Tandem fluid queues fed by homogeneous on-off sources

We consider a tandem fluid model with multiple consecutive buffers. The inp ut of buffer j + 1 is the output from buffer j, while the first buffer is f ed by a, possibly infinite, number of independent homogeneous on-off source s. 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 greater than or equal to 2, (ii) explicit exp ressions for corresponding moments, and (iii) an explicit expression for th e correlation between two buffer contents, again from the second buffer on. These results make use of a key observation concerning the aggregate conte nts of several consecutive buffers. For the case in which the active period s of the sources are exponential, the Laplace-Stieltjes transform is invert ed. If there is only one source, all results are also valid for the first b uffer. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 60K25.