Performance Modeling of Communication Networks with Markov Chains

Abstract 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, D...

[1]  Jean C. Walrand,et al.  Comparison of Multichannel MAC Protocols , 2008, IEEE Transactions on Mobile Computing.

[2]  Marcel F. Neuts,et al.  Matrix-Geometric Solutions in Stochastic Models , 1981 .

[3]  Edward W. Knightly,et al.  Starvation mitigation through multi-channel coordination in CSMA multi-hop wireless networks , 2006, MobiHoc '06.

[4]  Jean C. Walrand,et al.  A Distributed Algorithm for Optimal Throughput and Fairness in Wireless Networks with a General Interference Model , 2008 .

[5]  J. Medhi,et al.  Stochastic models in queueing theory , 1991 .

[6]  Raj Jain,et al.  The art of computer systems performance analysis - techniques for experimental design, measurement, simulation, and modeling , 1991, Wiley professional computing.

[7]  A. Girotra,et al.  Performance Analysis of the IEEE 802 . 11 Distributed Coordination Function , 2005 .

[8]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[9]  J. Sztrik.  An introduction to queuing networks , 1990 .

[10]  Edward D. Lazowska,et al.  Quantitative system performance - computer system analysis using queueing network models , 1983, Int. CMG Conference.

[11]  Jean C. Walrand,et al.  WiFlex: Multi-Channel Cooperative Protocols for Heterogeneous Wireless Devices , 2008, 2008 IEEE Wireless Communications and Networking Conference.

[12]  Jean C. Walrand.  Communication networks - a first course , 1991 .

[13]  Soung Chang Liew,et al.  Back-of-the-Envelope Computation of Throughput Distributions in CSMA Wireless Networks , 2007, 2009 IEEE International Conference on Communications.

[14]  Jean Walrand.  An introduction to queuing networks , 1988 .

[15]  Sheldon M. Ross,et al.  Introduction to probability models , 1975 .

[16]  Kristen Nygaard,et al.  SIMULA: an ALGOL-based simulation language , 1966, CACM.

[17]  Hao Wu,et al.  Large-scale network simulation: how big? how fast? , 2003, 11th IEEE/ACM International Symposium on Modeling, Analysis and Simulation of Computer Telecommunications Systems, 2003. MASCOTS 2003..

[18]  Basil S. Maglaris,et al.  Throughput Analysis in Multihop CSMA Packet Radio Networks , 1987, IEEE Trans. Commun..

[19]  Bruce Hajek,et al.  Decentralized dynamic control of a multiaccess broadcast channel , 1982 .

[20]  James R. Jackson,et al.  Jobshop-Like Queueing Systems , 2004, Manag. Sci..

[21]  Ronald W. Wolff,et al.  Stochastic Modeling and the Theory of Queues , 1989 .