Fluid queues and regular variation
This paper considers a fluid queueing system, fed by N independent sources that alternate between silence and activity periods. We assume that the distribution of the activity periods of one or more sources is a regularly varying function of index zeta. We show that its fat tail gives rise to an even fatter tail of the buffer content distribution, viz., one that is regularly varying of index zeta + 1. In the special case that zeta is an element of (-2, -1), which implies long-range dependence of the input process, the buffer content does not even have a finite first moment. As a queueing-theoretic by-product of the analysis of the case of N identical sources, with N --> infinity, we show that the busy period of an M/G/infinity queue is regularly varying of index zeta iff the service time distribution is regularly varying of index zeta.
fluid queue regular variation buffer content long-range dependence