Bounding techniques for transient analysis of G-networks with catastrophes

Abstract : We apply stochastic comparisons in order to bound the transient behavior of G-networks with catastrophes. These networks belong to Gelenbe's networks, with both positive and negative customers (or signals). We consider catastrophes where the signal deletes all customers in a queue. G-networks have a known product form steady-state distribution, but it is still impossible to obtain the transient distributions by a closed form. In the present paper, we propose to define smaller queueing systems providing bounds for subnetworks of the G-network with catastrophes. We apply stochastic comparisons by mapping functions to build bounding models. We derive transient performance measure bounds for applications as malware software infections. For instance, we obtain bounds for the first time of infection, or the number of times a station has been infected in a time interval. We study the tradeoff between the size of the subnetwork and the quality of the bounds with respect to parameters
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VALUETOOLS 2011 : 5th International ICST Conference on Performance Evaluation Methodologies and Tools, May 2011, Paris France. ICST, Proceedings VALUETOOLS 2011 : 5th International ICST Conference on Performance Evaluation Methodologies and Tools, pp.197 - 206, 2011
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https://hal.archives-ouvertes.fr/hal-01301868
Contributeur : Médiathèque Télécom Sudparis & Institut Mines-Télécom Business School <>
Soumis le : mercredi 13 avril 2016 - 10:52:01
Dernière modification le : jeudi 3 mai 2018 - 16:58:02

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  • HAL Id : hal-01301868, version 1

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Hind Castel-Taleb, Idriss Ismael Aouled, Nihal Pekergin. Bounding techniques for transient analysis of G-networks with catastrophes. VALUETOOLS 2011 : 5th International ICST Conference on Performance Evaluation Methodologies and Tools, May 2011, Paris France. ICST, Proceedings VALUETOOLS 2011 : 5th International ICST Conference on Performance Evaluation Methodologies and Tools, pp.197 - 206, 2011. 〈hal-01301868〉

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