories. The considered nets represent an extension of the well known subclass of marked graphs, defined as having a unique consistent firing count vector, independently of the stochastic interpretation of the net model. In particular, persistent and monoTsemiflow nets subclasses are considered. Upper and lower throughput bounds are computed using linear programming problems defined on the incidence matrix of the underlying net. The bounds proposed here depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases). From a different perspective, the considered subclasses of stochastic nets can be viewed as special classes of synchronized queueing networks, thus the proposed bounds can be applied to these networks. ...
Properties and Performance Bounds for Timed Marked Graphs
 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS  I: FUNDAMENTAL THEORY AND APPLICATIONS
, 1992
"... A class of synchronized queueing networks with deterministic routing is identified to be equivalent to a subclass of timed Petri nets called marked graphs. First some structural and behavioral properties of marked graphs are recalled and used to show interesting properties of this class of performan ..."
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Cited by 22 (8 self)
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A class of synchronized queueing networks with deterministic routing is identified to be equivalent to a subclass of timed Petri nets called marked graphs. First some structural and behavioral properties of marked graphs are recalled and used to show interesting properties of this class of performance models. In particular, ergodicity is derived from boundedness and liveness of the underlying Petri net representation, which can be efficiently computed in polynomial time on the net structure. In case of unbounded (i.e., nonstronglyconnected) marked graphs, ergodicity is computed as a function of the average transition firing delays. Then the problem of computing both upper and lower bounds for the steadystate performance of timed and stochastic marked graphs is studied. In particular, linear programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight (i.e., attainable) bounds for the throughput of transitions for marked graphs with dete...
Tight Polynomial Bounds for SteadyState Performance of Marked Graphs
, 1989
"... The problem of computing both upper and lower bounds for the steadystate performance of timed and stochastic Marked Graphs is studied. In particular, Linear Programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight (i.e., reachable) bounds for the t ..."
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Cited by 14 (11 self)
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The problem of computing both upper and lower bounds for the steadystate performance of timed and stochastic Marked Graphs is studied. In particular, Linear Programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight (i.e., reachable) bounds for the throughput of transitions for live and bounded Marked Graphs with time associated with transitions. These bounds depend on the initial marking and the mean values of the delays but not on the probability distributions (thus including both the deterministic and the stochastic cases). Connections between results and techniques typical of qualitative and quantitative analysis of Petri models are stressed. 1 Introduction One of the main problems in the actual use of timed and stochastic Petri net models for the performance evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. Exact performance results are usually obtained from the numerical solu...
SteadyState Performance Evaluation of Totally Open Systems of Markovian Sequential Processes
 Decentralized Systems, pages 427438. Elsevier Science Publishers B.V. (NorthHolland
, 1990
"... Totally open systems of Markovian sequential processes are defined as a subclass of stochastic Petri nets. They can be viewed as a generalization of a subclass of queueing networks in which complex sequential servers can be synchronized according to some particular schemes. Structural analysis of th ..."
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Cited by 7 (7 self)
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Totally open systems of Markovian sequential processes are defined as a subclass of stochastic Petri nets. They can be viewed as a generalization of a subclass of queueing networks in which complex sequential servers can be synchronized according to some particular schemes. Structural analysis of these nets is considered for avoiding the state explotion problem of the embedded Markov chain. Some qualitative properties interesting from a performance point of view are presented. In particular, a "potential ergodicity" property is characterized by means of two structural properties: consistency and synchronic distance relation. Necessary and sufficient ergodicity conditions and the computation of steadystate performance measures are studied. 1 Introduction Stochastic Petri nets constitute an adequate model for the evaluation of performance measures of concurrent systems [Mol 82, ABC 84, FN 85]. The Markovian model obtained from Petri nets by associating exponential distributions to the ...
On Liveness Analysis Through Linear Algebraic Techniques
 In Proceedings of the Annual General Meeting of ESPRIT Basic Research Action 3148 Design Methods Based on Nets (DEMON
, 1990
"... Proving properties of Place/Transition Nets through Linear Algebraic Techniques is very interesting because of the polynomial complexity of the algorithms used for this purpose. In this sense, many works have been devoted to the linear analysis of marking related properties (e.g. boundedness of the ..."
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Cited by 3 (3 self)
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Proving properties of Place/Transition Nets through Linear Algebraic Techniques is very interesting because of the polynomial complexity of the algorithms used for this purpose. In this sense, many works have been devoted to the linear analysis of marking related properties (e.g. boundedness of the state space, mutual exclusions, etc.). Nevertheless, few results exist related to linear analysis of liveness properties. In this note, we investigate some applications of linear techniques to partial characterization of liveness properties. First, a necessary condition for structural liveness in structural bounded nets is presented. It is based on the rank of the incidence matrix. Finally, given an initial marking, some sufficient conditions for dead transitions and for deadlockfreeness are presented. 1 Introduction The interest in parallel and distributed systems grows constantly according to the new domains of application of this kind of systems. One of the main problems arising from th...
Optimal stationarybehavior for a class of timed continuousPetri nets
"... This paper has been published as: B. Gaujal, A. Giua, ”Optimal stationary behavior for a class of timed continuous Petri nets,” Automatica, Vol. 40, No. 9, pp. 1505–1516, Sep 2004. In this paper, we consider a deterministic timed continuous Petri net model where conflicts at places are solved by usi ..."
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This paper has been published as: B. Gaujal, A. Giua, ”Optimal stationary behavior for a class of timed continuous Petri nets,” Automatica, Vol. 40, No. 9, pp. 1505–1516, Sep 2004. In this paper, we consider a deterministic timed continuous Petri net model where conflicts at places are solved by using stationary routing parameters. We show how to compute the stationary firing rate for all transitions via linear programming, so as to determine the optimal routing parameters that maximize userdefined linear functions of the firing rates. Finally, we discuss the relations with discrete Petri nets. 1
Performance Evaluation of Repetitive Automated Manufacturing Systems
 in: Proc. of the Rensselaer's Second Int. Conf. on CIM
, 1990
"... Steadystate performance evaluation of some repetitive automated manufacturing systems modelled by means of stochastic or deterministic timed Petri nets is considered. Basically, concepts and techniques developed by the authors in other works are applied to repetitive manufacturing systems in this p ..."
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Steadystate performance evaluation of some repetitive automated manufacturing systems modelled by means of stochastic or deterministic timed Petri nets is considered. Basically, concepts and techniques developed by the authors in other works are applied to repetitive manufacturing systems in this paper. Linear programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight upper and lower bounds for the performance measures of jobshop systems and decisionfree kanban systems in polynomial time on the net structure. The results can be extended to other models in which some decisions are allowed, such as producerconsumer systems with mutual exclusion. Exact performance measures for a class of systems containing sequential processes can be computed in polynomial time. 1 Introduction Modelling tools for designing complex manufacturing systems must be selected such that qualitative and quantitative analysis can be achieved in an efficient way....