Stationary analysis of tandem fluid queues fed by homogeneous on-off sources

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 greater than or equal to 2, the stationary content distribution of the ith buffer is obtained by the use of generating functions which are explicitly inverted.