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Titolo:
Overflow behavior in queues with many long-tailed inputs
Autore:
Mandjes, M; Borst, S;
Indirizzi:
Lucent Technol, Bell Labs, Murray Hill, NJ 07974 USA Lucent Technol Murray Hill NJ USA 07974 l Labs, Murray Hill, NJ 07974 USA CWI, NL-1090 GB Amsterdam, Netherlands CWI Amsterdam Netherlands NL-1090GB , NL-1090 GB Amsterdam, Netherlands
Titolo Testata:
ADVANCES IN APPLIED PROBABILITY
fascicolo: 4, volume: 32, anno: 2000,
pagine: 1150 - 1167
SICI:
0001-8678(200012)32:4<1150:OBIQWM>2.0.ZU;2-#
Fonte:
ISI
Lingua:
ENG
Soggetto:
RANGE DEPENDENCE; LARGE DEVIATIONS; STORAGE MODEL; FLUID QUEUES; LARGE NUMBER; DISTRIBUTIONS; PROBABILITIES; ASYMPTOTICS; ECONOMIES; SYSTEMS;
Keywords:
buffer overflow; large-deviations asymptotics; long-tailed on periods; long-range dependence; on-off sources; queueing theory; reduced-load approximation; regular variation; subexponentiality;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
48
Recensione:
Indirizzi per estratti:
Indirizzo: Mandjes, M Lucent Technol, Bell Labs, 600 Mt Ave,POB 636, Murray Hill, NJ 07974 USA Lucent Technol 600 Mt Ave,POB 636 Murray Hill NJ USA 07974 USA
Citazione:
M. Mandjes e S. Borst, "Overflow behavior in queues with many long-tailed inputs", ADV APPL P, 32(4), 2000, pp. 1150-1167

Abstract

We consider a fluid queue fed by the superposition of n homogeneous on-offsources with generally distributed on and off periods. The buffer space B and link rate C are scaled by n, so that we get nb and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponentially in the number of sources n. We specifically examine the scenariowhere b is also large. We obtain explicit asymptotics for the case where the on periods have a subexponential distribution, e.g., Pareto, Lognormal, or Weibull. The results show a sharp dichotomy in the qualitative behavior, depending on the shape of the function nu (t) := -logP(A* > t) for large t, A* representing the residual on period. If nu(.) is regularly varying of index 0 (e.g., Pareto, Lognormal), then, during the path to overflow, the input rate will only slightly exceed the link rate. Consequently, the buffer will fill 'slowly', and the typical time to overflow will be 'more than linear' in the buffer size. In contrast, if nu(.) is regularly varying of index strictlybetween 0 and 1 (e.g., Weibull), then the input rate will significantly exceed the link rate, and the time to overflow is roughly proportional to thebuffer size. In both cases there is a substantial fraction of the sources that remain in the on state during the entire path to overflow, while the others contribute at their mean rates. These observations lead to approximations for the overflow probability. The approximations may be extended to the case of heterogeneous sources. The results provide further insight into the so-called reduced-load approximation.

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Documento generato il 09/07/20 alle ore 19:26:28