Fluid level in a reservoir with an on-off source

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.

• Type: Journal
• Year: 2008
• Where: SIGMETRICS
• Authors: Varun Gupta, Peter G. Harrison
• Keywords: Density Function, Fluid Level, Fluid Level Probability, Hardware, SIGMETRICS 2008