Scheduling strategies and long-range dependence

Consider a single server queue with unit service rate fed by an arrival pro cess of the following form: sessions arrive at the times of a Poisson proce ss of rate lambda, with each session lasting for an independent integer tim e tau greater than or equal to 1, where P(tau = k ) = p(k) with p(k) simila r to alpha k(-(1 +alpha))L(k), where 1<alpha<2 and L(.) is a slowly varying function. Each session brings in work at unit rate while it is active. Thu s the work brought in by each arrival is regularly varying, and, because 1 < alpha < 2, the arrival process of work is long-range dependent. Assume th at the stability condition lambda E[tau] < 1 holds. By simple arguments we show that for any stationary nonpreemptive service policy at the queue, the stationary sojourn time of a typical session must stochastically dominate a regularly varying random variable having infinite mean; this is true even if the duration of a session is known at the time it arrives. On the other hand, we show that there exist causal stationary preemptive policies, whic h do not need knowledge of the session durations at the time of arrival, fo r which the stationary sojourn time of a typical session is stochastically dominated by a regularly varying random variable having finite mean. These results indicate that scheduling policies can have a significant influence on the extent to which long-range dependence in the arrivals influences the performance of communication networks.