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TRANSIENT ANALYSIS OF A FLUID QUEUE DRIVEN BY A BIRTH AND DEATH PROCESS SUGGESTED BY A CHAIN SEQUENCE

Bruno Sericola 1 P. R. Parthasarathy 2 K. V. Vijayashree 2
1 DIONYSOS - Dependability Interoperability and perfOrmance aNalYsiS Of networkS
Inria Rennes – Bretagne Atlantique , IRISA-D2 - RÉSEAUX, TÉLÉCOMMUNICATION ET SERVICES
Abstract : We analyse the transient behaviour of a fluid queue driven by a birth and death process (BDP) whose birth and death rates are suggested by a chain sequence. For the BDP suggested by a chain sequence, the stationary probabilities do not exist and hence the stationary buffer content distribution for fluid queues driven by such BDP does not exist. However, their transient distribution is obtained in a simple closed form by two different approaches: the first is the continued fraction approach and the second is an approach in terms of recurrence relation by an analysis similar to that of Sericola (1998). The probability for the buffer content to be empty at an arbitrary time is also studied. The variations in this performance measure are revealed in the form of graphs. Numerical illustrations are included.
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https://hal.inria.fr/hal-00713165
Contributor : Bruno Sericola <>
Submitted on : Friday, June 29, 2012 - 2:43:56 PM
Last modification on : Tuesday, June 15, 2021 - 4:13:51 PM

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  • HAL Id : hal-00713165, version 1

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Bruno Sericola, P. R. Parthasarathy, K. V. Vijayashree. TRANSIENT ANALYSIS OF A FLUID QUEUE DRIVEN BY A BIRTH AND DEATH PROCESS SUGGESTED BY A CHAIN SEQUENCE. Journal of Applied Mathematics and Stochastic Analysis, North Atlantic Science Publishing Company, 2005, 2. ⟨hal-00713165⟩

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