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The purpose of this tutorial presentation is to introduce G-Networks, or Gelenbe Networks, which are product form queueing networks which include normal or positive customers, as well as negative customers which destroy other customers, and triggers which displace other customers from one queue to another. We derive the balance equations for these models in the context of multiple customer classes, show the product form results, and exhibit the traffic equations which - in this case, contrary to BCMP and Jackson networks - are non-linear. This leads to interesting issues of existence and uniqueness of the steady-state solution. Gelenbe Network can be used to model large scale computer systems and networks in which signaling functions represented by negative customers and triggers are used to achieve flow and congestion control. | The purpose of this tutorial presentation is to introduce G-Networks, or Gelenbe Networks, which are product form queueing networks which include normal or positive customers, as well as negative customers which destroy other customers, and triggers which displace other customers from one queue to another. We derive the balance equations for these models in the context of multiple customer classes, show the product form results, and exhibit the traffic equations which - in this case, contrary to BCMP and Jackson networks - are non-linear. This leads to interesting issues of existence and uniqueness of the steady-state solution. Gelenbe Network can be used to model large scale computer systems and networks in which signaling functions represented by negative customers and triggers are used to achieve flow and congestion control. | ||
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* [https://link.springer.com/content/pdf/10.1007%2F3-540-45798-4_1.pdf https://link.springer.com/content/pdf/10.1007%2F3-540-45798-4_1.pdf] | * [https://link.springer.com/content/pdf/10.1007%2F3-540-45798-4_1.pdf https://link.springer.com/content/pdf/10.1007%2F3-540-45798-4_1.pdf] | ||
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| + | * [http://link.springer.com/content/pdf/10.1007/3-540-45798-4_1 http://link.springer.com/content/pdf/10.1007/3-540-45798-4_1], | ||
| + | : [http://dx.doi.org/10.1007/3-540-45798-4_1 http://dx.doi.org/10.1007/3-540-45798-4_1] | ||
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| + | * [https://dblp.uni-trier.de/db/conf/performance/performance2002.html#Gelenbe02 https://dblp.uni-trier.de/db/conf/performance/performance2002.html#Gelenbe02], | ||
| + | : [https://link.springer.com/chapter/10.1007/3-540-45798-4_1 https://link.springer.com/chapter/10.1007/3-540-45798-4_1], | ||
| + | : [https://www.scipedia.com/public/Gelenbe_2007a https://www.scipedia.com/public/Gelenbe_2007a], | ||
| + | : [https://rd.springer.com/chapter/10.1007/3-540-45798-4_1 https://rd.springer.com/chapter/10.1007/3-540-45798-4_1], | ||
| + | : [https://academic.microsoft.com/#/detail/1593962000 https://academic.microsoft.com/#/detail/1593962000] | ||
Latest revision as of 16:13, 21 January 2021
Abstract
The purpose of this tutorial presentation is to introduce G-Networks, or Gelenbe Networks, which are product form queueing networks which include normal or positive customers, as well as negative customers which destroy other customers, and triggers which displace other customers from one queue to another. We derive the balance equations for these models in the context of multiple customer classes, show the product form results, and exhibit the traffic equations which - in this case, contrary to BCMP and Jackson networks - are non-linear. This leads to interesting issues of existence and uniqueness of the steady-state solution. Gelenbe Network can be used to model large scale computer systems and networks in which signaling functions represented by negative customers and triggers are used to achieve flow and congestion control.
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Published on 01/01/2007
Volume 2007, 2007
DOI: 10.1007/3-540-45798-4_1
Licence: CC BY-NC-SA license
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