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Fluid level in a reservoir with an on-off source

Varun Gupta, Peter G. Harrison

Conference or Workshop Paper
10th workshop on mathematical performance modeling and analysis (MAMA 2008)
December, 2008
Performance Evaluation Review
Volume 36
Issue 2
DOI 10.1145/1453175.1453206

We obtain the Laplace transform of the fluid level probability density function, in terms of the on-period density function, for a fluid queue (or reservoir) with on-off input at equilibrium. We further obtain explicit expressions for the moments of fluid level in terms of the moments of the on-period and hence derive an algorithm for the moments of fluid level at every queue in a tandem network. It turns out that to calculate the kth moment at the ith queue, only the first k+1 moments of the on-period of the input process to the first queue are required.

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