Stochastic Upper and Lower Bounds for General Markov Fluids
F. Ciucu, F. Poloczek, and J. Schmitt. 28th International Teletraffic Congress (ITC 28), Würzburg, Germany, (September 2016)
Abstract
Promising perspectives of a hypothetical `Tactile Internet', or `Internet
at the speed of light', whereby network latencies become imperceptible to
users, have (again) triggered a broad interest to understand and mitigate
Internet latencies. In this paper we revisit the queueing analysis of the
versatile Markov Fluid traffic model, which was mainly investigated in the
1980-90s, yet
with questionable accuracy. We derive upper bounds on the tail distribution
of the queue size, which improve state-of-the-art results by an exponential
factor $O(ąppa^n)$, where $0<\p̨pa<1$ and $n$ is the number of
multiplexed sources; additionally, we provide the first lower bounds. The
underlying results are quite general in that they can be easily adapted to
derive the delay distribution for SP, FIFO, and EDF scheduling. Our overall
results rely on a powerful martingale methodology which was recently shown
to be remarkably accurate.
%0 Conference Paper
%1 Ciucu2016
%A Ciucu, Florin
%A Poloczek, Felix
%A Schmitt, Jens
%B 28th International Teletraffic Congress (ITC 28)
%C Würzburg, Germany
%D 2016
%K itc itc28
%T Stochastic Upper and Lower Bounds for General Markov Fluids
%U https://gitlab2.informatik.uni-wuerzburg.de/itc-conference/itc-conference-public/-/raw/master/itc28/Ciucu2016.pdf?inline=true
%X Promising perspectives of a hypothetical `Tactile Internet', or `Internet
at the speed of light', whereby network latencies become imperceptible to
users, have (again) triggered a broad interest to understand and mitigate
Internet latencies. In this paper we revisit the queueing analysis of the
versatile Markov Fluid traffic model, which was mainly investigated in the
1980-90s, yet
with questionable accuracy. We derive upper bounds on the tail distribution
of the queue size, which improve state-of-the-art results by an exponential
factor $O(ąppa^n)$, where $0<\p̨pa<1$ and $n$ is the number of
multiplexed sources; additionally, we provide the first lower bounds. The
underlying results are quite general in that they can be easily adapted to
derive the delay distribution for SP, FIFO, and EDF scheduling. Our overall
results rely on a powerful martingale methodology which was recently shown
to be remarkably accurate.
@inproceedings{Ciucu2016,
abstract = {Promising perspectives of a hypothetical `Tactile Internet', or `Internet
at the speed of light', whereby network latencies become imperceptible to
users, have (again) triggered a broad interest to understand and mitigate
Internet latencies. In this paper we revisit the queueing analysis of the
versatile Markov Fluid traffic model, which was mainly investigated in the
1980-90s, yet
with questionable accuracy. We derive upper bounds on the tail distribution
of the queue size, which improve state-of-the-art results by an exponential
factor $O(ąppa^n)$, where $0<\p̨pa<1$ and $n$ is the number of
multiplexed sources; additionally, we provide the first lower bounds. The
underlying results are quite general in that they can be easily adapted to
derive the delay distribution for SP, FIFO, and EDF scheduling. Our overall
results rely on a powerful martingale methodology which was recently shown
to be remarkably accurate.},
added-at = {2016-08-31T16:30:53.000+0200},
address = {Würzburg, Germany},
author = {Ciucu, Florin and Poloczek, Felix and Schmitt, Jens},
biburl = {https://www.bibsonomy.org/bibtex/25a97cfbe5a380a640bffc14da2e0d416/itc},
booktitle = {28th International Teletraffic Congress (ITC 28)},
days = {12},
interhash = {897384909c378dac2a6f5f0be22487ec},
intrahash = {5a97cfbe5a380a640bffc14da2e0d416},
keywords = {itc itc28},
month = {Sept},
timestamp = {2020-05-26T16:53:35.000+0200},
title = {Stochastic Upper and Lower Bounds for General Markov Fluids},
url = {https://gitlab2.informatik.uni-wuerzburg.de/itc-conference/itc-conference-public/-/raw/master/itc28/Ciucu2016.pdf?inline=true},
year = 2016
}