Necessary and sufficient ergodicity condition for open synchronized queueing networks

Florin, Gérard; Natkin, Stéphane

doi:10.1109/32.16598

Cited by 32 publications

(26 citation statements)

References 5 publications

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“…One of the advantages of this MGF-based method is that it can be extended to deal with stochastic Petri nets that have an infinite number of states. The examples studied by [11][12] will be used in this method. The research is of highly theoretical interest.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Integration of Petri nets and moment generating function approaches for system performance evaluation

Zhou

Guo²,

DiCesare

1993

Journal of Systems Integration

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Abstract. This article integrates arbitrary stochastic Petri nets (ASPN) and moment generating function approaches for performance evaluation of discrete event dynamic systems (DEDS). These systems include computer integrated manufacturing systems, resource-shared distributed systems, and communication networks. ASPN can describe various DEDS in which the time duration for activities may be a random variable of arbitrary distributions. In ASPN models, transitions with firing delays of general distributions are used to model these activities. Using our proposed perfbrmance analysis methodology, we first represent a system as an ASPN model, then generate its reachability graph and convert it into a state machine Petri net, derive the transfer functions of interesting performance measures through stepwise reductions, and finally obtain the analysis results. This method makes it possible to obtain analytical solutions of important performance indices. We use a robotic assembly system to illustrate the method. We obtain several important performance measures of a closed form. Finally, we discuss the limitations of this approach and future research.

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Section: Conclusion and Future Researchmentioning

confidence: 99%

Integration of Petri nets and moment generating function approaches for system performance evaluation

Zhou

Guo²,

DiCesare

1993

Journal of Systems Integration

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“…where m(p) τ is the marking of place p at time τ and the notation = AS means equal almost surely [15]. Similarly, the steady state throughput, χ, in an ergodic Petri net is defined as:…”

Section: Definition 3 [14] a Marked Graph (Mg) Is An Ordinary Petri mentioning

confidence: 99%

Accurate Performance Estimation for Stochastic Marked Graphs by Bottleneck Regrowing

Rodríguez

Júlvez

2010

Computer Performance Engineering

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Abstract. The adequate system performance is usually a critical requirement to be checked during the verification phase of a system. Thus, accurately measuring the performance of current industrial systems, which are often modelled as a Discrete Event Systems (DES), is a need. Due to the state explosion problem, the performance evaluation of DES becomes increasingly difficult as the size of the systems increases. Some approaches, such as the computation of performance bounds, have been developed to overcome this problem. In this paper we propose a new method to produce performance bounds that are sharper than the ones that can be achieved with current methods. The core of our method is an iterative algorithm that initially considers the most constraining bottleneck cycle of the system and adds other cycles to it in each iteration. The proposed method is deeply explained and then applied to a broad set of Marked Graphs.

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“…Solutions that have been proposed are often based on (approximate) truncation techniques [21] or lumping [6, 7, 10, 361, thereby still performing the solution at the state space level, or they are based on product-form results which allow for an efficient convolution or mean-value analysis style of solution [16, 171. In all these cases, the "trick" is to circumvent the explicit generation of the overall state space before solution, or to decrease the size of the state space. As another trick to circumvent the explicit generation of the underlying Markov chain, we have recently proposed (after similar but less general work by Florin and Natkin [18,19,201) a class of infinite SPNs that allows for a matrix-geometric solution [23]. To allow for such a solution, we require the marking process underlying the SPN to exhibit a regular structure.…”

Section: Introductionmentioning

confidence: 99%

SPN2MGM: tool support for matrix-geometric stochastic Petri nets

Haverkort

Proceedings of IEEE International Computer Performance and Dependability Symposium

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In this paper we present the tool SPN2MGM that can be used to construct and solve stochastic Petri nets using matrix-geometric techniques. The tool automatically recognizes the "matrix-geometric structure" of the Markov chain underlying the stochastic Petri net, and solves the Markov chain with these well-known and efficient techniques.W e informally characterize the class of stochastic Petri nets of interest (a formal definition has been given in an earlier paper) after which we briefly touch upon the matrix-geometric solution approach. W e then present an overview of SPN2MGM by discussing the model class supported and the internal methods used. W e finish the paper with a case study in the area of queues with breakdowns. In particular, we present a model of a queueing system in which checkpointing can be used to shorten the recovery process after serverbreakdowns have occurred.

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Necessary and sufficient ergodicity condition for open synchronized queueing networks

Cited by 32 publications

References 5 publications

Integration of Petri nets and moment generating function approaches for system performance evaluation

Integration of Petri nets and moment generating function approaches for system performance evaluation

Accurate Performance Estimation for Stochastic Marked Graphs by Bottleneck Regrowing

SPN2MGM: tool support for matrix-geometric stochastic Petri nets

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