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Summary: Queueing Systems 33 (1999) 7389 73
Scheduling strategies and long-range dependence
Venkat Anantharam
Department of Electrical Engineering and Computer Sciences, University of California,
Berkeley, CA 94720, USA
E-mail: ananth@vyasa.eecs.berkeley.edu
Received March 1998; revised February 1999
Consider a single server queue with unit service rate fed by an arrival process of the
following form: sessions arrive at the times of a Poisson process of rate , with each
session lasting for an independent integer time 1, where P( = k) = pk with pk
k-(1+)
L(k), where 1 < < 2 and L(·) is a slowly varying function. Each session brings
in work at unit rate while it is active. Thus the work brought in by each arrival is regularly
varying, and, because 1 < < 2, the arrival process of work is long-range dependent.
Assume that the stability condition E[] < 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, which do
not need knowledge of the session durations at the time of arrival, for which the stationary
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