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Multiplexing On-Off Sources with Subexponential On Periods: Part II (1997)
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BibTeX
@MISC{Jelenković97multiplexingon-off,
author = {Predrag R. Jelenković and Aurel A. Lazar},
title = { Multiplexing On-Off Sources with Subexponential On Periods: Part II},
year = {1997}
}
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Abstract
We consider an aggregate arrival process A N obtained by multiplexing N On-Off sources with exponential Off periods of rate λ and generally distributed On periods τ on. When N goes to infinity, with λN → Λ, AN approaches an M/G/ ∞ type process. For a fluid queue with the limiting M/G/ ∞ arrivals A ∞ t, regularly varying On periods with noninteger exponent, and capacity c, we obtain a precise asymptotic behavior of the queue length random variable QP t observed at the beginning of the arrival process activity periods P[Q P t> x] ∼ Λ r+ρ−c P[τ c−ρ on> u]du x → ∞, x/(r+ρ−c) where ρ = EA ∞ t < c; r (c ≤ r) is the rate at which the fluid is arriving during an On period. (In particular, when P[τ on> x] ∼ x −α,1 < α < 2, the above formula applies to the so-called long-range dependent On-Off sources.) Based on this asymptotic result and the results from a companion paper we suggest a computationally efficient approximation for the case of finitely many long-tailed On-Off sources. The accuracy of this approximation is verified with extensive simulation experiments.
Keyphrases
on-off source part ii efficient approximation aggregate arrival process many long-tailed on-off source arrival process activity period precise asymptotic behavior extensive simulation experiment exponential period queue length random variable qp formula applies fluid queue so-called long-range dependent on-off source companion paper asymptotic result noninteger exponent type process
