An efficient numerical technique to calculate buffer statistics

Mushfiqur Rahman; Amjad Ali Soomro

doi:10.1016/0165-6074(89)90264-0

An efficient numerical technique to calculate buffer statistics

Mushfiqur Rahman^*, Amjad Ali Soomro

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

Abstract

A numerical solution is presented for obtaining the buffer statistics of a G/G/1 queue. The moment generating function G_M(z) of the number of blocks buffered at the completion of a service is assumed to be known via the Pollaczek Khinchine formula. Only finite number of arrivals during a service time are allowed. To compute the buffer statistics, poles of the denominator polynomial of G_M(z) and the residue at each pole are evaluated. The procedure is very efficient and stable; the computational complexity grows slowly as the order of the polynomial increases.

Original language	English
Pages (from-to)	129-138
Number of pages	10
Journal	Microprocessing and Microprogramming
Volume	26
Issue number	2
DOIs	https://doi.org/10.1016/0165-6074(89)90264-0
State	Published - Jun 1989

Bibliographical note

Funding Information:
The authors wish to acknowledge King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for support of this research.

Keywords

Buffer overflow probabilities
Error correcting code
Moment generating function
Queue

ASJC Scopus subject areas

General Engineering

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10.1016/0165-6074(89)90264-0

Cite this

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title = "An efficient numerical technique to calculate buffer statistics",

abstract = "A numerical solution is presented for obtaining the buffer statistics of a G/G/1 queue. The moment generating function GM(z) of the number of blocks buffered at the completion of a service is assumed to be known via the Pollaczek Khinchine formula. Only finite number of arrivals during a service time are allowed. To compute the buffer statistics, poles of the denominator polynomial of GM(z) and the residue at each pole are evaluated. The procedure is very efficient and stable; the computational complexity grows slowly as the order of the polynomial increases.",

keywords = "Buffer overflow probabilities, Error correcting code, Moment generating function, Queue",

author = "Mushfiqur Rahman and Soomro, \{Amjad Ali\}",

note = "Funding Information: The authors wish to acknowledge King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for support of this research.",

year = "1989",

month = jun,

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AU - Rahman, Mushfiqur

AU - Soomro, Amjad Ali

N1 - Funding Information: The authors wish to acknowledge King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for support of this research.

PY - 1989/6

Y1 - 1989/6

N2 - A numerical solution is presented for obtaining the buffer statistics of a G/G/1 queue. The moment generating function GM(z) of the number of blocks buffered at the completion of a service is assumed to be known via the Pollaczek Khinchine formula. Only finite number of arrivals during a service time are allowed. To compute the buffer statistics, poles of the denominator polynomial of GM(z) and the residue at each pole are evaluated. The procedure is very efficient and stable; the computational complexity grows slowly as the order of the polynomial increases.

AB - A numerical solution is presented for obtaining the buffer statistics of a G/G/1 queue. The moment generating function GM(z) of the number of blocks buffered at the completion of a service is assumed to be known via the Pollaczek Khinchine formula. Only finite number of arrivals during a service time are allowed. To compute the buffer statistics, poles of the denominator polynomial of GM(z) and the residue at each pole are evaluated. The procedure is very efficient and stable; the computational complexity grows slowly as the order of the polynomial increases.

KW - Buffer overflow probabilities

KW - Error correcting code

KW - Moment generating function

KW - Queue

UR - https://www.scopus.com/pages/publications/0024682519

U2 - 10.1016/0165-6074(89)90264-0

DO - 10.1016/0165-6074(89)90264-0

M3 - Article

AN - SCOPUS:0024682519

SN - 0165-6074

VL - 26

SP - 129

EP - 138

JO - Microprocessing and Microprogramming

JF - Microprocessing and Microprogramming

IS - 2

ER -

An efficient numerical technique to calculate buffer statistics

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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