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

We study a fluid flow queueing system with m independent sources alternatin g between periods of silence and activity; m greater than or equal to 2. Th e distribution function of the activity periods of one source, is supposed to be intermediate regular varying. We show that the distribution of the ne t increment of the buffer during an aggregate activity period (i.e. when at least one source is active) is asymptotically tail-equivalent to the distr ibution of the net input during a single activity period with intermediate regular varying distribution function. In this way, we arrive at an asympto tic representation of the Palm-stationary tail-function of the buffer conte nt at the beginning of aggregate activity periods. Our approach is probabil istic and extends recent results of Boxma (1996; 1997) who considered the s pecial case of regular variation. AMS 1991 Subject Classification: Primary 60K25; 60F10; 68M20; 90B15.