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.

Queueing theory (msc 60K25), Performance evaluation; queueing; scheduling (msc 68M20), Queues and service (msc 90B22)
Logistics (theme 3), Energy (theme 4)
CWI. Probability, Networks and Algorithms [PNA]

Boxma, O.J, & Dumas, V. (1997). Fluid queues with long-tailed activity period distributions. CWI. Probability, Networks and Algorithms [PNA]. CWI.