Fluid queues with long-tailed activity period distributions

This is a survey paper on fluid queues, with a strong emphasis on recent at tempts 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 act ivity periods of at least one source is assumed to be long-tailed, which ma y give rise to long-range dependence. We consider the effect of this tail b ehaviour on the steady-state distributions of the buffer content at embedde d points in time and at arbitrary time, and on the busy period distribution . Both exact results and bounds are discussed. (C) 1998 Elsevier Science B. V. All rights reserved.