Asymptotics of palm-stationary buffer content distributions in fluid flow queues

We study a fluid flow queueing system with m independent sources alternating between periods of silence and activity; m >= 2. The distribution function of the activity periods of one source, is supposed to be intermediate regular varying. We show that the distribution of the net increment of the buffer during an aggregate activity period (i.e. when at least one source is active) is asymptotically tail-equivalent to the distribution of the net input during a single activity period with intermediate regular varying distribution function. In this way, we arrive at an asymptotic representation of the Palm-stationary tail-function of the buffer content at the beginning of aggregate activity periods. Our approach is probabilistic and extends recent results of Boxma (1996; 1997) who considered the special case of regular variation.