Tandem fluid queues fed by homogeneous on–off sources

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 j2, (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

STATIONARY ANALYSIS OF TANDEM FLUID QUEUES FED BY HOMOGENEOUS ON-OFF SOURCES

Abstract: We consider a fluid system composed of multiple buffers in series. The first buffer receives fluid from a finite superposition of independent identical on-off sources. The active and silent periods of sources are exponentially distributed. The ith buffer releases fluid in the (i + 1)th buffer. Assuming that the input rate of one source is greater than the service rate of the first buffer, the output process of each buffer can be modeled by an on-off source with the active period distributed as the busy period of an M/M/1 queue. For i ≥ 2, the stationary content distribution of the ith buffer is obtained by the use of generating functions which are explicitly inverted