Scheduling strategies and long-range dependence |
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Authors: | Anantharam Venkat |
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Institution: | (1) Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720, USA |
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Abstract: | 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 λ, with each session lasting for an independent integer time τ ⩾ 1, where P(τ = k) = p
k
with p
k
~ αk
−(1+α)
L(k), where 1 < α < 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 < α < 2, the arrival process of work is long-range dependent. Assume that
the stability condition λEτ] < 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 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.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | single server queue scheduling policies long-range dependence |
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