Transient analysis of a fluid queue driven by a birth and death process suggested by a chain sequence

Transient analysis of a fluid queue driven by a birth and death process suggested by a chain sequence

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Article ID: iaor20091431
Country: United States
Volume: 2005
Issue: 2
Start Page Number: 143
End Page Number: 158
Publication Date: May 2005
Journal: Journal of Applied Mathematics and Stochastic Analysis
Authors: , ,
Keywords: networks: flow, queues: applications
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. 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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