Some New Markovian Models for Traffic and Performance Evaluation of Telecommunication Networks

A new queueing model is proposed, namely the $MM\,\sum_{k=1}^{K}{CPP_k}/GE/c/L\,G$ -Queue, also known as the Sigma queue. A steady state solution for this queue in a computable form is presented, based on an analytic methodology applying certain non-trivial transformations on the balance equations,...

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Bibliographic Details
Published inNetwork Performance Engineering pp. 642 - 664
Main Authors Chakka, Ram, Van Do, Tien
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2011
SeriesLecture Notes in Computer Science
Subjects
Batch Size
Compound Poisson Process
Generalize Exponential
Optical Burst Switching
Spectral Expansion
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Summary:A new queueing model is proposed, namely the $MM\,\sum_{k=1}^{K}{CPP_k}/GE/c/L\,G$ -Queue, also known as the Sigma queue. A steady state solution for this queue in a computable form is presented, based on an analytic methodology applying certain non-trivial transformations on the balance equations, which turn out to be of the QBD-M (Quasi Simultaneous-Multiple-Bounded Births and Deaths) type. As a consequence, existing methods such as the spectral expansion method or the matrix-geometric method can be used to obtain the steady state probabilities. The utility of this queue is demonstrated through the performance analysis of an optical burst switching (OBS) node. Numerical results show the impact of the burstiness of arrival process on the performance of the OBS multiplexer.
Bibliography:Original Abstract: A new queueing model is proposed, namely the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$MM\,\sum_{k=1}^{K}{CPP_k}/GE/c/L\,G$\end{document}-Queue, also known as the Sigma queue. A steady state solution for this queue in a computable form is presented, based on an analytic methodology applying certain non-trivial transformations on the balance equations, which turn out to be of the QBD-M (Quasi Simultaneous-Multiple-Bounded Births and Deaths) type. As a consequence, existing methods such as the spectral expansion method or the matrix-geometric method can be used to obtain the steady state probabilities. The utility of this queue is demonstrated through the performance analysis of an optical burst switching (OBS) node. Numerical results show the impact of the burstiness of arrival process on the performance of the OBS multiplexer.
ISBN:3642027415
9783642027413
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-02742-0_27