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Stationary Solution to the Fluid Queue Fed by an M/M/1 Queue

Nelly Barbot 1 Bruno Sericola 1
1 ARMOR - Architectures and network models
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes, Ecole Nationale Supérieure des Télécommunications de Bretagne
Abstract : We consider an infinite capacity buffer receiving fluid at a rate depending on the state of an M/M/1 queue. We obtain a new analytic expression for the joint stationary distribution of the buffer level and the state of the M/M/1 queue. This expression is obtained by the use of generating functions which are explicitly inverted. The case of a finite capacity fluid queue is also considered.
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Submitted on : Tuesday, May 23, 2006 - 8:21:48 PM
Last modification on : Friday, February 4, 2022 - 3:23:03 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:03:13 PM


  • HAL Id : inria-00072306, version 1


Nelly Barbot, Bruno Sericola. Stationary Solution to the Fluid Queue Fed by an M/M/1 Queue. [Research Report] RR-4281, INRIA. 2001. ⟨inria-00072306⟩



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