An application of superpositions of two-state Markovian sources to the modelling of self-similar behaviour

Allan T. Andersen; Bo Friis Nielsen

doi:10.1109/INFCOM.1997.635130

An application of superpositions of two-state Markovian sources to the modelling of self-similar behaviour

Allan T. Andersen, Bo Friis Nielsen

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Abstract

We present a modelling framework and a fitting method for modelling second order self-similar behaviour with the Markovian arrival process (MAP). The fitting method is based on fitting to the autocorrelation function of counts a second order self-similar process. It is shown that with this fitting algorithm it is possible closely to match the autocorrelation function of counts for a second order self-similar process over 3-5 time-scales with 8-16 state MAPs with a very simple structure, i.e. a superposition of 3 and 4 interrupted Poisson processes (IPP) respectively and a Poisson process. The fitting method seems to work well over the entire range of the Hurst (1951) parameter

Original language	English
Title of host publication	IEEE INFOCOM Kobe, Japan
Publisher	IEEE Press
Publication date	1997
Pages	196-204
ISBN (Print)	0-8186-7780-5
DOIs	https://doi.org/10.1109/INFCOM.1997.635130
Publication status	Published - 1997
Event	16th Joint Conference of the IEEE Computer and Communications Societies - Kobe, Japan Duration: 7 Apr 1997 → 12 Apr 1997 https://ieeexplore.ieee.org/xpl/conhome/4979/proceeding

Conference

Conference	16th Joint Conference of the IEEE Computer and Communications Societies
Country/Territory	Japan
City	Kobe
Period	07/04/1997 → 12/04/1997
Internet address	https://ieeexplore.ieee.org/xpl/conhome/4979/proceeding

Bibliographical note

Copyright: 1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

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title = "An application of superpositions of two-state Markovian sources to the modelling of self-similar behaviour",

abstract = "We present a modelling framework and a fitting method for modelling second order self-similar behaviour with the Markovian arrival process (MAP). The fitting method is based on fitting to the autocorrelation function of counts a second order self-similar process. It is shown that with this fitting algorithm it is possible closely to match the autocorrelation function of counts for a second order self-similar process over 3-5 time-scales with 8-16 state MAPs with a very simple structure, i.e. a superposition of 3 and 4 interrupted Poisson processes (IPP) respectively and a Poisson process. The fitting method seems to work well over the entire range of the Hurst (1951) parameter",

author = "Andersen, {Allan T.} and Nielsen, {Bo Friis}",

note = "Copyright: 1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE; 16th Joint Conference of the IEEE Computer and Communications Societies, IEEE INFOCOM 1997 ; Conference date: 07-04-1997 Through 12-04-1997",

year = "1997",

doi = "10.1109/INFCOM.1997.635130",

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AU - Nielsen, Bo Friis

N1 - Copyright: 1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

PY - 1997

Y1 - 1997

N2 - We present a modelling framework and a fitting method for modelling second order self-similar behaviour with the Markovian arrival process (MAP). The fitting method is based on fitting to the autocorrelation function of counts a second order self-similar process. It is shown that with this fitting algorithm it is possible closely to match the autocorrelation function of counts for a second order self-similar process over 3-5 time-scales with 8-16 state MAPs with a very simple structure, i.e. a superposition of 3 and 4 interrupted Poisson processes (IPP) respectively and a Poisson process. The fitting method seems to work well over the entire range of the Hurst (1951) parameter

AB - We present a modelling framework and a fitting method for modelling second order self-similar behaviour with the Markovian arrival process (MAP). The fitting method is based on fitting to the autocorrelation function of counts a second order self-similar process. It is shown that with this fitting algorithm it is possible closely to match the autocorrelation function of counts for a second order self-similar process over 3-5 time-scales with 8-16 state MAPs with a very simple structure, i.e. a superposition of 3 and 4 interrupted Poisson processes (IPP) respectively and a Poisson process. The fitting method seems to work well over the entire range of the Hurst (1951) parameter

U2 - 10.1109/INFCOM.1997.635130

DO - 10.1109/INFCOM.1997.635130

M3 - Article in proceedings

SN - 0-8186-7780-5

SP - 196

EP - 204

BT - IEEE INFOCOM Kobe, Japan

PB - IEEE Press

T2 - 16th Joint Conference of the IEEE Computer and Communications Societies

Y2 - 7 April 1997 through 12 April 1997

ER -

An application of superpositions of two-state Markovian sources to the modelling of self-similar behaviour

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