Analysis of stochastic Petri nets with signals

Marin, Andrea; Balsamo, Simonetta; Harrison, Peter G.

doi:10.1016/j.peva.2012.06.003

Cited by 29 publications

(19 citation statements)

References 30 publications

(83 reference statements)

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“…Both these results provide a way to elegantly prove the product-form of a CTMC but they consider only pairwise synchronisations and hence they cannot be straightforwardly applied to study our models. We show that they can still be used by introducing a passage to the limit for a transition rate in a similar fashion of what has been done in [9], [23], [31]. Proofs of product-forms based on quasi-reversibility are simple to handle and compositional in the sense that they allow the combination of the models that we study here with others which are known to be quasi-reversible while maintaining the product-form of the equilibrium distribution.…”

Section: Technical Contributions and Related Workmentioning

confidence: 76%

“…The proof method based on the passage to the limit for modelling instantaneous propagation of transitions is inspired by the approach used in [9], [23], [31] for different networks and is alternative to the process algebraic one recently proposed in [24]. Notice that, thanks to the passage to the limit β → ∞, proving the product-form of a component as the one shown in Figure 1 can be readily done by considering the simplified model shown in Figure 2, in the sense that if the latter is quasi-reversible also the former is quasi-reversible.…”

Section: Theoremmentioning

confidence: 99%

“…Even more interestingly, for a class of product-form models, including the ones studied in this paper, the performance indices can be derived without even generating the joint state space. Successful applications of product-form theory include the BCMP theorem [4], the modelling of neural networks [28], the analysis of systems with fork and join constructs [31], the loss networks [29] and the performance evaluation of wireless networks [7], just to mention a not exhaustive list.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Product-Form Model for the Analysis of Systems with Aging Objects

Cavallin

Marin

Rossi

2015

2015 IEEE 23rd International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems

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Abstract-In this paper we propose a new model for the analysis of systems with aging objects such as Time-To-Live cache. We consider a model with an underlying Continuous Time Markov Chain in which objects can be completely or partially rejuvenated. In the former case the object becomes fresh, while in the latter all the objects are simultaneously rejuvenated so that the youngest becomes fresh. We show that under the so-called Independent Reference Model assumption our model is numerically tractable and has a product-form equilibrium distribution. Furthermore, we consider the case in which the object aging stops after a certain threshold and hence the partial rejuvenation introduces a probabilistic behaviour. Also in this case, we can derive a product-form equilibrium distribution under some mild conditions. The models presented in this paper may be interpreted as a new class of G-networks with catastrophes and partial flushing.

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Section: Technical Contributions and Related Workmentioning

confidence: 76%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Product-Form Model for the Analysis of Systems with Aging Objects

Cavallin

Marin

Rossi

2015

2015 IEEE 23rd International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems

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“…In fact, if a CTMC is ρ-reversible then its steady-state distribution can be expressed as a ratio between two products of rates (see Proposition 8) and this clearly simplifies the task of obtaining a product-form solution for the model. Nevertheless, coherently with the product-form theory developed in the literature (see, e.g., [7,4,2,9]), the formulation of conditions on the isolated components is desirable so that one has not to construct the whole joint process. In other words, we are interested in finding sufficient conditions under which the composition of high level stochastic models (e.g., Markovian process algebra components) originates a joint model which is ρ-reversible for some renaming ρ.…”

Section: Resultsmentioning

confidence: 99%

On Discrete Time Reversibility modulo State Renaming and its Applications

Marin

Rossi

2015

Proceedings of the 8th International Conference on Performance Evaluation Methodologies and Tools

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Time reversibility plays an important role in the analysis of continuous and discrete time Markov chains (DTMCs). Specifically, the computation of the stationary distribution of a reversible Markov chain has been proved to be very efficient and does not require the solution of the system of global balance equations. A DTMC is reversible when the processes at forward and reversed time are probabilistically indistinguishable. In this paper we introduce the concept of ρ-reversibility, i.e., a notion of reversibility modulo a renaming of the states, and we contrast it with the previous definition of dynamic reversibility especially with respect to the assumptions on the state renaming function. We discuss the applications of discrete time reversibility in the embedded and uniformized chains of continuous time processes.

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“…Therefore we adopt ordinary stochastic Petri nets (SPNs) to model and evaluate the performance. Stochastic Petri nets is a powerful tool for system performance evaluation [21][22][23]. In this paper, the basic theory of stochastic Petri nets is applied to model and evaluate performance of storage systems.…”

Section: Performance Evaluationmentioning

confidence: 99%

A Retrieval Optimized Surveillance Video Storage System for Campus Application Scenarios

Chen

et al. 2018

Journal of Electrical and Computer Engineering

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This paper investigates and analyzes the characteristics of video data and puts forward a campus surveillance video storage system with the university campus as the specific application environment. Aiming at the challenge that the content-based video retrieval response time is too long, the key-frame index subsystem is designed. The key frame of the video can reflect the main content of the video. Extracted from the video, key frames are associated with the metadata information to establish the storage index. The key-frame index is used in lookup operations while querying. This method can greatly reduce the amount of video data reading and effectively improves the query's efficiency. From the above, we model the storage system by a stochastic Petri net (SPN) and verify the promotion of query performance by quantitative analysis.

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Analysis of stochastic Petri nets with signals

Cited by 29 publications

References 30 publications

A Product-Form Model for the Analysis of Systems with Aging Objects

A Product-Form Model for the Analysis of Systems with Aging Objects

On Discrete Time Reversibility modulo State Renaming and its Applications

A Retrieval Optimized Surveillance Video Storage System for Campus Application Scenarios

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