Fluid queues with long-tailed activity period distributions

This is a survey paper on fluid queues, with a strong emphasis on recent attempts to represent phenomena like long-range dependence. The central model of the paper is a fluid queueing system fed by $N$ independent sources that alternate between silence and activity periods. The distribution of the activity periods of at least one source is assumed to be long-tailed, which may give rise to long-range dependence. We consider the effect of this tail behaviour on the steady-state distributions of the buffer content at embedded points in time and at arbitrary time, and on the busy period distribution. Both exact results and bounds are discussed.