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1. S. Aalto and W. Scheinhardt, Tandem fluid queues fed by homogeneous on-off sources, Operations Research Letters, vol. 27, no. 2, pp. 73-82, 2000 (link)(bib)

   Abstract: We consider a tandem fluid model with multiple consecutive buffers. The input of buffer $j+1$ is the output from buffer $j$, while the first buffer is fed by a, possibly infinite, number of independent homogeneous on-off sources. The sources have exponentially distributed silent periods and generally distributed active periods. Under the assumption that the input rate of one source is larger than the maximum output rate of the first buffer, we are able to characterize the output from each buffer. Due to this fact we find (i) an equation for the Laplace-Stieltjes transform of the marginal content distribution of any buffer $j\geq 2$, (ii) explicit expressions for corresponding moments, and (iii) an explicit expression for the correlation between two buffer contents, again from the second buffer on. These results make use of a key observation concerning the aggregate contents of several consecutive buffers. For the case in which the active periods of the sources are exponential, the Laplace-Stieltjes transform is inverted. If there is only one source, all results are also valid for the first buffer.