# Performance modeling of communication networks with Markov chains [electronic resource] / Jeonghoon Mo.

Material type: TextSeries: Synthesis digital library of engineering and computer science | Synthesis lectures on communication networks ; # 5.Publication details: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) :: Morgan & Claypool,, c2010Description: 1 electronic text (viii, 80 p. : ill.) : digital fileISBN: 9781598299182 (electronic bk.)Subject(s): Computer networks -- Mathematical models | Markov processes -- Mathematical models | Markov Chain modeling | Continuous time Markov chain | Discrete time Markov chain | Performance modeling | Communication networks | Markov property | Queueing theory | Queueing network | Balance equation | Steady state distribution | Uniformization | Limiting probability | Production form solution | Jackson network | BCMP network | Wireless LAN | Wi-Fi | Blocking probability | Slotted ALOHA | Bianchi model | CSMA Markov chain | Multi-channel MACDDC classification: 004.6 LOC classification: TK5105.5 | .M667 2010Online resources: Abstract with links to resource Also available in print.Item type | Current library | Call number | Status | Date due | Barcode |
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Ebooks | Indian Institute of Technology Delhi - Central Library | Available |

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Part of: Synthesis digital library of engineering and computer science.

Series from website.

Includes bibliographical references (p. 75-76).

1. Performance Modeling -- System, Model and Modeling -- What Are System, Model and Modeling -- Why Modeling -- Classifications of Models -- Performance Models -- Simulation Models -- Mathematical (Analytical) Models -- Performance Study Steps -- Towards a Good Performance Modeler -- Summary --

2. Markov Chain Modeling -- What is Markov Chain Modeling -- Discrete Time Markov Chains -- Defining States -- Solving Discrete Time Markov Chains (DTMC) -- Steady State Distribution [pi] of DTMC -- Power of Transition Probability Matrix -- Solving the Balance Equations -- Calculation of Performance Value -- Continuous Time Markov Chain (CTMC) -- Definition -- CTMC Model: Rate Matrix -- Birth-and-Death Process -- Solving CTMC (S,Q ) -- Solving Balance Equations of (S,Q ) -- Uniformization: (S,Q ) [right arrow] (S, P) -- Summary --

3. Developing Markov Chain Performance Models -- Performance Modeling Steps -- A Simple Forwarding System -- Cellular System with Blocking -- Slotted ALOHA -- Wi-Fi Network - CSMA Markov Chain -- A Multi-Channel MAC Protocol Model -- Summary --

4. Advanced Markov Chain Models -- The Bianchi Model -- Overview -- The DTMC Model of a Backoff Timer -- Network Model -- A Multichannel MAC Protocol with a Fixed Duration, A Queueing Network Model -- Overview -- Model Description -- Numerical Example -- Summary --

A. Exercises -- Bibliography -- Author's Biography -- Index.

Abstract freely available; full-text restricted to subscribers or individual document purchasers.

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This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMC) and continuous time Markov chain (CTMC). We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probability technique, and the uniformization. We try to minimize the theoretical aspects of the Markov chain so that the book is easily accessible to readers without deep mathematical backgrounds. We then introduce how to develop a Markov chain model with simple applications: a forwarding system, a cellular system blocking, slotted ALOHA, Wi-Fi model, and multichannel based LAN model. The examples cover CTMC, DTMC, birth-death process and non birth-death process. We then introduce more difficult examples in Chapter 4, which are related to wireless LAN networks: the Bianchi model and Multi-Channel MAC model with fixed duration. These models are more advanced than those introduced in Chapter 3 because they require more advanced concepts such as renewal-reward theorem and the queueing network model. We introduce these concepts in the appendix as needed so that readers can follow them without difficulty. We hope that this textbook will be helpful to students, researchers, and network practitioners who want to understand and use mathematical modeling techniques.

Also available in print.

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