Impact of bursty traffic on queues (Q1862208)

In a discrete single server queue with deterministic service the tail distribution of the stationary queue length \(q\) is analysed. The special feature of the paper is the bursty/self-similar/long-range dependent input. The number of entering customers per time unit is modelled by the number of busy servers of an M/G/\(\infty\) queue with a heavy-tailed service time distribution \(G(x)\). Unlike the case of Poisson-type traffic, where the tail of the distribution of \(q\) decreases exponentially, in the bursty case the tail \(P(q>x)\) of the queue length decreases slower as some (definite) power of \(\int_x^\infty(1-G(t))dt\) as \(x\to \infty\).